
==== Front
iScience
iScience
iScience
2589-0042
Elsevier

S2589-0042(24)02004-2
10.1016/j.isci.2024.110779
110779
Review
A comprehensive study of various superconductors for superconducting nanowire single photon detectors applications
Tripathy Sangita 13
Tyagi Kriti kriti.tyagi@nplindia.org
123∗
Pratap Pratiksha 12
1 CSIR-National Physical Laboratory, Dr. K.S. Krishnan Marg, New Delhi 110012, India
2 Academy of Scientific & Innovative Research (AcSIR), Ghaziabad 201002, India
∗ Corresponding author kriti.tyagi@nplindia.org
3 These authors contributed equally

22 8 2024
18 10 2024
22 8 2024
27 10 110779© 2024 The Author(s)
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Summary

Research activities in the field of superconducting nanowire single photon detectors (SNSPDs) have exhibited major progress over the last two decades. The low dark count rate, low jitter time, low recovery time, and ultrafast response time in an extended wavelength range, along with several improvements in the material parameters, cryogenic environment, and associated electronics make SNSPDs a superior choice over other photo-detectors. The struggle in simultaneously optimizing these parameters made the pace of SNSPD research steady, until the report of unit system detection efficiency at low temperatures for WSi SNSPD. Due to the difficulty in maintaining the low temperature for a long time, researchers are currently focusing on using high transition temperatures cuprate-based superconductors. These have the added advantages of making a portable SNSPD combined with faster response dynamics required for commercial SNSPD applications. In this review, we have discussed different models for single photon detection, followed by research activities carried out employing different superconducting materials over the last 20 years. The ongoing research toward utilizing oxide-based superconductors as photon detection devices along with a few suggestions for improving the device performance is discussed. This review will fill the gap required for a detailed study of different classes of superconductors for SNSPD applications.

Graphical abstract

Physics; Superconductivity

Subject areas

Physics
Superconductivity
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pmcIntroduction

The superconducting single photon detectors (SNSPDs) have captured significant scientific interest over the last two decades through their unique capability of cooper pair breaking by photon absorption. The advantages such as high efficiency, extremely low dark count rates, short timing jitter, fast recovery time with no after-pulsing, and enhanced sensitivity from ultra-violet to infrared region, makes SNSPD superior over their counter parts, such as; superconducting tunnel junctions (STJ), photo multiplier tubes (PMT), transition edge sensors (TES), semiconducting avalanche photo-diodes (SPAD), and superconducting hot-electron bolometers (HEB).1,2

Significance of superconducting single photon detector devices

The research on implementing superconductors as light detectors started with the remarkable discovery of the destruction of superconductivity in lead (Pb) films by Laser radiations, the physics of which could not be explained by simple resistive heating.3 The basic working principle behind SNSPDs was derived from the concept of radiation bolometers fabricated from semiconducting and superconducting thin films.4 Goltsman et al. fabricated 1 μm long, 0.2 μm wide, and 5 nm thick niobium nitride (NbN) nanowire-based SNSPD device using a visible light of 810 nm wavelength as the photon source.5 The schematic operation of a typical SNSPD is shown in Figure 1. Here, the polarization controller plays a key role in forwarding polarized photons, the attenuator controls the average number of photons in a light field, the cryocooler maintains the necessary temperature for photon detection, and the bias tee passes the DC bias current to the device and AC signal from the device back to the amplifier. The oscilloscope or photon counter finally counts and characterizes the output signal.6Figure 1 Schematic diagram shows the operation of a typical SNSPD

The ultrahigh count rate (number of photons registered per unit time) in GHz, high detection efficiency (probability of converting absorbed photons into electrical signals) of >90%,7 low dark count rate (false count rate which is not due to real photons) of 10−4 Hz,8 small jitter timing (uncertainty between receipt of photons and response at the output) of 4.6 ps,9 and ultrafast reset time (time taken by the device to be ready for absorbing the next photon following signal detection at the output) of few ps10 has uniquely established SNSPDs over their earlier competitors. This unique quantum technology has been effectively used in fields such as; quantum information science for secure data transmission,11,12 quantum teleportation,13 long-distance imaging and space communications (LIDAR),14,15 astronomical rays detection in infrared regime,16 fluorescence spectroscopy for lifetime measurements of excited atoms using time-correlated photon counting,17 and medical sciences for X-ray and CT scan imaging,18,19 and so forth.

Progress in superconducting single photon detectors devices

The analysis of current-voltage (I-V) curves obtained for different materials plays significant role in explaining the nature of photo-response. The sharp step in voltage for a given switching current (bolometric response) stands as a primary requirement for any material to be called an ideal photon detector. The mathematical expression is given by4;δV=IR0[1R0(dRdT)]δT

where δV and δT represent changes in voltage and temperature, I, R0, and dRdT represent the current, resistance, and temperature dependant resistance change for the material, respectively.

The successful response from NbN devices20 encouraged different research groups to study and improve the device parameters in other nitride-based SNSPDs in terms of active area geometry, coupling to the optical source, cryogenic environment, and associated electronics.21,22 The niobium titanium nitride (NbTiN),23 tantalum nitride (TaN),19,24 molybdenum nitride (MoN),25 and vanadium nitride (VN) (exhibited unit intrinsic detection efficiency)26 based devices have been successfully used as SNSPDs. The recently developed NbTiN-based devices have been reported of 99.5% intrinsic detection efficiency. Among silicon-based materials, NbSi27 and MoSi28 have successfully responded to infrared photons with detection efficiencies of 98% in the later.

The cuprate oxide-based SNSPDs with their faster breakdown and recombination dynamics of quasi-particles compared low TC superconductors have gathered scientific interest in the SNSPD community. They tend to satisfy the growing demand for ultrafast response and quicker data transmission required in different fields.29 They provide an option of using liquid nitrogen, a cheaper coolant compared to liquid helium, requiring lesser maintenance of the cryostat.30 Therefore, cuprate oxide-based detectors create a prospect of economic and technological ease. The few underlying challenges for putting these devices for applications will be discussed in detail.

Figure 2 shows the progress in SNSPD research from the time of its inception in 2006 until now, which reflected a continuous progress. A few numbers of research publications and patents in the period of 2006–2010 indicated lack of scientific outlook in SNSPD research in initial days of its discovery. A visible rise in both publications and patents were noted in later years. Dauler et al. in 2014, reviewed the methods employed to develop fully packaged, high-performance SNSPDs along with the discussion about performance metrics of the fully developed SNSPD systems.31 A detailed overview of the applications of SNSPDs was provided by Yamashita et al.,32 You et al.12 and Zadeh et al.33 addressed the performance and other issues related with SNSPDs, in addition to their applications toward quantum information.Figure 2 Research papers and patents published in the area of SNSPD and related applications, since its inception

It is essential to consider material’s inherent properties, cost and technical problems that arise during device fabrication, before choosing the superconducting material for SNSPD. There are closed-cycle cryostats that reach sufficiently low temperatures for the continuous operation of SNSPDs with excellent performance parameters, which are commercially available.35 The high transition temperature superconducting materials are interesting, since, the phenomena of photon detection in high-TC materials provides a new approach to study the complex superconducting fluctuation phenomena. Secondly, they provide a technological solution for single-photon detection providing compact and cost-effective systems, which can use liquid nitrogen and enable mass deployment. The cuprate oxide superconductors occupy privileged position due to their layered structure and higher upper critical parameters. However, the larger band gap and difficulty in maintaining stoichiometric ratio at nano-dimensions hinders reaching desired transition temperature. The superconducting properties are degraded during nano-patterning, mainly due to phase fluctuations and altered oxygen stoichiometry. In the present review, we aim at summarizing the progress made, thus far, using numerous superconducting materials in the recent past toward SNSPD development. We have emphasized on role of dimensionality, patterning technique, and working environments for photon detectors, along with progress achieved so far in the same field.

Photon detection mechanism

The hysteretic I-V curve resulting upon the interruption of zero-voltage state of current conduction in an SNSPD device predicts its key parameters. Out of the few models proposed to understand the stepwise phenomena taking place during photon detection, two widely accepted models are36;(i) Hotspot model for high-energy photons

(ii) Vortex model for lower energy photon

The widely accepted Hotspot model provides an easier way to understand the detection mechanism.37 Here, the absorption of a visible or near-infrared photon breaks the cooper pairs locally with the generation of quasi–particles forming a local non-superconducting hotspot region (temperature>TC). A gradual rise in hotspot size toward both the sideways subsidizes the absorbed heat (Joule’s heating effect). The bias current (IB) is to be maintained close to the critical current (IC) throughout the detection process. A voltage peak is detected at the output as the current across the wire-width exceeds IC.5 The quasi-particles follow a relaxation process through heat distribution to the surrounding by electron-electron, electron-phonon interactions, and heat dissipation to the substrate, in presence of low-temperature environment provided by the cryocooler.38 The hotspot formation has been studied in terms of both thermal and electrical models. The thermal model uses the idea of time dependent heat balance equations2;Cd∂T∂t=J2∂ρ+κd∇2T+α(T−T0)

where, J is the current density and ρ is the electrical resistivity through the wire.

The electric model applies the concept of rise and decay times of the electrical signals, i.e., the nanowires are electrically represented as the series connection of an inductor LK and a time dependent resistor Rn(t), which is then parallelly connected to an external load (Z0 ≈ 50Ω). Here, the rise time and decay time are represented as39;ζ1=LK/(Z0+Rn(t))andζ2=LK/Z0

Both thermal and electrical models provide straight forward explanation for the hotspot mechanism.

The Vortex model explains the photon detection process by BKT phase transition.40 In this model, the magnetic vortices arising due to transport or bias current (IB) travel across the width of nanowires, provided IB is lesser than critical current (IB > IC) and temperature is lesser than theoretical value provided by BKT theory (T < TBKT).41 The schematic representation of different mechanisms associated with vortex model in SNPSDs is given in Figure 3.34 The reduction in energy barrier for superconducting charge carriers finally gives rise to a resistive transition. The Lorentz force leads to the movement of vortex-antivortex pairs across the sideways.36 The power-law dependence of applied voltage on current (V ∼ I3) for T < TBKT supports theory of vortex states arising due to topological defects.42 However, the threshold values of energy and current for resistive transitions are dependent on dimension of devices. The phase slips in 1D quantum confinement Matsuda, Komiyama,43 vortex pair dissociation in 2D quantum confinements,44 and vortex-antivortex pair formation in 3D quantum confinements42 explains thermal, electrical, and quantum fluctuations to alter the superconducting states.Figure 3 Schematic representation of different mechanisms associated with vortex model in SNPSDs

SNSPD detection models show (A) hotspot formation by the breaking of cooper-pairs, (B) spread in hotspot size, (C) vortex-antivortex depairing, and (D) vortex crossing from both edges of wire. Reproduced with permission.34 Copyright 2014, American Physical Society.

Altogether, the crystallinity and energy gap of the material, device geometry, and energy of photons play major role in deciding the photon detection model.36 The THz radiations in infrared regime required to fulfill the long-distance communication requirements follow the vortex model, especially in high TC superconductors.1 It has also been confirmed through experiments using THz radiations in YBCO-based optical detectors.45,46

Device geometry and patterning effects

The geometry of device and dimensions (length, width, and thickness) of the patterned wire affect the superconducting properties and SNSPD device key parameters. Jiang et al. reported an ultrahigh JC of 109 A/cm2 in 500 nm thick, 50 nm long, and 200 nm wide YBCO nanobridges patterned by UV photolithography.47 The JC was attributed to a uniform wire width, which was shorter than the transverse penetration depth (λL). The dimension of superconducting wires also affects the efficiency and dark count rate of an SNSPD device. The kinetic inductance of the device (LK=(μ0λ2)(L/A)) also depends on length of wires, which in turn influences the jitter time and reset time of the SNSPD.36 The jitter time and reset time were observed to reduce with decreasing length of the wires.48,49 Hence, the length of superconducting wires requires to be optimized for fixed width and thickness. The reset time can be decreased by increasing the load impedance on the detector or by making use of parallel nanowire geometry to reduce the inductance. However, a decrease in detector efficiency due to latching effect was noted.50,51

The width of nanowires is vital, providing a defined path for the current flow. Any kind of fluctuation leading to phase slips are more probable in 1D wires (w < ᴧ, ᴧ = 2λL2/d, λL = London penetration depth of material, and t < ξ).44 The wire width affects superconducting critical parameters such as TC, JC, normalized resistance (RN), coherence length (ξ), penetration depth (λ), and transition width (ΔT). The oxygen loss during the patterning of ultra-narrow oxide wires leads to reduced superconducting parameters. Hence, the TC and RN values decrease with decreasing wire width.52,53 The phase slips leading to the broadening of R-T curves fitted well with given equations for RN, for wires width ≪4.4ξ.54 They also reported a non-linear change in superconducting parameters by varying width of YBCO wires, and the maximum JC of 108 J/cm2 was noted for 95 nm wide wires.55 The role of wire width for photon number resolution was analyzed by comparing 100–150 nm wide MgB2 nanowires. The 100 nm wide wires detected both lower and higher energy photons, whereas, 150 nm wide wires could not resolve lower energy photons.56 Marshili et al. fixed other parameters and varied wire widths, and reported difference in detection efficiency for 20 nm and 30 nm wide NbN wires.57 The optimization of thickness is equally important for designing SNSPD device. Arpaia et al. observed non-thermal and non-bolometric response exhibited by 50 nm thick meander patterned YBCO wires to 1550 nm wavelength photons, which showed switching and recovery currents for 15 nm thick YBCO wires. It was attributed to the Joule’s heating effect due to decreased thermal conductivity at reduced thickness.54 The amount of doping in superconductors decides the c-axis length of unit cells and influences the electrical and thermal conductivity. High-quality uniform nanowires of optimum thickness are required for hysteretic I-V curves with bolometric response.58 The microwires of NbN, MoSi, and WSi of 0.5–5 μm width has shown photo-response to visible lights.26,59,60 Thus, IB and wire dimension plays a crucial role here in approaching the required depairing current density. With decreasing thickness and increasing width of the microwires, the energy gaps is modified as per requirement for the detection of photons in wider wires.59 The band gap can also be modified by the suitable concentration of dopant, following which dimensions can be optimized.61,62,63

The initially fabricated nano-bridge structures were followed by meander patterning in a rectangular or circular geometry, which maximized the region of active absorption. The idea of the meander pattern was modified to series + parallel (n+ m) geometries, where a set of ultrathin parallel nanowires were connected in series to the external load. Ejrnaes et al. suggested the (3 + 8) geometry for minimal latching and faster optical response.64 The detectors designed with this kind of geometry lead to cascade switching, i.e., switching in one leading to switching in all, which results large amplitude of output signal due to the maximum absorption of photons.

Materials used for superconducting single photon detectors

Nitride-based superconducting single photon detectors

Niobium nitride

The nitrides of transition metal possess various favourable characteristics such as high-melting point, hardness, abrasive resistivity and so forth and they are superconducting in nature.65,66 Among the transition metal nitrides, Nb4N3 and NbN are known to possess higher TC.67 The high TC observed in these compounds coupled with stability observed at ambient temperatures makes them suitable for different superconducting device applications such as, single-photon detectors,68,69 radio-frequency resonators70 and bolometric mixers71,72 and so forth. The presence of strong N≡N bond leads to small free energy of formation, thus, making the synthesis of nitrides difficult as compared to other counterparts e.g., oxides.

NbN has played a governing role in single-photon detection using superconducting nanowires. Goltsman et al.5 demonstrated supercurrent assisted hotspot mechanism in ultrathin NbN strip employed for single photon detection in visible and infrared range. Consequently, QE of 20% was reported for 0.81 μm photons with a negligible dark count. The response time corresponding to 10 GHz photon counting rate was measured to be ∼100 ps. Although different fabrication processes were used to produce NbN structures for single-photon detection, the recovery time has been underrated for long, owing to the kinetic inductance of the meander until 2006, when Rosfjord et al.73 at Massachusetts Institute of Technology obtained high detection efficiency in NbN-based SNSPD. They added an optical cavity and anti-reflection coating to a nanowire photodetector, thus, creating an integrated nano-electro photonic device capable of showcasing enhanced performance as compared to the original device. As shown in Figure 4, the device was illuminated from the rear portion of the chip through the anti-reflection coating and the substrate. The photons that fail to get absorbed at NbN wire initially enter the optical cavity, thus, having a greater probability of being absorbed by NbN. The thickness of the optical cavity was chosen such that, the destructive interference leads to the a reduction of reflectance on the surface of NbN wire. The group reported a DE of 57% at 1550 nm and 67% at 1064 nm wavelength with a small pixel size of 3.3 x 3.0 μm2. An important advancement made by Stern and Farr74 has been to increase the pixel size (15 × 15 μm2), so as to efficiently couple to fiber optic waveguide.Figure 4 Integrated nano-electro photonic device

(A) SEM image of nine interleaved nanowire SNSPD array,75 and (B) a chip mounting block holding SNSPD chip, Reproduced with permission.75 Copyright 2018, IOP Science.

Based on the physics governing device operation, SNSPDs are known to achieve the required single-photon detection properties simultaneously. However, there are practical limitations involved in attaining them concurrently. The AC-coupled amplifier has to be attached to the readout signal. The amplifier, due to its non-linear interaction with the detector, limits the high-counting rates desirable for high efficiency in SNSPDs. Also, the small active area required to achieve lower kinetic inductance69 ensures fast reset times and thus high count rates, however, this leads to strenuous optical coupling with high efficiency. The reset time can be reduced by either using a parallel nanowire configuration to decrease the inductance or by enhancing the load impedance of the detector. However, these attempts lead to a lower efficiency as a result of latching.76 Owing to such conditions limiting the detector performance, Rosenberg et al.77 stressed the system performance parameters that can be established simultaneously to gauge the advantages of SNSPDs for various applications. They discussed NbN-based SNSPD system that can simultaneously achieve 68% detection efficiency at 1550 nm with a photon flux of 100 million pps, kHz noise count rates, and few kcps dark count rates along with a timing resolution of <80 ps.77

In 2016, Wu et al. reported the performance of SNSPDs deposited on MgF2 substrate78 to be comparable to other counterparts such as sapphire and MgO.79 The choice of MgF2 results owing to promising material properties such as wide bandgap, low refractive index, and wide optical transmission range. When compared to NbN, there is only a slight mismatch in the lattice constant. The mechanical strength and hardness of MgF2 coupled with outstanding optical properties makes MgF2 suitable for thin-film deposition followed by SNSPD fabrication. The front-side illuminated detector exhibited a system detection efficiency of 12.8% at a 100 Hz dark count rate while the backside illuminated SNSPD displayed 33% system detection efficiency at a similar dark count rate. The increase in efficiency with the addition of an optical cavity was attributed to enhancement in absorptance for the backside illuminated detector.

In addition to focusing on the physics regulating the device operation, several reports on improvement in the device design were recorded. For instance, by improving the NbN SNSPDs device design (i.e., devices with varied spacings of 80, 120, 160, 200, 240, 280, 320, and 360 nm having fill factor in the range 18–50%), Yamashita et al.80 achieved a maximum system detection efficiency of 68.7% for moderate fill-factor of 18%. By concluding the simulation of the optical absorptance, they found that by appropriate tuning of the device design, high absorptance is achievable in the device, in spite of a low filling factor. In addition to the improvement in photon counting rate, a low filling-factor device design is believed to minimize complications in fabricating defect-free long nanowires. Similarly, Wang et al.81 optimized NbN SNSPD design employing position-dependent detection efficiency. They proposed that: (1) The optimized device design of the meander wire NbN detector aids in boosting absorption by amending the field distribution across the length of the wire, and (2) The absorption at the edges can be improved by the deposition of a silicon nanowire atop of the superconducting nanowire. This practice enhances the total absorption efficiency and also the internal detection efficiency of the meandering wire pattern. Further integration of the proposed structure with a cavity structure makes it possible to achieve absorption efficiencies of 97% and 85% for perpendicular and parallel polarization, respectively. The polarization-sensitive absorptance of the nanowire leads to polarization-sensitive detection efficiency of the SNSPD meander. In order to resolve this problem, Huang et al. fabricated NbN SNSPDs having spiral structure and finally embedded in an optical cavity. The optical cavity combining spiral structure employed for the fabrication of SNSPDs removes the current crowding effect leading to a system detection efficiency of 52.5% at 1550 nm at a dark count rate of 100 Hz.

An approach was developed by Huang et al.75 to increase the detection speed in NbN SNSPDs by replacing long individual nanowires with multiple single nanowires in an array. This arrangement led to a decrease in kinetic inductance and consequently rise in the count rate. They reported a detector with nine interleaved nanowires having 70% system detection efficiency at a dark count rate of 200 Hz and wavelength of 1550 nm. The SNSPD attained the highest count rate of 0.93 GHz at a system detection efficiency of 7% and an ability to resolve up to nine photons.

The variation of hotspot relaxation time τth (a key factor that defines maximum count rate), for NbN-based SNSPDs, with parameters such as bath temperature, nanowire linewidth, type of substrate, and so forth were studied by Zhang et al.82 They established that τth enhanced with increase in bias-current, and a direct correlation between τth and degree of disorder in NbN films deposited on various substrates was obtained.

In spite of the large number of investigations on QKD based on SNSPDs, the lower efficiency achieved in the initial years limited their widespread usage.73,83 Hadfield et al.,84 in 2006, integrated a cryogen-free SNSPD system that acts as a receiver in a fiber-based QKD link. They illustrated that by using the twin SNSPDs, it becomes possible to exchange a secure key over 12.2 dB link-loss, using the BB84 protocol. Tanaka et al.85 successfully demonstrated QKD transmission at 625 MHz clock rate using 97 km field-installed fiber through practical clock synchronization using the same protocol. The QKD transmission system reported by Tanaka et al. entailed all the functions required86 and thus, proved as a solid foundation for a complete QKD system.

Another important advancement was a demonstration of the first entanglement-based QKD experiment over 100 km optical-fiber.86,87,88 For this, the researchers made use of different components, namely, (1) NbN-based SNSPDs, (2) an entangled photon-pair source consisting of fiber-coupled periodically poled lithium niobate waveguide coupled with ultra-low loss filters, and (3) Mach-Zehnder Interferometers. The combined effect of all components aided in the attainment of an entanglement-based QKD experiment over 100-km optical fiber, having a sifted key to 16 kbit and quantum-bit-error-rate of 6.9%, using BBM92 protocol. Making use of the progress experienced by SNSPDs and optical-fiber technology, Stucki et al.89 implemented the COW protocol and reported a quantum key exchange spanning a distance of 250 km with 15 bits/s. Recently, NbN ultrathin films with incomparable homogeneity have been grown by atomic layer deposition (ALD) technique,90,91 the use of which in SNSPD showcases saturated internal detection efficiency in the entire bias range. The sputtering technique used for the growth of epitaxial NbN thin films results in enhanced TC and JC and decreased resistivity values, as compared to polycrystalline films, however reduces device detection efficiency.92,93 The growth by molecular beam epitaxy (MBE) leads to minimal defects in the grown epitaxial film and helps in achieving saturated detection efficiency. There have been reports on different nanofabrication techniques for NbN-based SNSPDs in the literature.94,95,96 Korneeva et al. reported that a micron-wide NbN bridge would result in SNSPDs with appreciable count rate and enormous detection area.97

The superconducting properties of 4.5–7 nm thick Nb films fabricated for SNSPD applications were improved by a 1 nm thick aluminum nitride (AlN) capping layer. The 4.5 nm thick, 50 nm wide Nb/AlN devices exhibited a wide range of cut-off wavelength (1310–2010 nm), single-photon sensitivity, and enhanced detection efficiency (an order higher) for reducing the working temperature from 2.26 K to 315 mK.98 Jia et al. deposited 30 nm thick Nb5N6 buffer layer on 6 nm thick NbN thin film, deposited on silicon substrate. The TC at zero-resistance state for the hybrid layers was 13.5 K, corresponding to a critical current density of 107 A/cm2. The JC value was one order higher than that obtained for bare NbN film, indicating the role of the Nb5N6 buffer layer in raising the superconducting properties of ultrathin NbN film.99 Xu et al. obtained enhanced superconducting properties in NbN thin film-based SNSPD devices fabricated on silicon substrates by using Nb5N6 buffer layer. The TC corresponding to a zero-resistance state for a 3 nm thick NbN film coated with a 20 nm thick buffer layer was 10.3 K, as compared to 7.4 K for bare NbN thin films. Moreover, the devices with Nb5N6 buffer layer exhibited higher hysteresis current, lesser jitter time, and faster photo-response compared to bare NbN devices.100

Niobium titanium nitride

With a view to improving detection parameters such as photon-counting rate and detection efficiency, researchers started studying other superconducting materials as a replacement to NbN. Dorenbos et al.101 studied NbTiN as a potential candidate for SNSPDs, having critical temperature (15 K) and critical current density (5.8 × 106 A/cm2) comparable to NbN. The NbTiN-based detectors were fabricated on the silicon substrate, which allowed a straightforward integration in complex electronic circuits. The other advantages of Si substrate include the rectification of impedance matching problem and easier integration between the optical cavity and fiber coupling. The NbTiN SNSPDs exhibited low dark count rates while still matching the efficiency of NbN-based detectors, thus, resulting in an unmatched signal-to-noise ratio. However, these improved parameters could not collectively provide an improved detection efficiency (<0.5% at 960 nm). To improve the device performance of NbTiN-based SNSPDs, Miki et al.102 prepared epitaxial NbTiN thin film on MgO substrate using load-lock reactive magnetron sputtering. They reported of device efficiency of 1.4% at 100 Hz and 25% lower kinetic inductance in NbTiN-based detectors as compared to NbN detectors. The authors hinted at the scope for further improvement in efficiency by optimizing the composition ratio of the NbTi target pellet. Similar to the work done by Dorenbos et al.,101 Tanner and co-workers103 used Si substrate for improved device performance. The group reported the performance of NbTiN-based SNSPDs contrived using oxidized silicon substrate in the wavelength ranging from 830 to 1700 nm. The highest efficiency at 1310 nm wavelength achieved with front-side illumination was published to be comparable to the outcome attained with the backside illumination process. The detection efficiency of 23.2% reported at λ = 1310 nm, with the dark-count rate of 1 kHz coupled with improved reset times and low jitter timings established NbTiN-based SNSPDs as a suitable option for time-correlated single-photon counting experiments. In addition, response curves independent of the polarization effect were produced using a suitable averaging method. Zichi et al. focused on optimizing Nb and Ti concentration in 9 nm thick NbxTi1-xN superconducting thin films and reporting of the best critical parameters at x = 0.62. The device fabricated of 20 μm active area and operated at 2.5 K temperature exhibited its optimum detection efficiency (80%) at 1550 nm wavelength at 2.5K. A jitter time of 19.5 ps was noted.104

Besides the investigation of the type of substrate material suitable for improving the detection efficiency of NbTiN-based SNSPDs, the optimization of device design helps to achieve efficient detectors suited for applications such as time-domain reflectometers105 and quantum cryptography.106,107 Schuck et al.108 studied a variety of detector designs and probed the noise performance of such detectors. The NbTiN-based SNSPDs were patterned directly on top of Si3N4 waveguides. Jia et al.109 showed that by increasing the composition of Ti to double the value as used for usual NbTiN films, lattice-mismatch, and low resistivity can simultaneously be enhanced thus, improving the efficiency of NbTiN-based SNSPDs. For applications such as laser ranging and quantum computing, that consist of non-idealistic photons, it becomes crucial to improve the timing resolution of the detectors. The 8–13 nm thick NbTiN-based SNSPDs fabricated by Gourgues et al. exhibited system detection efficiency values of 64% and 82% for Laser wavelengths of 1550 nm and 785 nm, respectively, and 100% internal detection efficiency in the visible spectrum, for devices operated at 2.5 K operating temperature.110 To achieve unparalleled timing resolution, Zadeh et al.111 optimized the custom readout electronics followed by fixing it inside a cryostat at the 30K stage. The group demonstrated a device consisting of high efficiency, low-timing jitter, low dark-count rate, and high photon-detection rates. The device performance of SNSPDs based on material with a low superconducting energy gap was thought to provide high detection efficiency even in the case of low-energy incident photons. The same group fabricated an 8–11 nm thick NbTiN-based SNSPD device and reported a jittered time of 7.7 ps (10–16 ps range), and system detection efficiency of 80–90% in 780–1000 nm and 1310–1550 nm wavelength range.112 Chang et al. fabricated NbTiN-based SNSPDs on SiO2 membranes by sputtering, and meander nanowires were patterned by EBL. The devices exhibited 94%–98% system detection efficiency with 15–26 ps jitter time at 2.7 K temperature when shined with 1260–1625 nm wavelength photons. Their best detection parameters obtained were the detection efficiency of 99.5% (jitter time of 35 ps) for 1350 nm photons.113 Chang et al. also obtained more than 70% system detection efficiency and less than 15 ps jitter time with 40–60 nm wide, 7.5–9.5 nm thick NbTiN-based SNSPD devices operated at 2.5 K temperature, and shined with 2 μm wavelength Laser lights. The observance of 100% and 80% internal detection efficiencies at 3 and 4 μm Laser wavelength, respectively, indicated their efficiency to function in the mid-infrared range with very good time resolution.114 The role of polarizability of incoming photons on the efficiency of fiber-coupled NbTiN SNSPD detectors fabricated over 20, 25, and 50 μm diameter cross-sectional areas were studied by Chang et al. for visible, near-infrared, and telecom wavelength photons. A more than 80% system detection efficiency was noted for 20 μm wide device, whereas, a 70% efficiency was obtained for 50 μm wide device, with a jitter time of sub 20 ps for all the devices. Also, a polarization dependency for NIR and telecom wavelength was observed in the devices, which increased for increasing photon wavelengths.115 The 50–100 nm wide Nb0.15Re0.85 nanowires with meander structure covering a circular detection area of 10–16 μm area showed a recovery time of 8–19 ns and a jitter time of 35 ps at the readout circuit when illuminated with 1301 nm wavelength light and operated at 2.8 K temperature.116

Other nitrides (tantalum nitride, molybdenum nitride, and vanadium nitride)

For TaN, excluding TC and superconducting energy gap, both being appreciably smaller, most of its considerable parameters match those of NbN. Due to the smaller superconducting gap, TaN-based SNSPDs were thought of as a potential alternative to NbN SNSPDs in infrared and near-infrared regimes. Owing to their hardness and chemically inert nature, nitride compounds are used mainly for mechanical and microelectronic applications.117,118 A fine tailoring of the stoichiometry in nitride compounds by varying deposition conditions leads to variation in the properties of nitrides (ranging from insulator to superconductor). K. Il’in et al.119 fabricated ultra-thin films of TaN and discussed their normal and superconducting properties with an aim to employ TaN material for SNSPD device fabrication. The transition temperature of 5 nm thick TaN film patterned into a meander structure with 110 nm width was reported to be 8.3K, having a critical current density of 4 MA/cm2 at 4.2 K temperature. Such SNSPDs demonstrated 20% detection efficiency at wavelength <700 nm. Engel et al.120 showed that TaN-based SNSPDs recorded improved detection properties at higher wavelengths as compared to NbN-based detectors. A detection model that takes into account the quasi-particle multiplication and diffusion was employed to describe TaN-based detector performance. TaN devices recorded the optimum, temperature-independent performance at ∼2K. Engel and co-workers took TaN-based SNSPD research further by studying the temperature dependency of detection efficiency in NbN and TaN-based SNSPDs.121 They found that the detectors having significant inhomogeneities are capable of achieving high efficiencies when operated at low temperatures. Korneeva et al. reported that the hot-spot formation over a larger area in MoN-based SNSPD resulted in saturated detection efficiency at a wavelength of 1064 nm.122 Similarly, a TC value of 9 K for VN-based SNSPD with saturated detection efficiency at 900 nm was reported by Evtikhiev and Rodin.123

Silicon-based devices

WSi

Despite of other parameters improved in NbN-based SNSPD devices in quantum optics measurements,106,124,125 the low system detection efficiency126 limits its use for photon detection applications. The low efficiency could be due to various reasons. Firstly, polycrystalline NbN offers a lesser degree of freedom in the optimization of optical coupling and detector absorption. Secondly, the internal detection efficiency of NbN-based SNSPDs does not show saturation with bias current. The crystal structure of NbN films determines its superconducting properties.127 Thus, NbN films cannot be employed for use in large-area device fabrication.128 This sets a limitation on the choice of substrate and also the design parameters for optical structures to be used for the enhancement of absorption in NbN nanowires. The amorphous superconductors are predicted to offer various advantages over NbN and NbTiN-based detectors. In amorphous materials the superconducting gap energy is low, thus, providing a higher intrinsic detection efficiency at longer wavelengths. The substrate requirements are not strict and they can be used with a variety of substrates. The free carrier concentration in amorphous superconductors is low, which leads to low critical current densities and hence a large hotspot size in the event of absorption of an incident photon.129

WSi has been investigated as an alternative material by the group at the National Institute of Standards and Technology, USA. Baek et al.,129 in 2011, developed WSi-based SNSPD with a detection area of 16 × 16 μm2 and saturated internal quantum efficiency in the wavelength range from visible to 1850 nm. WSi was predicted to overcome the limitations posed by NbN nanowires, thus leading to the fabrication of highly efficient WSi-based SNSPDs. Marsili et al.130 reported that WSi nanowires have a number of advantages over NbN and NbTiN nanowires and that WSi nanowire-based SNSPDs approach the ideal performance of single-photon detectors. The nanowires of WSi are robust with respect to structural defects, providing enhanced compatibility with the structures that aided in enhancing detector absorption and optical coupling, easily deposited on a variety of substrates and WSi-based SNSPDs have shown saturated detection efficiency with respect to the bias current IB,129 in near-infrared region.

Recently, great advancement has been attained in the improvement of SNSPD device efficiency.130 The detection efficiency of the WSi-based device upon integration with the optical cavity was found to be greater than 90% in the wavelength range of 1520 nm–1610 nm. The parameters that led to exceptional efficiency are dark-count rate (∼1 cps), timing jitter (∼150 ps), and reset time (40 ns). The achievement of a high detection efficiency in WSi was related to the intrinsic photon detection mechanism observed in an SNSPD device.131 The small superconducting energy gap of WSi coupled with low carrier density as compared to materials such as NbN, led to the creation of a large number of quasi-particles per each absorbed photon. In addition to the rise in detection efficiency, the operation of WSi SNSPDs was also investigated at 2.5K (70% of its TC). Verma et al.132 showed that, at 2.5K, the detection efficiency saturated at 78 ± 2% at 1310 nm wavelength. The high efficiency achieved at temperatures extremely close to critical temperature emerged to be a distinctive characteristic of WSi. Despite the favorable value of efficiency, the jitter time was found to be ∼191 ps. This increased jitter time was an outcome of noise in the readout, which can be improved by making use of cryogenic amplifiers. WSi-based SNSPDs were also employed for deep-space optical communication.133 Allmaras et al.133 developed a 64-pixel array of WSi SNSPD, with a diameter array of 320 m, to be used as a ground receiver.

Molybdenum silicide

Despite of a large number of materials studied for SNSPDs, a material with optimum detection parameters was still been searched for. For some materials, the TC was reported to be too low. Nanowire fabricated from a 4.5 nm WSi film had a TC of 3K129 and required to be operated below 1K in order to achieve a high detection efficiency. In WSi-based detectors, saturation in internal detection efficiency was observed only at temperatures below 2K at 155 nm wavelength, with a critical current value as low as 2 μA at 2K. The highest efficiency obtained to date is 93%, with a restriction of operating temperatures near 120 mK. The NbSi-based SNSPDs showed TC of ∼2K.134 Korneeva et al.135 studied SNSPDs based on metal-silicon alloy, MoSi, having TC values higher than those of WSi and NbSi. A 25 nm thick Mo0.75Si0.25 film was reported to have a Tc of 7.5 K,136 while a 50 nm thick Mo0.80Si0.20 film had TC of 7.3 K.137 The bulk superconducting energy gap for Mo0.75Si0.25 film is 2.28 meV which is less than half the gap of NbN (4.9 meV). Thus, MoSi-based SNSPDs were believed to provide higher critical temperatures as compared to WSi, which requires an expensive and complicated cooling system to achieve optimum performance at temperatures below 1 K. The MoSi thin films have TC values > 4K, thus, MoSi-based SNSPDs could be operated at temperature >2K, employing economic, less complex, and efficient closed cycle cryogenic systems.138

Korneeva et al.135 fabricated SNSPDs based on 4 nm thick MoxSi1-x thin films with 25% and 20% Si content i.e., Mo0.75Si0.25 and Mo0.80Si0.20, respectively. The electrical resistivity for Mo0.75Si0.25 and Mo0.80Si0.20 films at 10 K were 220 μΩ and 185 μΩ, respectively. The higher TC of Mo0.80Si0.20 led to higher critical current in these devices as compared to devices made from Mo0.75Si0.25. A 7μm × 7μm detector demonstrated a 1/e voltage decay time (6 ns) limited by kinetic inductance. The timing jitter (120 ps) was found to be restricted by amplifier noise RMS. The highest detection efficiency value of 18% was achieved at 1.2 μm wavelength. The MoSi-based SNSPDs allowed integration with optical cavities, thus allowing front-side illumination, and were predicted to have high potential for SNSPD development.

An attempt to increase the performance of MoSi SNSPDs was reported by Verma et al. The device was embedded inside an optical stack to enhance the absorption at 1550 nm wavelength.139 The highest efficiency of 87.1 ± 0.5% at 1542 nm, with a timing jitter of 76 ps was obtained at a temperature of 0.7 K. These SNSPDs were observed to showcase high saturated internal efficiency even at temperature as low as 2.3 K. Their polarization dependence was 2.8% with a linear dependence of count rate on input photon flux. The devices at 2.3 K exhibited performance comparable to WSi-based SNSPDs at <1 K and thus, limited the use of complex cryogenics. The potential candidature of MoSi thin films for SNSPD applications was further confirmed by Li et al.140 wherein, the detailed low-temperature nano-optical studies of silicon-on-insulator waveguide integrated MoSi SNSPD were carried out. The MoSi-based devices qualified for on-chip single-photon detection in optical quantum information processing. The authors combined the advantages of MoSi-based device and traveling wave SNSPD design. A hair-pin-shaped MoSi-based SNSPD device was fabricated atop a single-mode SOI waveguide. The integration of the waveguide with MoSi-SNSPD leads to a high light absorption rate. The uniformity of the MoSi hairpin device was confirmed via photo-response mapping. The high Tc of MoSi-based SNSPDs coupled with large critical current indicated that those devices could exhibit improved performance at ∼2.5 K.

Banerjee et al.141 carried out a comprehensive study of various properties of MoSi thin films toward SNSPD applications. A TC of 5.5 K and a critical current density of 0.36 MA/cm2 for 5 nm thick film at 3.6 K demonstrated that MoSi nanowires can be employed for SNSPD applications even at elevated temperatures. The prime motive of the work was the optimization of MoSi nano-films for realizing uniform large-area SNSPD focal-plane array and integration with advanced optical architecture. In order to optimize SNSPDs to work under 400 nm wavelength range, Wollman et al.142 designed SNSPDs working in the wavelength range of 250–370 nm and termed them as UV SNSPDs. The MoSi-based UV SNSPDs possessed the capability to operate at temperatures as high as 4.2K. The active area of these detectors was 56 μm diameter with a timing resolution of 60 ps (FWHM), dark count rate of ∼0.25 cps, and efficiency range of 70–80% and they were non-responsive to visible and infra-red photons. These parameters established MoSi-based UV SNSPDs as suitable candidates for applications such as UV fluorescent lifetime imaging microscopy, LIDAR, trapped-ion quantum-information processing, and photon-starved UV astronomy.

NbSi

The efficiency of SNSPDs was moderate in the visible spectrum range and dropped significantly for wavelengths above 1μm. The use of optical cavities was an efficient way of enhancing the efficiency in the infrared range.73 However, this approach became inapplicable for photons with energy lesser than that required to induce a detection event. With an aim to achieve high efficiency in the near-infrared range, Dorenbos et al.134 fabricated NbSi-based SNSPD and compared its characteristics with NbTiN-based device. A 10 nm thick layer of Nb0.48Si0.52 was deposited on oxidized silicon using a co-sputtering technique. The critical temperature reported for 10 nm thick Nb0.48Si0.52 film was ∼2K. The detection efficiency of the NbSi detector was ten times higher as compared to NbTiN-based detector when measured in the 1100–1900 nm wavelength range. In order to record a direct comparison of the sensitivity, both NbSi and NbTiN detectors were placed in close vicinity and an optical fiber was staged atop the detectors such that, both the detectors were illuminated with approximately same intensity. The critical current value of NbSi SNSPD was measured to be 2.2 μA. It was further predicted that high detection efficiency at infrared wavelength was enhanced by improving the NbSi detector geometry followed by fiber coupling.103

MoGe

A high detection efficiency was achieved in WSi-based SNSPD, along with the observation of a large timing jitter. The critical current in WSi was lower as compared to NbN, thus, leading to a low signal-to-noise ratio and consequently higher timing jitter.129,143,144 The TC of WSi SNSPD was nearly 3K, which required operation below 1 K for obtaining the desired system detection efficiency. However, operation at such low temperatures requires expensive and specialized cryogenic equipment. Verma et al.131 fabricated SNSPD based on amorphous Mo0.75Ge0.25 and noticed that the superconducting gap in MoGe was adequate to carry out the operation of SNSPD close to 2.5K, but low enough to yield a hotspot size sufficient enough to be able to produce saturated internal detection efficiency even for wider nanowire geometries. The deposited Mo0.75Ge0.25 films of 7.5 nm thickness were deposited on the Si wafer using DC magnetron sputtering.

The system detection efficiencies of nanowires with 110 nm and 150 nm widths are shown in Figure 5. A greater than 20% detection efficiency along with a timing jitter of 187 ps was noticed at temperatures close to 2.5K. The efficiency of MoGe-based SNSPD could be further improved by embedding it inside an optical stack alike its WSi counterpart. The MoGe-based SNSPDs exhibited improved detection parameters as compared to WSi SNSPDs. Over the entire bias range, the dark count rate for MoGe SNSPDs was <500 cps, as compared to ∼1000 cps for WSi detectors. The phenomenon of latching observed for WSi SNSPDs led to lower recovery time as compared to MoGe. The higher signal-to-noise ratio and high switching current led to improved timing jitter for MoGe SNSPDs in comparison to WSi detectors. All these properties established MoGe-based detectors useful for applications requiring operation in a close-cycle cryocooler at 2.5 K.Figure 5 System detection efficiency vs. bias current for MoGe-based SNSPDs with varying width and temperatures

System detection efficiency vs. bias current for MoGe-based SNSPDs with width (A) 110 nm and (B) 150 nm performed at different temperatures 250 mK, 1 K, 2 K, 2.5 K, Reproduced with permission,131 Copyright 2014, Applied Physics Letters.

MgB2

Day and Nagamatsu in 2001145,146 reported superconductivity in a new class of inexpensive, simple, and high performance superconductor, MgB2. A TC of ∼39K reported for MgB2 was the record high for a non-oxide compound. In the years to follow, attention was paid to the growth of MgB2 films for different applications.147,148,149 The unique properties, such as a superconducting energy gap similar to NbN, high TC, adequate anisotropy, and transparency of grain boundaries qualifies it to be used for the fabrication of superconducting devices. In early 2007, Monticone et al.150 fabricated 250–500 nm wide MgB2 meander lines using the e-beam lithography technique. They reported a critical current density of 8 MA/cm2 at 9.5 K for meander lines of 270 nm width. The strong phonon-electron coupling in MgB2 along with the high phonon frequency observed in boron bond-stretching mode gave rise to smaller electron-phonon relaxation time and phonon escape time, indicating faster response, as compared to NbN-based detectors.151 Khafizov et al.152 intended to understand the underlying photon response mechanism in current-biased MgB2 micro-bridges by performing time-resolved photo impedance measurements. They observed a picosecond kinetic photo-response indicating the possibility of using MgB2 bridges as potential candidates for efficient and fast photon detection. Different groups153,154 fabricated 10-nm thick MgB2 thin films with TC ∼21 K, using molecular-beam epitaxy, and studied its photodetection properties.

Shibata et al.155 studied the optical response of MgB2-based detectors. A lift-off technique using a Si/C mask was employed to fabricate 100–150 nm wide, 10 nm thick MgB2 nanowires. While a 150 nm wide nanowire showed the capability of detecting a single photon at 405 nm wavelength but ceased to detect a 1560 nm photon, the nanowire having 100 nm width could detect photons in the range of 405–1560 nm. In various studies, 5 nm thick MgB2 films, having TC > 30 K, have been deposited using a hybrid physical chemical vapor deposition technique (HPCVD).151,156,157 Charaev et al. recently reported a response time of ns range with observance of single-photon detection (up to 20 K temperature) in 100 μm long, 1–5 μm wide, and 12 nm thick MgB2 microwires at 1.55 μm optical wavelength.158 Thus, MgB2 can possibly be employed as a high-performance SNSPD.

Oxide-based superconductors

Enomoto et al. fabricated the first oxide-based superconducting detector in a 150 nm thick microwire constriction of BaPb0.7Bi0.3O3-based Josephson junction. The peak responsivity at 1–8 μm range gave a basic idea of the preferable light range for the detectors.159 Yoshisato et al. fabricated micro lines from granular YBCO thick films, which functioned as Josephson junctions along the grain boundaries of particles and showed excellent response to microwave radiations.160 Leung et al. observed a bolometric response in 1 μm thick YBCO granular film deposited over the sapphire substrate.161 The YBCO patterns of 50–200 μm length, 10–100 μm width, and 40 nm thickness deposited over MgO substrate exhibited bolometric and non-bolometric responses in nano and pico seconds range, for T ∼ TC and T≪TC, respectively, as reported by Freknel et al. They used a laser source of 630–1060 nm range to illuminate the devices.162 Carr et al. observed a fast bolometric response in YBCO thin films of 50–500 μm width and 40–320 nm thickness deposited over sapphire and MgO substrates.163 Zheng et al. observed a bolometric R-T behavior with few non-linear regions in 150 nm thick YBCO thin films of 200 × 10 μm2 cross-section area when illuminated with 10.6 mm CO2 Laser source.164 Eidelloth reported slow and fast responses, with higher and lower responsivity, respectively, in 200 nm thick YBCO thin films.165 The response dynamics were affected by crystallinity, bias current, operating temperature, and Laser frequency in all the above studies. Eidelloth and Frank observed an inverse dependence of wavelength on the responsivity for 0.8–80 μm thick bridges of Bi-Sr-Ca-Cu-O thin films of 1.5 × 1 mm2 cross-section area when shined with visible photons.166 Schneider et al. observed photo-response in Tl-Ba-Ca-Cu-O patterns of 10 mm × 10 mm×1 μm dimensions with the maximum responsivity of 10 V/W when shined with a CO2 Laser of 10–500 μm wavelength. A faster response with sharper peak for lower energy photons (λ > 66 μm) and vice-versa was observed. Also, the faster response observed at T≪TC slowed down with temperature approaching the TC.167 In all the above photon detection events, a significant role of grain boundaries leading to faster responses along inter-granular phase slips was observed. The non-bolometric signals from granular superconducting thin films were attributed to the Josephson effect, which led to phase slips along the grain boundaries.168,169 In some way, the experimental observations in cuprate oxides encouraged studying the phase slips and other associated physics that lead to faster responses in the later designed oxide-based detectors.

In oxide-based superconductors, charge transfer along adjacent CuO2 planes is responsible for superconductivity, which is supported by the fact that rise in TC with increasing CuO2 layers in some families. There have been more than 200 high TC superconductors (HTS) discovered so far. We have discussed material properties and photo-response exhibited by a few HTS materials.

LSCO

Litombe et al. fabricated 80 nm wide La2-xSrxCuO4/LaSrAlO4 wires by e-beam lithography and Ar+ ion milling. They emphasized optimum milling parameters for the retainment of good superconducting properties. The TC of 41 K and a JC of 108 A/cm2 were reported in 200 nm wide and 26.4 nm thick LSCO wires.52 Figure 6A shows a patterned LSCO wire to pass current and measuring of voltage across the nanowires. The critical current density against applied voltage as a function of wire width is shown in Figure 6B. Shibata et al. studied photo-response in 10 μm long, 100 nm wide, and 5 nm thick La1.85Sr0.15CuO4 films deposited over LaSrAlO4 substrate. A TC of 41.6 K with higher switching current values at lower temperatures and vice-versa explained the temperature-dependent resistive phase transitions (Figure 6C). The temperature of 30 K was reported to be the detection threshold.170Figure 6 LSCO nanowires

(A) Patterned LSCO wire for the passing of I and measuring of V across the nanowires, (B) Critical current density against applied voltage, as a function of wire width.

(A and B) Reproduced with permission.52 Copyright 2014, Elsevier.

(C) I-V curves as a function of different temperatures for LSCO nanowires; inset shows I-V at 3 K temperature. Reproduced with permissions.170 Copyright 2017, IOP Publishing group.

Rare-earth cuprate oxides

The cuprate-based HTSs consist of an active block: (CuO2[R(CuO2) n-1, where R = rare earth or Y, n = 1, 2, …) and a charge reservoir block: (EO(AO)m EO, where E = Ca, Sr, Ba, and so forth, A = Bi, Tl, Pb, Hg, Cu or rare earth element, and m = 0,1, 2). The RBa2Cu3O6+δ (RBCO) where R represents rare earth elements such as; Nd, Gd, Sm, Er, Eu, Tm, Yb, Lu, and so forth174 have shown TC of 90–100 K. The TC value varies as a function of temperature, pressure, and oxygen content during bulk synthesis as well as thin film depositions. A reduction in dimensionality is observed to affect the atomic arrangement and oxygen stoichiometry. Therefore, thin films of rare earth cuprates show lower TC compared to their bulk form, possibly due to the modified band gap at reduced dimensions. These materials have shown a wide range of potential applications in fields of energy storage, power transmission, MRI, Josephson junction set-ups, and IR sensors, and so forth.175,176,177

YBCO

YBa2Cu3O6+δ has been explored the most for photon detection among the rare earth cuprates, possibly due to its easier way of synthesis with the proper stoichiometry of atoms maintained in bulk and thin film form. The YBa2Cu3O6+δ unit cell has a perovskite (ABO3) structure with two BaCuO3 layers lying on both sides of the central YCuO3 unit cell. The CuO chains in the orthogonal YBCO are distorted because of the possession of the initially vacant (1/2, 0, 0) site. The orthorhombic phase is defined by lattice parameters; a = 3.82 Å, b = 3.89 Å, and c = 11.68 Å along (100), (010), and (001) directions, respectively. An individual perovskite cell contains a Barium atom at the body center of the top and bottom unit-cell, Yttrium at the body center of the middle one, Cupper atoms at the corners, and Oxygen atoms at the middle edge position. In YBCO crystal, the layers are stacked, along the c-axis, in the following sequence CuO-BaO-CuO2-Y-CuO2-BaO-CuO.178 The parameters such as unit cell parameter, critical current density, and conductivity, and so forth have different values along the c-axis and ab-plane.

In YBa2Cu3O6+δ, the arrangement of oxygen atoms in the unit cell during target synthesis and thin film deposition leads to superconductivity for x = 6+δ. It is an insulator at zero doping (δ = 0) with anti-ferromagnetic spin ordering and tetragonal crystal structure (for temperature of 700-900oC). A transition from tetragonal to superconducting orthorhombic phase takes place when the temperature is decreased with a simultaneous increase in the oxygen content. For p = 0.16 (where p is the number of holes per copper atom), the maximum TC of ∼94 K is reported in bulk YBCO crystals. The superconductivity starts depleting for x > 7 (p = 0.27) (Figure 8A). Thus, in YBCO, the critical parameters are influenced by oxygen concentration.179,180 It is essential to have optimized growth conditions in layered cuprates. Also, the low reflectivity (<10%) and low transmissivity (∼20%) of YBCO thin films for 1–2.5 eV photons (visible region) point to the high absorption of radiations, which would lead to a good photo-response from these devices.181

Several groups have studied the photo-response in YBa2Cu3O7-x. Curtz et al. deposited 12 nm thick YBCO film over the STO surface by RF magnetron sputtering with gold and PBCO capping layer. The 50 μm wide YBCO bridge was fabricated by photolithography and FIB using Ga3+ ion with 50 pA beam current. The dependence of resistivity on temperature and current density was studied in detail, and a JC(0) value of 4.1 MA/cm2 was reported.183 Probst et al. have elaborated the photo-response from 15 to 50 nm thick micro bridges of YBCO deposited over sapphire (Al2O3) (back illumination provided for better photo-response). The TC and JC values were plotted for 2 μm × 4.5 μm wires, which exhibited a linear scaling with decreasing wire thickness. A clear I-V hysteresis loop was obtained for 30 nm thin films with distinct switching values for voltage and current. The optical measurements for 30 nm thick films represented a response of 600 mV amplitude to low energetic THz radiations. In contrast, a 120 mV voltage was observed for comparatively high energetic optical pulses.184 Nawaz et al. carried out transport measurements for a set of 200–3000 nm long, 40–200 nm wide, and 50 nm thick Au capped YBCO/MgO nanowires, patterned using e-beam lithography. The hysteretic I-V curves, along with JC values as a function of wire-width were plotted for both capped and uncapped wires. A maximum JC of 108 A/cm2 was reported for 95 nm wide capped wire, exhibiting Josephson-like steps in I-V curves, which were attributed to phase slips in the ultra-narrow wires.185 The same group studied voltage signals as a function of temperature and bias current for 40 nm × 90 nm×50 nm YBCO/LAO wires. The critical current scaling with temperature i.e., IC = I0 [1-(TTC)2]3/2 (as per G-L equations) was observed, and a JC max of 20 MA/cm2 was reported.55 Amari et al. fabricated 450 μm long nanowires of three different widths (100, 200, and 750 nm) and 30 nm thickness from YBCO thin films by Ar+ ion etching, e-beam lithography, and oxygen plasma etching. There were observed higher switching values of current-voltage for lower temperatures, and vice-versa. The IC-T scaling equation fitted well with the experimental data with a JC max = 4.3 MA/cm2 for 100 nm wide wire. The inductance (L) and normalized resistance (RN) decreased with the increasing wire width for varying temperatures, which provided an idea of photo response dynamics.186

Arpaia et al. studied photo response to X-rays by 20–150 nm thick YBCO-based detectors. The nature of I-V hysteresis curves was studied in detail as a function of temperature. There were observed wider loops with sharper switching values for lower temperatures, and the JC –T scaling law followed the G-L equations as derived for thin films.187 Ejrnaes et al. observed hysteretic I-V loops for 80 nm long, 65 nm wide, and 10 nm thick YBCO/MgO nano strips. The wires with JC beyond 5 MA/cm2 showed sharp switching voltage, whereas, flux flow such as behavior was noted for JC below 5 MA/cm2. The hysteretic I-V curves up to 9.3 K were analyzed, and the highest JC value of 34 MA/cm2 was reported. It was a crucial achievement in the direction of single photon sensitivity.188 The phase slip signals in 2 μm × 300 nm × 8.2 nm YBCO/STO nanowires were studied by Lyatti et al. They studied the switching and re-trapping currents for different widths of nanowires and operating temperatures. The higher LED irradiance shifted the switching current to a lower value, and vice-versa. Moreover, the photon-induced switching or hotspot formation was studied as single photon events considering the decay time constants involved. This was another crucial development toward approaching single photon counts in high TC cuprate oxides.189 Kumar et al. observed ultrafast response, consisting of 850 ps rise time, 1250 ps day time, and 100 ps timing jitter in YBa2Cu3O7-x-based microwires at 76 K temperature.190 Amari et al. studied I-V characteristics in 30 nm thick YBa2Cu3O7-x nanowires of 0.5–500 μm × 0.1–5 μm cross-section, capped with CeO2 and Au and patterned by Laser beam lithography. A sharp resistive transition occurred for temperatures above 85 K and hysteretic I-V curves (JC maximum of 10 MA/cm2) with broader loop area were observed for decreasing operating temperatures.191

BSCCO

The Bi2Sr2Ca2Cu3O10 (B2223) coated wires were first used for current transport and superconducting maglev trains. The TC and c-axis length increases with increasing n-value from 1 to 3, which confirms the role of interlayer coupling among CuO2 layers.192 The brittleness of these materials along their plane of unit cell repetition has hindered their exploration for device applications for a long time.

Seifert et al. in 2021, fabricated 15 nm thick Bi2Sr2CaCu2O8 thin films by mechanical exfoliation from bulk BSCCO crystal. The film was transferred onto the SiO2 substrate followed by coupling with a silicon nitride (SiN) waveguide and capped with hexagonal boron nitride (hBN). A TC of 91 K for 100 nm wide patterns fabricated by He+ FIB was noted. The I-V curves exhibited hysteretic behavior at the 15–30 K temperature range, required for self-stabilized hotspot formation in nanowires (Figure 7D). The nano-bridges responded to 1550 nm long radiations with a fast rise time of 220 ps followed by a slow decay time of 2 ns. The responsivity (ratio of the output voltage to Laser power) showed its maximum and minimum values at 15 K and 77 K, respectively. Thus, an easier fabrication, higher TC, and ultrafast detection provided BSCCO a unique position in the family of cuprate-based detectors.173 Ghosh et al. comparatively studied I-V characteristics and photo-response in BSCCO in the visible range for 30 μm × 700 nm × 9 n nanowires and 3 μm × 300 nm × 12 nm nanowires. It was concluded that the responsivity of the detector can be improved by increasing the length and reducing the width and thickness of the superconducting nanowires.193 Merino et al. recently reported a single photon response in 2.5 μm × 250 nm cross-sectional BSCCO nanopatterns deposited over SiO2 and capped with hBN. The distinct hysteretic I-V curves were observed up to 30 K temperature for 1550 nm wavelength photons placing BSCCO as the first among high TC superconductors to provide single photon detection (Figures 7A and 7B).171 Charaev et al. also fabricated 56 μm × 100 nm cross-sectional BSCCO nanopatterns of 10–15 nm thickness over SiO2 substrate and capped with hBN (Figure 7C). The devices showed single photon response up to 25 K with distinct hysteretic I-V curves for 1550 nm light.172Figure 7 BSCCO nanowires for photodetection

(A) BSCCO nanowire, capped with hBN and patterned by He+ ion beam, (B) I-V characteristic curve for 250 nm thick BSCCO nanowire at 20 K temperature (inset shows temperature dependent critical current (blue) and re-trapping current (red) values), Reproduced with permission,171 Copyright 2023, IOP publishing group.

(C) I-V characteristic curve for 100 nm wide, 10–15 nm thick BSCCO nanopattern at 3.7 K temperature, Reproduced with permission,172 Copyright 2024, Springer Nature Ltd (D) I-V characteristic curve for 100 nm wide, 15 nm thick BSCCO nanowire (inset shows temperature dependent critical current (blue) and re-trapping current (red) values), Reproduced with permission,173 Copyright 2021, IOP Publishing group.

Electron doped cuprates

The electron-doped cuprates have faster photo-response compared to hole-doped cuprates, hence they have attracted scientific interest over the past few years.182,194 The partial substitution of cerium (Ce) into RCuO4 (R = La, Nd, Pr, and so forth) gives rise to this class of superconductors.195 The electron and hole doped superconductors can be distinguished from the difference in their crystal structure and p-T phase diagram (Figure 8B).Figure 8 Hole doped and electron doped cuprates

(A) Phase diagram of YBa2Cu3O7-x showing various short orders arising as a function of hole doping and temperature, (B) Comparative phase diagram for electron and hole doped cuprates. Reproduced with permission.182 Copyright 2010, American Physical Society.

Long et al. studied photo-response in 100 nm wide, 200 nm thick wires of La2-xCexCuO4 deposited over STO with TC of 26 K for x = 0.11, which exhibited faster optical reflectivity to 790 nm long Ti: sapphire Laser beams, and the response was more rapid at lower temperature.196 As reported by Charpentier et al., the 250 nm long, 150 nm wide, and 75 nm thick nanowires of Pr1.85Ce0.15CuO4 (PCCO) fabricated over (LAO)0.3-Sr2TaAlO6 substrate showed TC of 17 K. The observation of hysteretic I-V curves at the 3–17 K range established PCCO as a suitable material for photon detection.197 The pump-probe experiments showing faster response dynamics in Nd2-xCexCuO4 films conducted by Avella et al.198 encouraged Romano et al.194 to fabricate sub-micron wires by photolithography to carry out photon detection measurements. The lack of ample work on electron doped cuprates in SNSPD gives a scope to study these materials and associated challenges for the same. Ejrnaes et al. fabricated microwire photo-detectors of 12.5 μm × 3 μm cross-sectional area of Nb0.15Re0.85, where they observed single photon response to 1.5 μm wavelength at an operating temperature below 2 K, along with the maximum current density of 0.26 MA/cm2.199

F/S heterostructure for functional capping

Few oxide capping layers with similar unit cell crystallography were grown over the oxide ultrathin films, which provided protection against contamination, moisture, and CO2 and influenced the TC, mainly by facilitating charge transfer along CuO2 planes through the interface. The Au capping layer is commonly used to preserve and influence the electro-optical properties of superconducting thin films. However, Au cannot be used for SNSPD device fabrication, due to its high reflectivity and high electrical conductivity. The ferromagnetic capping, especially La0.7Sr0.3MnO3 (LSMO) and La0.7 Ca0.3MnO3 (LCMO), being structurally compatible with YBCO crystal structure, can provide favorable outcomes in the direction of photon detection.200,201 As reported by Arpaia et al.,187 the LSMO/YBCO exhibited enhanced TC and faster relaxation time compared to YBCO or Au/YBCO. The post-annealing in the presence of oxygen (O2) or ozone (O3) restored the oxygen stoichiometry.202 The interfaces with spin diffusion length (2ξF) of ≈10 nm along LSMO/YBCO/LSMO multilayer provided a bound state to study and exploit interface effects.203

Arpaia et al. deposited 15 nm thin film of La0.7Sr0.3MnO3 over 50 nm thick YBa2Cu3O7-x film. It helped to retain the uniformity of thin films during patterning, and the TC was enhanced by around 2 K. The rise in TC was attributed to a fall in resistance due to the parallel combination of RYBCO and RLSMO. The photo-response of YBCO/LSMO exhibited voltage amplitude twice as that of bare YBCO films, as shown in Figure 9A. Pepe et al. observed a faster photo-response to Laser radiations for YBCO/LSMO bilayers, compared to YBCO monolayer, in terms of reflectivity change with respect to delay time in pump-probe measurements,204 as shown in Figure 9B. Some other studies found reduced dark counts for YBCO/LSMO nanowires, as compared to those found for YBCO nanowires. As shown in Figures 9C and 9D, the optical responses from YBCO and YBCO/LSMO nanowires (insets compare I-V hysteresis loops at 5 K temperature) indicated distinct and broader I-V curves for the bilayers.205 Moreover, a good quality capping layer over oxide thin films is required before patterning to obtain SNSPD devices with superior photon sensing capability.Figure 9 Comparison of photo response curves for YBCO nanowires with and without ferromagnetic capping layers

(A) Comparison of voltage output amplitude of YBCO and YBCO/LSMO nanowires. Reproduced with permission,206 Copyright 2014, IOP Publishing Ltd.

(B) Comparison of reflectivity to LASER signal with time for YBCO and YBCO/LSMO. Reproduced with permission,204 Copyright 2009, Elsevier.

(C) Output signal with respect to delay time for YBCO and (D) YBCO/LSMO nanowires, respectively (insets show I-V hysteresis loops at 5 K temperature). Reproduced with permission,205 Copyright 2017, SPIE Proceedings.

Underdoped high TC superconductor cuprate nanowires

The formation of charge density wave (CDW) in the underdoped cuprate oxide superconductors creates a different order parameter, named correlation length (larger than coherence length (ξ) of optimally doped materials). The CDW periodically opposes the change in resistance due to varying electric or magnetic fields (oscillating magneto-resistance).207,208 A rise in the first upper critical field (HC1) with a lesser TC has been found for the underdoped HTS.209 Another study carried out by Ramshaw et al. for measuring HC with varying oxygen doping confirmed a higher value of critical field (HC2) at the underdoped state (p < 0.11) with the minimum HC2 at p = 0.11.210 The reduction in oxygen concentration in ultrathin HTS films increases the resistivity due to the reduced number of charge carriers and reduced coupling among adjacent CuO2 layers. However, this concept worked in favor of SNSPDs. Andersson et al. fabricated underdoped YBCO nanowires with 50 nm thickness and 100–600 nm width over LaAlO3 and obtained broader hysteretic I-V curves, as compared to 15 nm thick optimally doped wires with other parameters similar (Figure 10).211Figure 10 I-V curves of YBCO nanowires grown with decreasing thickness and decreasing oxygen doping

The inset shows the schematic comparison of I-V curves for nanowires with lesser thickness and optimal oxygen doping. Reproduced with permission,202 Copyright 2017, American Physical Society.

Thus, a higher resistivity and higher switching value for I-V curves of underdoped nanowires favored their implementation toward SNSPD realization.

Discussion on different critical parameters

The superconducting critical parameters (temperature, magnetic field, and current density) exhibit parabolic interdependency on each other. However, the nature of curves and their upper critical values get modified with dimensions. The magnetic field shows a quadratic dependence on temperature, i.e., HC(T) = HC(0)[1-(TTC)2],212 whereas, the current density is dependent on temperature as follows; JC = J0[1-(TTC))]n; where n value depends on dimension and crystallinity of the thin film.213 It is experimentally confirmed that n = 3/2 for cuprate thin films deposited over different substrates.214 Therefore, a low working temperature essentially helps to achieve higher values of HC and JC, preferred for better superconducting properties.

The critical current sets an upper limit on biasing current that has to be passed through a uniform wire. It is essential to achieve a higher JC for desired SNSPD properties. An ultrahigh JC of 1.3 × 109A/cm2 was reported by Jiang et al. for YBCO nano-bridges joining two bulk superconductors.47 A high JC of 108 A/cm2 at 4.2K was reported by Nawaz et al. for Au capped 200 × 50 × 50 nm3 YBCO/MgO(110).185 A JC value of 107 A/cm2 was reported by Borsoi for Au/Ti capped YBCO/CeO2/YSZ.215 More importantly, the hysteretic I-V curves for JC > 5 × 106 A/cm2, reported for YBCO ultrathin films emphasized switching taking place due to high current density rather than grain boundaries material and geometry.216 It is required to have patterned wires with higher JC values for SNSPD devices. The voids, lattice defects, twin domains, and grain boundaries on the film and substrate surface act as pinning centers for the magnetic field and retain the higher critical current. Hence, a sufficient number of pinning centers along the surface can maintain a higher critical current. The pinning centers are artificially injected into thin films in the form of 0D (vacancies), 1D (columns), 2D (planar defects), and 3D (flux tube or doping of nano-particles) defects. These have notably enhanced the value of JC.217 There have been enhancements noticed in the in-field JC through the substitution of atoms of other elements such as Nd, Gd, Sm, Eu, Dy, Tb, Pr, La and so forth into the Y site of YBCO by specific concentrations, attributed to induced strain effect on the CuO2 planes by doped atoms.218 The BZO nano-rods doped into YBCO thin films acted as 1D defects, and enhanced the JC and irreversible magnetic field.219 A significant rise in TC from 7 K to >100 K was observed by the doping of a certain amount of calcium ions into the Bi-Sr-Cu-O system.220 However, no report exists on adopting pinning centers for SNSPD devices, the reason being, that pinning centers can affect the superconducting properties of HTSs, due to their shorter coherence length as compared to the distance between adjacent flux tubes.212

Two temperature (2T) model

Semenov et al.39 explained the two temperature models by using the concept of different values of temperatures, i.e., Te and Tp for electron and phonon sub-systems, respectively, to understand the non-equilibrium photo-response in HTSs. The idea was to simplify the understanding of photo-response in three steps,221 i.e.,(a) breaking of cooper pairs into quasi-particles

(b) heat exchange between electrons and phonons

(c) heat flow from the phonon system to the substrate

The heat distribution among electron, phonon, and substrate systems is schematically represented in Figure 11. The time constants are; τe-e (rise time due to heat absorption by electron system), τe-p (decay time by heat dissipation from electron system to phonons), and τp-s (decay time by heat dissipation from phonons to substrates). They were obtained by fitting the specific heat constants for electron and phonon systems (ce, cp, respectively), power absorbed into the film (P(t)), and the temperature changes (dTe, dTp) for electron, phonon into the heat balance equations.222cedTedt=αP(t)V−Ceτe−p(τe−τp)

cpdTpdt=Cpτp−e(τe−τp)−Cpτp−s(τp−τs)

Figure 11 Heat conduction model in SNSPD systems

(A) Schematic picture showing heat transfer among electron-phonon-substrate system, (B and C) reset time (τreset) as a function of ratios of bias current to critical current densities (r = JB/JC) for Nb (LTS) and YBCO (HTS) Reproduced with permission.223 Copyright 2019, IOP Publishing group.

α = coefficient of absorption of radiation, V = volume of specimen.

The calculated values of time constants were comparable to the observed values. In HTS cuprates, the electronic system takes an active part in quasi-particles and photo response, whereas, the phonon system remains in thermal equilibrium. It was confirmed from the following values; τe-e = 0.56 ps and τe-p = 1.1 ps for YBCO thin film micro-bridges.222 The time constants for YBCO thin films were one order lower than those of NbN thin films, which pointed to a faster relaxation dynamic in the cuprates. The larger Cp/Ce value of 38 in YBCO, compared to that of 6.5 in NbN indicated a lesser rate of back-flow of heat from the phonon system to the electron system in cuprates.224 Haldar et al. compared different parameters of the 2T model calculated for Nb and YBCO, and observed photo-response in YBCO three orders faster than in Nb.223 Thus, the 2T model explains the nonequilibrium, ultrafast response in cuprate thin films.

Summary and conclusion

In this review, we have focused on summarizing the working principle, fabrication, and overall applications of nanowire-based photon detectors made of both high and low TC superconducting materials. The SNSPD device performance depends on the optimization of its characteristic interdependent parameters (detection efficiency, count rate, dark count rate, jitter time, and reset time). An inter-comparison of the superconducting properties pertaining to materials that have been used toward SNSPD fabrication are listed in Table 1. Traditionally, NbN and NbTiN superconductors are employed for the fabrication of SNSPD, whereas, the high TC cuprates hold an adventitious position in terms of faster temporal response over conventional low TC materials. However, the fast or non-bolometric response hinders the photon resolution. The critical parameters (I-V, JC, TC) varying with operating conditions have been discussed. It is desirable to employ high TC superconductors for the fabrication of SNSPD so as to fully exploit their use.225 We have discussed two significant advances for improved photon detection by the application of (i) ferromagnetic capping, and (ii) underdoped nanowires. In the approach toward realizing SNSPDs using two-dimensional high TC materials, single-photons have been detected in superconducting nanowires fabricated out of Bi2Sr2CaCu2O8+δ thin flakes of with single-photon response up to 25 K, which stands as a milestone in SNSPD. However, the inability to scale up the detector’s active area is the limitation of exfoliated flakes. The major works in HTS oxide materials are summarized in Table 2.Table 1 Inter-comparison of superconducting parameters of materials used for SNSPD applications

Materials	NbN	NbTiN	WSi	TaN	MoGe	MoSi	NbSi	MgB2	YBCO	
Bulk Tc (K)	16	17	5	5	7.4	7.5	3.1	39	93	
Tc (K) Thickness (nm)	8.6
(3 nm)	9.6
(4.5 nm)	3.7
(4.5 nm)	8.3
(5 nm)	4.4
(7.5 nm)	4.2
(4 nm)	2
(10 nm)	39
(350 nm)	85.5
(3unit cell)	
Band gap 2Δo (meV)	4.9	5.17	1.52	1.52	2.2	2.28	0.94	11.86	28.29	
JC (MA/cm2) Meas. Temp. (K)	2-4 (4.2K)	8
(2.9 K)	0.8
(250 mK)	4
(4.2 K)	1.2
(250mK)	1.1–2.5
(1.7 K)	0.14
(300mK)	1.1
(3 K)	14.4
(78 K)	

Table 2 Major works carried out with HTS superconductors toward SNSPD applications

Material	Patterning	Active area geometry	Outcomes	Reference	
YBCO/CeO2/Al2O3 (capping)	CE, ion milling	2 μm × 4.5 μm × 15–50 nm	distinct I-V curves for w = 30 nm, fast and slow responses as function of temperature and energy of the signal	Probst et al.184	
YBCO/STO/PBCO (capping)	PL, CE, and FIB	15-450 μm × 0.5–20 μm × 12 nm	R-T as a function of wire width, V-J and ρ-J with varying T, JC as function of T/TC, JC = 4.1 MA/cm2	Bo et al.226	
YBCO/MgO/
Au (capping)	EBL, Ar+ etching	200-3000 nm × 40–200 nm × 50 nm	Hysteretic I-V, sharp R-T with Au capping, JC max = 100 MA/cm2 for w = 95 cm	Mori et al.211	
LSCO/LSAO	MBE, EBL
(λ = 1560 nm)	Nano-strips, 10 μm × 100 nm × 5 nm	Hysteretic I-V at 3 K, JC = 23MA/cm2, Photo-response up to 30 K temperature	Shibata et al.170	
BSCCO/SiO2	He+ FIB (λ = 1550 nm)	15 μm × 200 nm × 15 nm	Hysteretic I-V curve, fast and slow responses to optical signal as a function of temperature, GHz operation speed	Seifert et al.173	
CeO2/YBCO/
Al2O3	IBE, EBL, Oxygen etching	100 μm × 100 nm × 30 nm	I-V as a function of T; R-T, and L-T as a function of wire width, inductance measured by resonant method, helpful in device performance	Lyatti et al.58	
LSMO (15nm)/YBCO (50nm)/LAO	by PLD, patterning: EBL, Ar+ etching	10 μm × 100–300 nm × 50 nm	JC = 7.5 × 105 A/cm2, the signal increased by twice as compared to YBCO following LSMO capping	Arpaia et al.206	
Au (capping)/
YBCO/MgO/	EBL, Ar+ etching	200 nm × 50–2000 nm × 10 nm	JC = 130 MA/cm2, Josephson-like steps in I-V curve for V = 10.3 GHz	Nawaz et al.185	
YBCO/MgO	EBL, Ar+ etching	80 nm × 65 nm × 10 nm	Hysteretic I-V curve, sharp voltage peaks for dark counts up to 9.3 K, JC = 34 MA/cm2	Ejrnaes et al.188	
YBCO/STO	FIB	2 μm × 300 nm × 8.2 nm	I-V hysteretic curve, continuous switching and re-trapping current for illumination with visible radiation at 77 K temperature	Lyatti et al.189	
hBN/BSCCO/SiO2	He+ patterning	56 μm × 100 nm×10–15 nm	hysteretic I-V curves, single photon response up to 25 K for 1550 nm light	Charaev et al.172	
hBN/BSCCO/SiO2	He+ patterning	2.5 μm × 250 nm	hysteretic I-V curves, single photon response up to 25 K for 1550 nm light	Merino et al.171	
[PLD-Pulsed laser deposition, EBL-Electron beam lithography, PL-Photolithography, CE-Chemical etching, IBE-Ion beam etching, and FIB-Focussed ion beam].

This review led to the revelation of the following major points.1. The material for SNSPD should have a low density of states and a low band gap, so as to allow incident photons to break a larger number of cooper pairs. The higher band gap (2Δ) in high TC cuprates (20–25 meV in YBCO compared to 1.5 meV in NbN) hinders them from photon number resolution.

2. A uniform geometry with a small cross-section area allows the hotspot to spread across the wire width. The difficulty in approaching high-quality ultrathin oxide wires with available patterning techniques prevents the utilization of these for SNSPDs.

3. The nonequilibrium heat distribution among electron and phonon systems in high TC cuprates, as stated in the 2T model prevents it from showing a bolometric response required for detectable signals.

4. An oxide-based HTS for single photon detection with optimized key parameters for practical applications is yet to be realized.

Acknowledgments

The authors are grateful to the Director, 10.13039/501100007851 CSIR-NPL for state-of-the art facilities.

Author contributions

ST: Conceptualization, data collection, formal analysis, writing of original draft, and review, and editing, KT: project administration, supervision, writing of original draft, review, and editing, and PP: methodology, writing, review, and editing.

Declaration of interests

The authors declare that they do not have any competing financial interests of personal relationships which could affect the work reported in this article.
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References

1 Hadfield R.H. Single-photon detectors for optical quantum information applications Nat. Photonics 3 2009 696 705 10.1038/nphoton.2009.230
2 Natarajan C.M. Tanner M.G. Hadfield R.H. Superconducting nanowire single-photon detectors: physics and applications Supercond. Sci. Technol. 25 2012 063001 10.1088/0953-2048/25/6/063001
3 Testardi L.R. Destruction of superconductivity by laser light Phys. Rev. B 4 1971 2189 2196 10.1103/PhysRevB.4.2189
4 Kraus H. Superconductive bolometers and calorimeters Supercond. Sci. Technol. 9 1996 827 842 10.1088/0953-2048/9/10/001
5 Gol’Tsman G. Okunev O. Chulkova G. Lipatov A. Semenov A. Smirnov K. Voronov B. Dzardanov A. Williams C. Sobolewski R. Picosecond superconducting single-photon optical detector Appl. Phys. Lett. 79 2001 705 707 10.1063/1.1388868
6 Guo Q. Li H. You L. Zhang W. Zhang L. Wang Z. Xie X. Qi M. Single photon detector with high polarization sensitivity Sci. Rep. 5 2015 9616 10.1038/srep09616 25875225
7 Xu G.Z. Zhang W.J. You L.X. Xiong J.M. Sun X.Q. Huang H. Ou X. Pan Y.M. Lv C.L. Li H. Superconducting microstrip single-photon detector with system detection efficiency over 90% at 1550 nm Photon. Res. 9 2021 958 967 10.1364/PRJ.419514
8 Shibata H. Fukao K. Kirigane N. Karimoto S. Yamamoto H. SNSPD with ultimate low system dark count rate using various cold filters IEEE Trans. Appl. Supercond. 27 2017 1 4 10.1109/TASC.2016.2631947
9 Korzh B. Zhao Q.Y. Allmaras J.P. Frasca S. Autry T.M. Bersin E.A. Beyer A.D. Briggs R.M. Bumble B. Colangelo M. Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector Nat. Photonics 14 2020 250 255 10.1038/s41566-020-0589-x
10 Vetter A. Ferrari S. Rath P. Alaee R. Kahl O. Kovalyuk V. Diewald S. Goltsman G.N. Korneev A. Rockstuhl C. Pernice W.H.P. Cavity-enhanced and ultrafast superconducting single-photon detectors Nano Lett. 16 2016 7085 7092 10.1021/acs.nanolett.6b03344 27759401
11 Koziy A.A. Losev A. Zavodilenko V.V. Kurochkin Y. Gorbatsevich A. Modern methods of detecting single photons and their application in quantum communications Quant. Electron. 51 2021 655 669 10.1070/QEL17566
12 You L. Superconducting nanowire single-photon detectors for quantum information Nanophotonics 9 2020 2673 2692 10.1515/nanoph-2020-0186
13 Takesue H. Dyer S.D. Stevens M.J. Verma V. Mirin R.P. Nam S.W. Quantum teleportation over 100 km of fiber using highly efficient superconducting nanowire single-photon detectors Optica 2 2015 832 835 10.1364/OPTICA.2.000832
14 Guan Y. Li H. Li X. Yin R. Zhang L. Wang H. Zhu G. Kang L. Chen J. Wu P. Lidar with superconducting nanowire single-photon detectors: Recent advances and developments Opt. Laser. Eng. 156 2022 107102 10.1016/j.optlaseng.2022.107102
15 Zhang B. Guan Y.-Q. Xia L. Dong D. Chen Q. Xu C. Wu C. Huang H. Zhang L. Kang L. An all-day lidar for detecting soft targets over 100 km based on superconducting nanowire single-photon detectors Supercond. Sci. Technol. 34 2021 034005 10.1088/1361-6668/abd576
16 O’Connor E. Shearer A. O’Brien K. Energy-sensitive detectors for astronomy: Past, present and future N. Astron. Rev. 87 2019 101526 10.1016/j.newar.2020.101526
17 Boso G. Ke D. Korzh B. Bouilloux J. Lange N. Zbinden H. Time-resolved singlet-oxygen luminescence detection with an efficient and practical semiconductor single-photon detector Biomed. Opt Express 7 2016 211 224 10.1364/BOE.7.000211 26819830
18 Zhang X. Wang Q. Schilling A. Superconducting single X-ray photon detector based on W0. 8Si02 AIP Adv. 6 2016 115104 10.1063/1.4967278
19 Yang C. Si M. Zhang X. Yu A. Huang J. Pan Y. Li H. Li L. Wang Z. Zhang S. Large-area TaN superconducting microwire single photon detectors for X-ray detection Opt Express 29 2021 21400 21408 10.1364/OE.422581 34265928
20 Gol'Tsman G. Okunev O. Chulkova G. Lipatov A. Dzardanov A. Smirnov K. Semenov A. Voronov B. Williams C. Sobolewski R. Fabrication and properties of an ultrafast NbN hot-electron single-photon detector IEEE Trans. Appl. Supercond. 11 2001 574 577 10.1109/77.919410
21 Yin R. Wang H. Zhang L. Wang X. Ma L. Guan Y. Yang Z. Chen Q. Tu X. Zhao Q. Saturating quantum efficiency of SNSPDs with disorder manipulation of NbN films Supercond. Sci. Technol. 36 2023 105016 10.1088/1361-6668/acf5aa
22 Cheng R. Wright J. Xing H.G. Jena D. Tang H.X. Epitaxial niobium nitride superconducting nanowire single-photon detectors Appl. Phys. Lett. 117 2020 132601 10.1063/5.0018818
23 Ma R. Shu R. Zhang X. Yu A. Huang J. Xiao Y. Yu H. Liu X. Li H. Eklund P. Single photon detection performance of highly disordered NbTiN thin films J. Phys. Commun. 7 2023 055006 10.1088/2399-6528/acd747
24 Qin Z. Bao H. Xu T. Chen S. Yang S. Li H. Wang Z. Tu X. Zhang L. Zhao Q. Thermal-property optimization dominated by the stoichiometric ratio in W-Si superconducting single-photon detectors Phys. Rev. Appl. 21 2024 024046 10.1103/PhysRevApplied.21.024046
25 Nishikawa M. Sawai K. Sakai K. Kirigane N. Ohnishi K. Nakano W. Matsuo Y. Shibata H. Fabrication of Superconducting Nanowire Single-Photon Detectors Using MoN IEEE Trans. Appl. Supercond. 32 2022 1 4 10.1109/TASC.2022.3144967
26 Zolotov P. Semenov A. Divochiy A. Goltsman G. A comparison of VN and NbN thin films towards optimal SNSPD efficiency IEEE Trans. Appl. Supercond. 31 2021 1 4 10.1109/TASC.2021.3059230
27 Lita A.E. Verma V.B. Chiles J. Mirin R.P. Nam S.W. Mo x Si1− x: A versatile material for nanowire to microwire single-photon detectors from UV to near IR Supercond. Sci. Technol. 34 2021 054001 10.1088/1361-6668/abeb00
28 Liu X. Xie B. Sun M. Jiao R. Multispectral MoSi superconducting nanowire single photon detector Opt Commun. 555 2024 130241 10.1016/j.optcom.2023.130241
29 Polakovic T. Armstrong W. Karapetrov G. Meziani Z.-E. Novosad V. Unconventional applications of superconducting nanowire single photon detectors Nanomaterials 10 2020 1198 10.3390/nano10061198 32575402
30 Moody G. Islam M.S. Materials for ultra-efficient, high-speed optoelectronics MRS Bull. 47 2022 475 484 10.1557/s43577-022-00337-y
31 Dauler E.A. Grein M.E. Kerman A.J. Marsili F. Miki S. Nam S.W. Shaw M.D. Terai H. Verma V.B. Yamashita T. Review of superconducting nanowire single-photon detector system design options and demonstrated performance Opt. Eng. 53 2014 081907 10.1117/1.OE.53.8.081907
32 Yamashita T. Miki S. Terai H. Recent progress and application of superconducting nanowire single-photon detectors IEICE Trans. Electron. E100.C 2017 274 282 10.1587/transele.E100.C.274
33 Zadeh E.I. Chang J. Johannes W.N.L. Gyger S. Elshaari A.W. Steinhauer S. Dorenbos S.N. Sander N. Zwiller V. Superconducting nanowire single-photon detectors: A perspective on evolution, state-of-the-art, future developments, and applications Appl. Phys. Lett. 118 2021 190502 10.1063/5.0045990
34 Renema J.J. Gaudio R. Wang Q. Zhou Z. Gaggero A. Mattioli F. Leoni R. Sahin D. de Dood M.J.A. Fiore A. van Exter M.P. Experimental test of theories of the detection mechanism in a nanowire superconducting single photon detector Phys. Rev. Lett. 112 2014 117604 10.1103/PhysRevLett.112.117604
35 Dang H. Wu D. Tan H. Tan J. Zhai Y. Wu S. Ma D. Xue R. Advances in cryogenic systems for the superconducting nanowire single photon detector and superconducting quantum computer IEEE Trans. Appl. Supercond. 34 2024 1 4 10.1109/TASC.2024.3350594
36 Holzman I. Ivry Y. Superconducting nanowires for single-photon detection: Progress, challenges, and opportunities Adv. Quant. Technol. 2 2019 1800058 10.1002/qute.201800058
37 Allmaras J.P. Modeling and Development of Superconducting Nanowire Single-Photon Detectors PhD thesis 2020 California Institute of Technology 10.7907/wgak-vs11
38 Yang J. Kerman A. Dauler E. Anant V. Rosfjord K. Berggren K. Modeling the electrical and thermal response of superconducting nanowire single-photon detectors IEEE Trans. Appl. Supercond. 17 2007 581 585 10.1109/TASC.2007.898660
39 Semenov A.D. Nebosis R.S. Gousev Y.P. Heusinger M.A. Renk K.F. Analysis of the nonequilibrium photoresponse of superconducting films to pulsed radiation by use of a two-temperature model Phys. Rev. B 52 1995 581 590 10.1103/PhysRevB.52.581
40 Kosterlitz J. Thouless D. Two-dimensional physics Progress Low Temp. Phys. 7 1978 371 433 10.1016/S0079-6417(08)60175-4
41 Wang Z. Chaudhary G. Chen Q. Levin K. Quantum geometric contributions to the BKT transition: Beyond mean field theory Phys. Rev. B 102 2020 184504 10.1103/PhysRevB.102.184504
42 Kadin A.M. Epstein K. Goldman A.M. Renormalization and the Kosterlitz-Thouless transition in a two-dimensional superconductor Phys. Rev. B 27 1983 6691 6702 10.1103/PhysRevB.27.6691
43 Matsuda Y. Komiyama S. Onogi T. Terashima T. Shimura K. Bando Y. Thickness dependence of the Kosterlitz-Thouless transition in ultrathin YBa2Cu3O7-x films Phys. Rev. B 48 1993 498 10.1103/PhysRevB.48.10498
44 Bezryadin A. Lau C. Tinkham M. Quantum suppression of superconductivity in ultrathin nanowires Nature 404 2000 971 974 10.1038/35010060 10801120
45 Jahani S. Yang L.-P. Tepole A.B. Bardin J.C. Tang H.X. Jacob Z. Probabilistic vortex crossing criterion for superconducting nanowire single-photon detectors J. Appl. Phys. 127 2020 143101 10.1063/1.5132961
46 Ma R. Huan Q. Huang J. Zhang X. Xiao Y. Xu H. Han H. Liu X. Peng W. Li H. Disorder enhanced relative intrinsic detection efficiency in NbTiN superconducting nanowire single photon detectors at high temperature Appl. Phys. Lett. 124 2024 072601 10.1063/5.0190139
47 Jiang H. Huang Y. How H. Zhang S. Vittoria C. Widom A. Chrisey D.B. Horwitz J.S. Lee R. Observation of ultrahigh critical current densities in high-TC superconducting bridge constrictions Phys. Rev. Lett. 66 1991 1785 1788 10.1103/PhysRevLett.66.1785 10043306
48 Pernice W.H.P. Schuck C. Minaeva O. Li M. Goltsman G.N. Sergienko A.V. Tang H.X. High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits Nat. Commun. 3 2012 1325 10.1038/ncomms2307 23271658
49 Calandri N. Zhao Q.-Y. Zhu D. Dane A. Berggren K.K. Superconducting nanowire detector jitter limited by detector geometry Appl. Phys. Lett. 109 2016 152601 10.1063/1.4963158
50 Annunziata A.J. Quaranta O. Santavicca D.F. Casaburi A. Frunzio L. Ejrnaes M. Rooks M.J. Cristiano R. Pagano S. Frydman A. Prober D.E. Reset dynamics and latching in niobium superconducting nanowire single-photon detectors J. Appl. Phys. 108 2010 084507 10.1063/1.3498809
51 Ejrnaes M. Casaburi A. Quaranta O. Marchetti S. Gaggero A. Mattioli F. Leoni R. Pagano S. Cristiano R. Characterization of parallel superconducting nanowire single photon detectors Supercond. Sci. Technol. 22 2009 055006 10.1088/0953-2048/22/5/055006
52 Litombe N.E. Bollinger A. Hoffman J.E. Božović I. La2− xSrxCuO4 superconductor nanowire devices Physica C 506 2014 169 173 10.1016/j.physc.2014.06.010
53 Papari G. Carillo F. Stornaiuolo D. Massarotti D. Longobardi L. Beltram F. Tafuri F. Dynamics of vortex matter in YBCO sub-micron bridges Physica C 506 2014 188 194 10.1016/j.physc.2014.06.017
54 Arpaia R. Golubev D. Baghdadi R. Ciancio R. Dražić G. Orgiani P. Montemurro D. Bauch T. Lombardi F. Transport properties of ultrathin YBa 2 Cu 3 O 7− δ nanowires: A route to single-photon detection Phys. Rev. B 96 2017 064525 10.1103/PhysRevB.96.064525
55 Arpaia R. Ejrnaes M. Parlato L. Tafuri F. Cristiano R. Golubev D. Sobolewski R. Bauch T. Lombardi F. Pepe G.P. High-temperature superconducting nanowires for photon detection Physica C 509 2015 16 21 10.1016/j.physc.2014.09.017
56 Shibata H. Takesue H. Honjo T. Akazaki T. Tokura Y. Single-photon detection using magnesium diboride superconducting nanowires Appl. Phys. Lett. 97 2010 212504 10.1063/1.3518723
57 Marsili F. Najafi F. Dauler E. Bellei F. Hu X. Csete M. Molnar R.J. Berggren K.K. Single-photon detectors based on ultranarrow superconducting nanowires Nano Lett. 11 2011 2048 2053 10.1021/nl2005143 21456546
58 Lyatti M. Savenko A. Poppe U. Ultra-thin YBa2Cu3O7− x films with high critical current density Supercond. Sci. Technol. 29 2016 065017 10.1088/0953-2048/29/6/065017
59 Chiles J. Buckley S.M. Lita A. Verma V.B. Allmaras J. Korzh B. Shaw M.D. Shainline J.M. Mirin R.P. Nam S.W. Superconducting microwire detectors based on WSi with single-photon sensitivity in the near-infrared Appl. Phys. Lett. 116 2020 242602 10.1063/5.0006221
60 Charaev I. Morimoto Y. Dane A. Agarwal A. Colangelo M. Berggren K.K. Large-area microwire MoSi single-photon detectors at 1550 nm wavelength Appl. Phys. Lett. 116 2020 242603 10.1063/5.0005439
61 Alfieri A. Anantharaman S.B. Zhang H. Jariwala D. Nanomaterials for quantum information science and engineering Adv. Mater. 35 2023 2109621 10.1002/adma.202109621
62 Hannachi E. Almessiere M.A. Slimani Y. Alshamrani R.B. Yasin G. Ben Azzouz F. Preparation and characterization of high-Tc (YBa2Cu3O7-δ) 1-x/(CNTs) x superconductors with highly boosted superconducting performances Ceramics Intern. 47 2021 23539 23548 10.1016/j.ceramint.2021.05.071
63 Chang J. Gao J. Esmaeil Zadeh I. Elshaari A.W. Zwiller V. Nanowire-based integrated photonics for quantum information and quantum sensing Nanophotonics 12 2023 339 358 10.1515/nanoph-2022-0652
64 Ejrnaes M. Casaburi A. Quaranta O. Marchetti S. Gaggero A. Mattioli F. Leoni R. Pagano S. Cristiano R. Characterization of parallel superconducting nanowire single photon detectors Supercond. Sci. Technol. 22 2009 055006 10.1088/0953-2048/22/5/055006
65 Sriram M.A. Kumta P.N. Ko E.I. Interaction of solvent and the nature of adducts on the chemical synthesis of molybdenum nitride powders Chem. Mater. 7 1995 859 864
66 Agrafiotis C.C. Puszynski J.A. Hlavacek V. Effect of metal particle morphology on the combustion of refractory metals in nitrogen J. Am. Ceram. Soc. 74 1991 2912 2917 10.1111/j.1151-2916.1991.tb06862.x
67 Buscaglia V. Caracciolo F. Ferretti M. Minguzzi M. Musenich R. Effect of pressure on the composition and superconducting Tc value of NbN prepared by combustion synthesis J. Alloys Compd. 266 1998 201 206 10.1016/S0925-8388(97)00482-9
68 Korneev A. Kouminov P. Matvienko V. Chulkova G. Smirnov K. Voronov B. Gol’tsman G.N. Currie M. Lo W. Wilsher K. Sensitivity and gigahertz counting performance of NbN superconducting single-photon detectors Appl. Phys. Lett. 84 2004 5338 5340 10.1063/1.1764600
69 Kerman A.J. Dauler E.A. Keicher W.E. Yang J.K.W. Berggren K.K. Gol’tsman G. Voronov B. Kinetic-inductance-limited reset time of superconducting nanowire photon counters Appl. Phys. Lett. 88 2006 111116 10.1063/1.2183810
70 Fabbricatore P. Fernandes P. Gualco G.C. Merlo F. Musenich R. Parodi R. Study of niobium nitrides for superconducting rf cavities J. Appl. Phys. 66 1989 5944 5949 10.1063/1.343621
71 Kawamura J. Blundell R. Tong C.Y.E. Gol’tsman G. Gershenzon E. Voronov B. Performance of NbN lattice-cooled hot-electron bolometric mixers J. Appl. Phys. 80 1996 4232 4234 10.1063/1.36330472
72 Hajenius M. Baselmans J.J.A. Gao J.R. Klapwijk T.M. Korte P.A.J.d. Voronov B. Gol'tsman G. Low noise NbN superconducting hot electron bolometer mixers at 1.9 and 2.5 THz Supercond. Sci. Technol. 17 2004 S224 S228 10.1088/0953-2048/17/5/026
73 Rosfjord K.M. Yang J.K.W. Dauler E.A. Kerman A.J. Anant V. Voronov B.M. Gol’tsman G.N. Berggren K.K. Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating Opt Express 14 2006 527 534 10.1364/OPEX.14.000527 19503367
74 Stern J.A. Farr W.H. Fabrication and characterization of superconducting NbN nanowire single photon detectors IEEE Trans. Appl. Supercond. 17 2007 306 309 10.1109/TASC.2007.898060
75 Huang J. Zhang W. You L. Zhang C. Lv C. Wang Y. Liu X. Li H. Wang Z. High speed superconducting nanowire single-photon detector with nine interleaved nanowires Supercond. Sci. Technol. 31 2018 074001 10.1088/1361-6668/aac180
76 Kerman A.J. Yang J.K.W. Molnar R.J. Dauler E.A. Berggren K.K. Electrothermal feedback in superconducting nanowire single-photon detectors Phys. Rev. B 79 2009 100509 10.1103/PhysRevB.79.100509
77 Rosenberg D. Kerman A.J. Molnar R.J. Dauler E.A. High-speed and high-efficiency superconducting nanowire single photon detector array Opt Express 21 2013 1440 1447 10.1364/OE.21.001440 23389125
78 Wu J.J. You L.X. Zhang L. Zhang W.J. Li H. Liu X.Y. Zhou H. Wang Z. Xie X.M. Xu Y.X. NbN superconducting nanowire single-photon detector fabricated on MgF2 substrate Supercond. Sci. Technol. 29 2016 065011 10.1088/0953-2048/29/6/065011
79 Miki S. Yamashita T. Fujiwara M. Sasaki M. Wang Z. Multichannel SNSPD system with high detection efficiency at telecommunication wavelength Opt. Lett. 35 2010 2133 2135 10.1364/OL.35.002133 20596170
80 Yamashita T. Miki S. Terai H. Wang Z. Low-filling-factor superconducting single photon detector with high system detection efficiency Opt Express 21 2013 27177 27184 10.1364/OE.21.027177 24216941
81 Wang Q. Renema J.J. Engel A. de Dood M. Design of NbN superconducting nanowire single-photon detectors with enhanced infrared detection efficiency Phys. Rev. Appl. 8 2017 034004 10.1103/PhysRevApplied.8.034004
82 Zhang L. You L. Yang X. Wu J. Lv C. Guo Q. Zhang W. Li H. Peng W. Wang Z. Xie X. Hotspot relaxation time of NbN superconducting nanowire single-photon detectors on various substrates Sci. Rep. 8 2018 1486 10.1038/s41598-018-20035-7 29367752
83 Verevkin A. Pearlman A. Slysz W. Zhang J. Currie M. Korneev A. Chulkova G. Okunev O. Kouminov P. Smirnov K. Ultrafast superconducting single-photon detectors for near-infrared-wavelength quantum communications J. Mod. Opt. 51 2004 1447 1458 10.1080/09500340408235284
84 Hadfield R.H. Habif J.L. Schlafer J. Schwall R.E. Nam S.W. Quantum key distribution at 1550 nm with twin superconducting single-photon detectors Appl. Phys. Lett. 89 2006 241129 10.1063/1.2405870
85 Tanaka A. Fujiwara M. Nam S.W. Nambu Y. Takahashi S. Maeda W. Yoshino K.i. Miki S. Baek B. Wang Z. Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization Opt Express 16 2008 11354 11360 10.1364/OE.16.011354 18648454
86 Hayashi M. Upper bounds of eavesdropper’s performances in finite-length code with the decoy method Phys. Rev. A. 76 2007 012329 10.1103/PhysRevA.76.012329
87 Hayashi M. General theory for decoy-state quantum key distribution with an arbitrary number of intensities New J. Phys. 9 2007 284 10.1088/1367-2630/9/8/284
88 Honjo T. Nam S.W. Takesue H. Zhang Q. Kamada H. Nishida Y. Tadanaga O. Asobe M. Baek B. Hadfield R. Long-distance entanglement-based quantum key distribution over optical fiber Opt Express 16 2008 19118 19126 10.1364/OE.16.019118 19582004
89 Stucki D. Walenta N. Vannel F. Thew R.T. Gisin N. Zbinden H. Gray S. Towery C.R. Ten S. High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres New J. Phys. 11 2009 075003 10.1088/1367-2630/11/7/075003
90 Cheng R. Wang S. Tang H.X. Superconducting nanowire single-photon detectors fabricated from atomic-layer-deposited NbN Appl. Phys. Lett. 115 2019 241101 10.1063/1.5131664
91 Knehr E. Kuzmin A. Vodolazov D.Y. Ziegler M. Doerner S. Ilin K. Siegel M. Stolz R. Schmidt H. Nanowire single-photon detectors made of atomic layer-deposited niobium nitride Supercond. Sci. Technol. 32 2019 125007 10.1088/1361-6668/ab48d7
92 Miki S. Fujiwara M. Sasaki M. Baek B. Miller A.J. Hadfield R.H. Nam S.W. Wang Z. Large sensitive-area NbN nanowire superconducting single-photon detectors fabricated on single-crystal MgO substrates Appl. Phys. Lett. 92 2008 061116 10.1063/1.2870099
93 Dane A.E. McCaughan A.N. Zhu D. Zhao Q. Kim C.S. Calandri N. Agarwal A. Bellei F. Berggren K.K. Bias sputtered NbN and superconducting nanowire devices Appl. Phys. Lett. 111 2017 122601 10.1063/1.4990066
94 Delacour C. Claudon J. Poizat J.P. Pannetier B. Bouchiat V. Espiau de Lamaestre R. Villegier J.C. Tarkhov M. Korneev A. Voronov B. Gol’tsman G. Superconducting single photon detectors made by local oxidation with an atomic force microscope Appl. Phys. Lett. 90 2007 191116 10.1063/1.2738195
95 Yang M. Liu L.H. Ning L.H. Jin Y.R. Deng H. Li J. Li Y. Zheng D.N. Fabrication of superconducting NbN meander nanowires by nano-imprint lithography Chin. Phys. B 25 2016 017401 10.1088/1674-1056/25/1/017401
96 Minaev N.V. Tarkhov M.A. Dudova D.S. Timashev P.S. Chichkov B.N. Bagratashvili V.N. Fabrication of superconducting nanowire single-photon detectors by nonlinear femtosecond optical lithography Laser Phys. Lett. 15 2018 026002 10.1088/1612-202X/aa8bd1
97 Korneeva Y.P. Vodolazov D.Y. Semenov A.V. Florya I.N. Simonov N. Baeva E. Korneev A.A. Goltsman G.N. Klapwijk T.M. Optical single-photon detection in micrometer-scale NbN bridges Phys. Rev. Appl. 9 2018 064037 10.1103/PhysRevApplied.9.064037
98 Jia T. Kang L. Zhang L. Zhao Q. Gu M. Qiu J. Chen J. Jin B. Doped niobium superconducting nanowire single-photon detectors Appl. Phys. B 116 2014 991 995 10.1007/s00340-014-5787-0
99 Jia X.Q. Kang L. Gu M. Yang X.Z. Chen C. Tu X.C. Jin B.B. Xu W.W. Chen J. Wu P.H. Fabrication of a strain-induced high performance NbN ultrathin film by a Nb5N6 buffer layer on Si substrate Supercond. Sci. Technol. 27 2014 035010 10.1088/0953-2048/27/3/035010
100 Xu T. Chen S. Shi H.K. Jia X.Q. Zhang L.B. Zhao Q.Y. Tu X.C. Kang L. Chen J. Wu P.H. Effect of buffer layer on thermal recovery of superconducting nanowire single-photon detector Supercond. Sci. Technol. 34 2021 074002 10.1088/1361-6668/ac0015
101 Dorenbos S.N. Reiger E.M. Perinetti U. Zwiller V. Zijlstra T. Klapwijk T.M. Low noise superconducting single photon detectors on silicon Appl. Phys. Lett. 93 2008 131101 10.1063/1.2990646
102 Miki S. Takeda M. Fujiwara M. Sasaki M. Otomo A. Wang Z. Superconducting NbTiN nanowire single photon detectors with low kinetic inductance Appl. Phys. Express 2 2009 075002 10.1143/APEX.2.075002
103 Tanner M.G. Natarajan C.M. Pottapenjara V.K. O’Connor J.A. Warburton R.J. Hadfield R.H. Baek B. Nam S. Dorenbos S.N. Ureña E.B. Enhanced telecom wavelength single-photon detection with NbTiN superconducting nanowires on oxidized silicon Appl. Phys. Lett. 96 2010 221109 10.1063/1.3428960
104 Zichi J. Chang J. Steinhauer S. Von Fieandt K. Los J.W.N. Visser G. Kalhor N. Lettner T. Elshaari A.W. Zadeh I.E. Zwiller V. Optimizing the stoichiometry of ultrathin NbTiN films for high-performance superconducting nanowire single-photon detectors Opt Express 27 2019 26579 26587 10.1364/OE.27.026579 31674536
105 Eraerds P. Legré M. Zhang J. Zbinden H. Gisin N. Photon counting OTDR: advantages and limitations J. Lightwave Technol. 28 2010 952 964 10.1109/JLT.2009.2039635
106 Takesue H. Nam S.W. Zhang Q. Hadfield R.H. Honjo T. Tamaki K. Yamamoto Y. Quantum key distribution over a 40-dB channel loss using superconducting single-photon detectors Nat. Photonics 1 2007 343 348 10.1038/nphoton.2007.75
107 Gisin N. Ribordy G. Tittel W. Zbinden H. Quantum cryptography Rev. Mod. Phys. 74 2002 145 195 10.1103/RevModPhys.74.145
108 Schuck C. Pernice W.H.P. Tang H.X. Waveguide integrated low noise NbTiN nanowire single-photon detectors with milli-Hz dark count rate Sci. Rep. 3 2013 1893 10.1038/srep01893 23714696
109 Jia X. Kang L. Yang X. Wang Z. Ren T. Jin B.B. Xu W. Chen J. Wu P. Ultrathin NbTiN films with high Ti composition for superconducting nanowire single photon detectors IEEE Trans. Appl. Supercond. 25 2014 1 4 10.1109/TASC.2014.2373818 32863691
110 Gourgues R. Los J.W.N. Zichi J. Chang J. Kalhor N. Bulgarini G. Dorenbos S.N. Zwiller V. Zadeh I.E. Superconducting nanowire single photon detectors operating at temperature from 4 to 7 K Opt Express 27 2019 24601 24609 10.1364/OE.27.024601 31510347
111 Zadeh I.E. Los J.W. Gourgues R. Steinmetz V. Bulgarini G. Dobrovolskiy S.M. Zwiller V. Dorenbos S.N. Single-photon detectors combining high efficiency, high detection rates, and ultra-high timing resolution APL Photonics 2 2017 11 10.1063/1.5000001
112 Esmaeil Zadeh I. Los J.W.N. Gourgues R.B.M. Chang J. Elshaari A.W. Zichi J.R. Van Staaden Y.J. Swens J.P.E. Kalhor N. Guardiani A. Efficient single-photon detection with 7.7 ps time resolution for photon-correlation measurements ACS Photonics 7 2020 1780 1787 10.1021/acsphotonics.0c00433
113 Chang J. Los J.W.N. Tenorio-Pearl J.O. Noordzij N. Gourgues R. Guardiani A. Zichi J.R. Pereira S.F. Urbach H.P. Zwiller V. Detecting telecom single photons with 99.5− 2.07+ 0.5% system detection efficiency and high time resolution APL Photonics 6 2021 036114 10.1063/5.0039772
114 Chang J. Los J.W.N. Gourgues R. Steinhauer S. Dorenbos S.N. Pereira S.F. Urbach H.P. Zwiller V. Esmaeil Zadeh I. Efficient mid-infrared single-photon detection using superconducting NbTiN nanowires with high time resolution in a Gifford-McMahon cryocooler Photon. Res. 10 2022 1063 1070 10.1364/PRJ.437834
115 Chang J. Zadeh I.E. Los J.W.N. Zichi J. Fognini A. Gevers M. Dorenbos S. Pereira S.F. Urbach P. Zwiller V. Multimode-fiber-coupled superconducting nanowire single-photon detectors with high detection efficiency and time resolution Appl. Opt. 58 2019 9803 9807 10.1364/AO.58.009803 31873623
116 Cirillo C. Chang J. Caputo M. Los J.W.N. Dorenbos S. Esmaeil Zadeh I. Attanasio C. Superconducting nanowire single photon detectors based on disordered NbRe films Appl. Phys. Lett. 117 2020 172602 10.1063/5.0021487
117 Rossnagel S.M. Characteristics of ultrathin Ta and TaN films J. Vac. Sci. Technol. B Microelectron. Nanometer Struct. Process. Meas. Phenom. 20 2002 2328 2336 10.1116/1.1520556
118 Setzu R. Baggetta E. Villegier J.C. Study of NbN Josephson junctions with a tantalum nitride barrier tuned to the metal-insulator transition J. Phys.: Conf. Ser. 97 2008 012077 10.1088/1742-6596/97/1/012077
119 Il’in K. Hofherr M. Rall D. Siegel M. Semenov A. Engel A. Inderbitzin K. Aeschbacher A. Schilling A. Ultra-thin TaN films for superconducting nanowire single-photon detectors J. Low Temp. Phys. 167 2012 809 814 10.1007/s10909-011-0424-3
120 Engel A. Aeschbacher A. Inderbitzin K. Schilling A. Il’in K. Hofherr M. Siegel M. Semenov A. Hübers H.W. Tantalum nitride superconducting single-photon detectors with low cut-off energy Appl. Phys. Lett. 100 2012 062601 10.1063/1.3684243
121 Engel A. Inderbitzin K. Schilling A. Lusche R. Semenov A. Hübers H.W. Henrich D. Hofherr M. Il'in K. Siegel M. Temperature-dependence of detection efficiency in NbN and TaN SNSPD IEEE Trans. Appl. Supercond. 23 2013 2300505 10.1109/TASC.2013.2239345
122 Korneeva Y. Florya I. Vdovichev S. Moshkova M. Simonov N. Kaurova N. Korneev A. Goltsman G. Comparison of hot spot formation in NbN and MoN thin superconducting films after photon absorption IEEE Trans. Appl. Supercond. 27 2017 1 4 10.1109/TASC.2017.2659661
123 Evtikhiev N.N. Kurbatova E.A. Cheremkhin P.A. Coefficients quantization at off-axis digital hologram wavelet compression KEn Energy 3 2018 523 534 10.18502/ken.v3i3.2066
124 Chen J. Altepeter J.B. Medic M. Lee K.F. Gokden B. Hadfield R.H. Nam S.W. Kumar P. Demonstration of a quantum controlled-NOT gate in the telecommunications band Phys. Rev. Lett. 100 2008 133603 10.1103/PhysRevLett.100.133603
125 Clausen C. Usmani I. Bussières F. Sangouard N. Afzelius M. De Riedmatten H. Gisin N. Quantum storage of photonic entanglement in a crystal Nature 469 2011 508 511 10.1038/nature09662 21228774
126 Correa R.E. Dauler E.A. Nair G. Pan S.H. Rosenberg D. Kerman A.J. Molnar R.J. Hu X. Marsili F. Anant V. Single photon counting from individual nanocrystals in the infrared Nano Lett. 12 2012 2953 2958 10.1021/nl300642k 22624846
127 Toth L. Transition Metal Carbides and Nitrides 2014 Elsevier
128 Kerman A.J. Dauler E.A. Yang J.K.W. Rosfjord K.M. Anant V. Berggren K.K. Gol’tsman G.N. Voronov B.M. Constriction-limited detection efficiency of superconducting nanowire single-photon detectors Appl. Phys. Lett. 90 2007 101110 10.1063/1.2696926
129 Baek B. Lita A.E. Verma V. Nam S.W. Superconducting a WxSi1− x nanowire single-photon detector with saturated internal quantum efficiency from visible to 1850 nm Appl. Phys. Lett. 98 2011 251105 10.1063/1.3600793
130 Marsili F. Verma V.B. Stern J.A. Harrington S. Lita A.E. Gerrits T. Vayshenker I. Baek B. Shaw M.D. Mirin R.P. Nam S.W. Detecting single infrared photons with 93% system efficiency Nat. Photonics 7 2013 210 214 10.1038/nphoton.2013.13
131 Verma V.B. Lita A.E. Vissers M.R. Marsili F. Pappas D.P. Mirin R.P. Nam S.W. Superconducting nanowire single photon detectors fabricated from an amorphous Mo0.75Ge0.25 thin film Appl. Phys. Lett. 105 2014 022602 10.1063/1.4890277
132 Verma V.B. Korzh B. Bussieres F. Horansky R.D. Lita A.E. Marsili F. Shaw M.D. Zbinden H. Mirin R.P. Nam S.W. High-efficiency WSi superconducting nanowire single-photon detectors operating at 2.5 K Appl. Phys. Lett. 105 2014 122601 10.1063/1.4896045
133 Allmaras J.P. Kozorezov A.G. Beyer A.D. Marsili F. Briggs R.M. Shaw M.D. Thin-Film Thermal Conductivity Measurements Using Superconducting Nanowires J. Low Temp. Phys. 193 2018 380 386 10.1007/s10909-018-2022-0
134 Dorenbos S.N. Forn-Díaz P. Fuse T. Verbruggen A.H. Zijlstra T. Klapwijk T.M. Zwiller V. Low gap superconducting single photon detectors for infrared sensitivity Appl. Phys. Lett. 98 2011 251102 10.1063/1.3599712
135 Korneeva Y.P. Mikhailov M.Y. Pershin Y.P. Manova N.N. Divochiy A.V. Vakhtomin Y.B. Korneev A.A. Smirnov K.V. Sivakov A.G. Devizenko A.Y. Goltsman G.N. Superconducting single-photon detector made of MoSi film Supercond. Sci. Technol. 27 2014 095012 10.1088/0953-2048/27/9/095012
136 Smith A.W. Clinton T.W. Tsuei C.C. Lobb C.J. Sign reversal of the Hall resistivity in amorphous Mo 3 Si Phys. Rev. B 49 1994 12927 12930 10.1103/PhysRevB.49.12927
137 Kubo S. Superconducting properties of amorphous MoX (X= Si, Ge) alloy films for Abrikosov vortex memory J. Appl. Phys. 63 1988 2033 2045 10.1063/1.341105
138 Lita A.E. Verma V.B. Horansky R.D. Shainline J.M. Mirin R.P. Nam S. Materials development for high efficiency superconducting nanowire single-photon detectors MRS Proc. 1807 2015 1 6 10.1557/opl.2015.544
139 Verma V.B. Korzh B. Bussières F. Horansky R.D. Dyer S.D. Lita A.E. Vayshenker I. Marsili F. Shaw M.D. Zbinden H. High-efficiency superconducting nanowire single-photon detectors fabricated from MoSi thin-films Opt Express 23 2015 33792 33801 10.1364/OE.23.033792 26832040
140 Li J. Kirkwood R.A. Baker L.J. Bosworth D. Erotokritou K. Banerjee A. Heath R.M. Natarajan C.M. Barber Z.H. Sorel M. Hadfield R.H. Nano-optical single-photon response mapping of waveguide integrated molybdenum silicide (MoSi) superconducting nanowires Opt Express 24 2016 13931 13938 10.1364/OE.24.013931 27410555
141 Banerjee A. Baker L.J. Doye A. Nord M. Heath R.M. Erotokritou K. Bosworth D. Barber Z.H. MacLaren I. Hadfield R.H. Characterisation of amorphous molybdenum silicide (MoSi) superconducting thin films and nanowires Supercond. Sci. Technol. 30 2017 084010 10.1088/1361-6668/aa76d8
142 Wollman E.E. Verma V.B. Beyer A.D. Briggs R.M. Korzh B. Allmaras J.P. Marsili F. Lita A.E. Mirin R.P. Nam S.W. Shaw M.D. UV superconducting nanowire single-photon detectors with high efficiency, low noise, and 4 K operating temperature Opt Express 25 2017 26792 26801 10.1364/OE.25.026792 29092164
143 Miki S. Yamashita T. Terai H. Wang Z. High performance fiber-coupled NbTiN superconducting nanowire single photon detectors with Gifford-McMahon cryocooler Opt Express 21 2013 10208 10214 10.1364/OE.21.010208 23609728
144 Verma V.B. Marsili F. Harrington S. Lita A.E. Mirin R.P. Nam S.W. A three-dimensional, polarization-insensitive superconducting nanowire avalanche photodetector Appl. Phys. Lett. 101 2012 251114 10.1063/1.4768788
145 Day C. New Conventional Superconductor Found with a Surprisingly High Tc Phys. Today 54 2001 17 18 10.1063/1.1372100
146 Nagamatsu J. Nakagawa N. Muranaka T. Zenitani Y. Akimitsu J. Superconductivity at 39 K in magnesium diboride Nature 410 2001 63 64 10.1038/35065039 11242039
147 Eom C.B. Lee M.K. Choi J.H. Belenky L.J. Song X. Cooley L.D. Naus M.T. Patnaik S. Jiang J. Rikel M. Polyanskii A. Thin film magnesium boride superconductor with very high critical current density and enhanced irreversibility field Nature 411 2001 558 560 10.1038/35079018 11385563
148 Kang W.N. Kim H.-J. Choi E.-M. Jung C.U. Lee S.-I. MgB2 superconducting thin films with a transition temperature of 39 Kelvin Science 292 2001 1521 1523 10.1126/science.1060822 11303089
149 Brinkman A. Mijatovic D. Rijnders G. Leca V. Smilde H.J.H. Oomen I. Golubov A.A. Roesthuis F. Harkema S. Hilgenkamp H. Superconducting thin films of MgB2 on Si by pulsed laser deposition Phys. C Supercond. 353 2001 1 4 10.1016/S0921-4534(01)00396-3
150 Monticone E. Portesi C. Borini S. Taralli E. Rajteri M. Superconducting MgB2 Nanostructures Fabricated by Electron Beam Lithography IEEE Trans. Appl. Supercond. 17 2007 222 224 10.1109/TASC.2007.898183
151 Cherednichenko S. Acharya N. Novoselov E. Drakinskiy V. Low kinetic inductance superconducting MgB2 nanowires with a 130 ps relaxation time for single-photon detection applications Supercond. Sci. Technol. 34 2021 044001 10.1088/1361-6668/abdeda
152 Khafizov M. Li X. Cui Y. Xi X. Sobolewski R. Mechanism of Light Detection in Current-Biased Superconducting MgB2 Microbridges IEEE Trans. Appl. Supercond. 17 2007 2867 2870 10.1109/TASC.2007.898372
153 Shibata H. Maruyama T. Akazaki T. Takesue H. Honjo T. Tokura Y. Photon detection and fabrication of MgB2 nanowire Phys. C Supercond. 468 2008 1992 1994 10.1016/j.physc.2008.05.248
154 Shishido H. Yoshida T. Ishida T. Ambient temperature epitaxial growth of MgB2 thin films with a Mg buffer layer Appl. Phys. Express 8 2015 113101 10.7567/APEX.8.113101
155 Shibata H. Review of superconducting nanostrip photon detectors using various superconductors IEICE Trans. Electron. E104.C 2021 429 434 10.1587/transele.2020SUI0001
156 Wang D. Zhang C. Zhang J. Zhang Y. Feng Q.R. Wang Y. Gan Z.Z. Degradation of MgB2 Ultrathin Films Under Different Environmental Conditions IEEE Trans. Appl. Supercond. 25 2015 1 9 10.1109/TASC.2014.2379722 32863691
157 Acharya N. Wolak M.A. Melbourne T. Cunnane D. Karasik B.S. Xi X. As-grown versus ion-milled MgB2 ultrathin films for THz sensor applications IEEE Trans. Appl. Supercond. 27 2017 1 4 10.1109/TASC.2016.2645126
158 Charaev I. Batson E.K. Cherednichenko S. Reidy K. Drakinskiy V. Yu Y. Lara-Avila S. Thomsen J.D. Colangelo M. Incalza F. Single-photon detection using large-scale high-temperature MgB2 sensors at 20 K Nat. Commun. 15 2024 3973 10.1038/s41467-024-47353-x 38729944
159 Enomoto Y. Murakami T. Optical detector using superconducting BaPb0.7Bi0.3O3 thin films J. Appl. Phys. 59 1986 3807 3814 10.1063/1.336720
160 Yoshisato Y. Takeoka A. Ikemachi T. Niki K. Yokoo T. Nakano S. Kuwano Y. Microwave detector using granular-type YBCO superconductors Jpn. J. Appl. Phys. 29 1990 1080 10.1143/JJAP.29.1080
161 Leung M. Broussard P.R. Claassen J.H. Osofsky M. Wolf S.A. Strom U. Optical detection in thin granular films of Y-Ba-Cu-O at temperatures between 4.2 and 100 K Appl. Phys. Lett. 51 1987 2046 2047 10.1063/1.98287
162 Frenkel A. Saifi M.A. Venkatesan T. England P. Wu X.D. Inam A. Optical response of nongranular high-T c Y1Ba2Cu3O7− x superconducting thin films J. Appl. Phys. 67 1990 3054 3068 10.1063/1.345435
163 Carr G.L. Quijada M. Tanner D.B. Hirschmugl C.J. Williams G.P. Etemad S. Dutta B. DeRosa F. Inam A. Venkatesan T. Xi X. Fast bolometric response by high Tc detectors measured with subnanosecond synchrotron radiation Appl. Phys. Lett. 57 1990 2725 2727 10.1063/1.103772
164 Zheng J.P. Ying Q.Y. Kwok H.S. Y-Ba-Cu-O thin film infrared detectors Phys. C Supercond. 168 1990 322 326 10.1016/0921-4534(90)90525-J
165 Eidelloth W. Optical response of highly oriented YBCO thin films IEEE Trans. Magn. 27 1991 2828 2831 10.1109/20.133798
166 Eidelloth W. Barnes F.S. Optical response of bulk Bi-Sr-Ca-Cu-O IEEE J. Quant. Electron. 25 1989 2405 2409 10.1109/3.42073
167 Schneider G. Lengfellner H. Betz J. Renk K.F. Prettl W. Infrared detection by Tl− Ba− Ca− Cu− O superconducting films Int. J. Infrared. Milli. Waves 12 1991 1 7 10.1007/BF01041878
168 Lau J.A. Verma V.B. Schwarzer D. Wodtke A.M. Superconducting single-photon detectors in the mid-infrared for physical chemistry and spectroscopy Chem. Soc. Rev. 52 2023 921 941 10.1039/D1CS00434D 36649126
169 Wollman E.E. Verma V.B. Walter A.B. Chiles J. Korzh B. Allmaras J.P. Zhai Y. Lita A.E. McCaughan A.N. Schmidt E. Recent advances in superconducting nanowire single-photon detector technology for exoplanet transit spectroscopy in the mid-infrared J. Astron. Telesc. Instrum. Syst. 7 2021 11004 10.1117/1.JATIS.7.1.011004
170 Shibata H. Kirigane N. Fukao K. Sakai D. Karimoto S. Yamamoto H. Photoresponse of a La1.85Sr0.15CuO4 nanostrip Supercond. Sci. Technol. 30 2017 074001 10.1088/1361-6668/aa6c3e
171 Merino R.L. Seifert P. Retamal J.D. Mech R.K. Taniguchi T. Watanabe K. Kadowaki K. Hadfield R.H. Efetov D.K. Two-dimensional cuprate nanodetector with single telecom photon sensitivity at T= 20 K 2D Mater. 10 2023 021001 10.1088/2053-1583/acb4a8
172 Charaev I. Bandurin D.A. Bollinger A.T. Phinney I.Y. Drozdov I. Colangelo M. Butters B.A. Taniguchi T. Watanabe K. He X. Single-photon detection using high-temperature superconductors Nat. Nanotechnol. 18 2023 343 349 10.1038/s41565-023-01325-2 36941357
173 Seifert P. Retamal J.R.D. Merino R.L. Sheinfux H.H. Moore J.N. Aamir M.A. Taniguchi T. Watanabe K. Kadowaki K. Artiglia M. A high-TC van der Waals superconductor based photodetector with ultra-high responsivity and nanosecond relaxation time 2D Mater. 8 2021 035053 10.1088/2053-1583/ac072f
174 Maple M. de Andrade M.C. Herrmann J. Dickey R.P. Dilley N.R. Han S. Superconductivity in rare earth and actinide compounds J. Alloys Compd. 250 1997 585 595 10.1016/S0925-8388(96)02832-0
175 Korina E. Karaberova A. Bol’shakov O. Bulatova E. Golovin M. Abramyan A. Stanković D.M. Enhancing Adrenaline Sensing with Lanthanum Cuprate: A Promising Approach for a Novel Sensor J. Electrochem. Soc. 171 2024 017513 10.1149/1945-7111/ad1ecb
176 Johrendt D. Rare earth based superconducting materials Rare Earth Chem. 1 2020 557 10.1515/9783110654929 Degruyter
177 Marzougui B. Marzouki A. Smida Y.B. Marzouki R. The Cuprate Ln2CuO4 (Ln: Rare Earth): Synthesis, Crystallography, and Applications 2023 10.5772/intechopen.109193
178 Capponi J.J. Chaillout C.W. Lejay P. Ngugen B. Raveau J.L. Soubeyroux J.L. Tournier R. Symmetry classification of states in high temperature superconductors Europhys. Lett. 3 1987 13019
179 Cava R.J. Batlogg B. Chen C.H. Rietman E.A. Zahurak S.M. Werder D. Single-phase 60-K bulk superconductor in annealed Ba 2 Y Cu 3 0 7− δ (0.3< δ< 0.4) with correlated oxygen vacancies in the Cu-O chains Phys. Rev. B 36 1987 5719 5722 10.1103/PhysRevB.36.5719
180 Jorgensen J. Veal B.W. Kwok W.K. Crabtree G.W. Umezawa A. Nowicki L.J. Paulikas A.P. Structural and superconducting properties of orthorhombic and tetragonal Y Ba 2 Cu 3 O 7− x: The effect of oxygen stoichiometry and ordering on superconductivity Phys. Rev. B 36 1987 5731 5734 10.1103/PhysRevB.36.5731
181 Thoma P. Ultra-fast YBa2Cu3O7-X Direct Detectors for the THz Frequency Range. Vol. 9 2014 KIT Scientific Publishing
182 Fournier P. T′ and infinite-layer electron-doped cuprates Physica C 514 2015 314 338 10.1016/j.physc.2015.02.036
183 Curtz N. Koller E. Zbinden H. Decroux M. Antognazza L. Fischer Ø. Gisin N. Patterning of ultrathin YBCO nanowires using a new focused-ion-beam process Supercond. Sci. Technol. 23 2010 045015 10.1088/0953-2048/23/4/045015
184 Probst P. Semenov A. Ries M. Hoehl A. Rieger P. Scheuring A. Judin V. Wünsch S. Il'in K. Smale N. Nonthermal response of YBa 2 Cu 3 O 7− δ thin films to picosecond THz pulses Phys. Rev. B 85 2012 174511 10.1103/PhysRevB.85.174511
185 Nawaz S. Arpaia R. Lombardi F. Bauch T. Microwave response of superconducting YBa2Cu3O7-δ nanowire bridges sustaining the critical depairing current: Evidence of Josephson-like behavior Phys. Rev. Lett. 110 2013 167004 10.1103/PhysRevLett.110.167004 23679634
186 Amari P. Feuillet-Palma C. Jouan A. Couedo F. Bourlet N. Géron E. Malnou M. Méchin L. Sharafiev A. Lesueur J. Bergeal N. Ion Irradiated YBa2Cu3O7 Nano-Meanders for Superconducting Single Photon Detectors 2016 10.48550/arXiv.1612.07730
187 Arpaia R. Andersson E. Trabaldo E. Bauch T. Lombardi F. Probing the phase diagram of cuprates with YBa 2 Cu 3 O 7− δ thin films and nanowires Phys. Rev. Mater. 2 2018 024804 10.1103/PhysRevMaterials.2.024804
188 Ejrnaes M. Parlato L. Arpaia R. Bauch T. Lombardi F. Cristiano R. Tafuri F. Pepe G.P. Observation of dark pulses in 10 nm thick YBCO nanostrips presenting hysteretic current voltage characteristics Supercond. Sci. Technol. 30 2017 12LT02 10.1088/1361-6668/aa94b9
189 Lyatti M. Wolff M.A. Gundareva I. Kruth M. Ferrari S. Dunin-Borkowski R.E. Schuck C. Energy-level quantization and single-photon control of phase slips in YBa2Cu3O7–x nanowires Nature 11 2020 763 10.1038/s41467-020-14548-x
190 Kumar A. Panna D. Bouscher S. Koriat A. Nitzav Y. Jacovi R. Kanigel A. Hayat A. Ultrafast low-jitter optical response in high-temperature superconducting microwires Appl. Phys. Lett. 122 2023 1 10.1063/5.0150805
191 Amari P. Kozlov S. Recoba-Pawlowski E. Velluire-Pellat Z. Jouan A. Couëdo F. Ulysse C. Briatico J. Roditchev D. Bergeal N. Scalable nanofabrication of high-quality YBa2Cu3O 7− δ nanowires for single-photon detectors Phys. Rev. Appl. 20 2023 044025 10.1103/PhysRevApplied.20.044025
192 Atikur Rahman M. Rahaman M.Z. Samsuddoha M.N. A review on cuprate based superconducting materials including characteristics and applications Am. J. Phys. Appl. 3 2015 39 56 10.11648/j.ajpa.20150302.15
193 Ghosh S. Jangade D.A. Deshmukh M.M. Nanowire bolometer using a 2D high-temperature superconductor Nanotechnology 34 2022 015304 10.1088/1361-6528/ac9684
194 Romano P. Riccio M. Guarino A. Martucciello N. Grimaldi G. Leo A. Nigro A. Electron doped superconducting cuprates for photon detectors Measurement 122 2018 502 506 10.1016/j.measurement.2018.02.010
195 Armitage N.P. Fournier P. Greene R.L. Progress and perspectives on electron-doped cuprates Rev. Mod. Phys. 82 2010 2421 2487 10.1103/RevModPhys.82.2421
196 Long Y. Zhao L. Zhao B. Qiu X. Zhang C. Fu P. Wang L. Zhang Z. Zhao S. Yang Q. Wang G. Femtosecond optical response of electron-doped superconductor La2−xCexCuO4 Phys. C Supercond. 436 2006 59 61 10.1016/j.physc.2005.12.056
197 Charpentier S. Arpaia R. Gaudet J. Matte D. Baghdadi R. Löfwander T. Golubev D. Fournier P. Bauch T. Lombardi F. Hot spot formation in electron-doped PCCO nanobridges Phys. Rev. B 94 2016 060503 10.1103/PhysRevB.94.060503
198 Avella A. Buonavolontà C. Guarino A. Valentino M. Leo A. Grimaldi G. de Lisio C. Nigro A. Pepe G. Disorder-sensitive pump-probe measurements on Nd 1.83 Ce 0.17 CuO 4±δ films Phys. Rev. B 94 2016 115426 10.1103/PhysRevB.94.115426
199 Ejrnaes M. Cirillo C. Salvoni D. Chianese F. Bruscino C. Ercolano P. Cassinese A. Attanasio C. Pepe G.P. Parlato L. Single photon detection in NbRe superconducting microstrips Appl. Phys. Lett. 121 2022 262601 10.1063/5.0131336
200 Soltan S. Albrecht J. Habermeier H.-U. Ferromagnetic/superconducting bilayer structure: A model system for spin diffusion length estimation Phys. Rev. B 70 2004 144517 10.1103/PhysRevB.70.144517
201 Przyslupski P. Komissarov I. Paszkowicz W. Dluzewski P. Minikayev R. Sawicki M. Magnetic properties of La 0.67 Sr 0.33 MnO3/YBa 2 Cu 3 O7 superlattices Phys. Rev. B 69 2004 134428 10.1103/PhysRevB.69.134428
202 Andersson E. Arpaia R. Trabaldo E. Bauch T. Lombardi F. Fabrication and electrical transport characterization of high quality underdoped YBa2Cu3O7-δ nanowires Supercond. Sci. Technol. 33 2020 064002 10.1088/1361-6668/ab807e
203 Pena V. Sefrioui Z. Arias D. Leon C. Santamaria J. Varela M. Pennycook S.J. Martinez J.L. Coupling of superconductors through a half-metallic ferromagnet: Evidence for a long-range proximity effect Phys. Rev. B 69 2004 224502 10.1103/PhysRevB.69.224502
204 Pepe G.P. Parlato L. Marrocco N. Pagliarulo V. Peluso G. Barone A. Tafuri F. Uccio U.S.d. Miletto F. Radovic M. Novel superconducting proximized heterostructures for ultrafast photodetection Cryogenics 49 2009 660 664 10.1016/j.cryogenics.2009.02.002
205 Parlato L. Ejrnaes M. Nasti U. Arpaia R. Taino T. Bauch T. Myoren H. Sobolewski R. Tafuri F. Lombardi F. Cristiano R. Investigation of Dark Counts in Innovative Materials for Superconducting Nanowire Single-Photon Detector Applications Photon Counting Applications 10229 2017 69 74 10.1117/12.2267647
206 Arpaia R. Ejrnaes M. Parlato L. Cristiano R. Arzeo M. Bauch T. Nawaz S. Tafuri F. Pepe G.P. Lombardi F. Highly homogeneous YBCO/LSMO nanowires for photoresponse experiments Supercond. Sci. Technol. 27 2014 044027 10.1088/0953-2048/27/4/044027
207 Litombe N.E.-S. Nanopatterning and Transport Properties of Cuprate Superconductors PhD Thesis 2015 Harvard University
208 Sochnikov I. Shaulov A. Yeshurun Y. Logvenov G. Bozović I. Large oscillations of the magnetoresistance in nanopatterned high-temperature superconducting films Nat. Nanotechnol. 5 2010 516 519 10.1038/NNANO.2010.111 20543834
209 Liang R. Bonn D.A. Hardy W.N. Broun D. Lower critical field and superfluid density of highly underdoped YBa 2 Cu 3 O 6+ x single crystals Phys. Rev. Lett. 94 2005 117001 10.1103/PhysRevLett.94.117001
210 Ramshaw B.J. Day J. Vignolle B. LeBoeuf D. Dosanjh P. Proust C. Taillefer L. Liang R. Hardy W.N. Bonn D.A. Vortex lattice melting and H c 2 in underdoped YBa2Cu3Oy Phys. Rev. B 86 2012 174501 10.1103/PhysRevB.86.174501
211 Mori Z. Tadokoro M. Zulhairi Z. Doi T. Koba S. Higo S. Hakuraku Y. Micropatterning of NdBa2Cu3O7 thin films using a KrF excimer laser Supercond. Sci. Technol. 14 2001 45 49 10.1088/0953-2048/14/1/308
212 Tinkham M. Introduction to Superconductivity 2004 Courier Corporation
213 Pashitskiĭ É. Vakaryuk V. Ryabchenko S. Fedotov Y. Temperature dependence of the critical current in high-T c superconductors with low-angle boundaries between crystalline blocks Low Temp. Phys. 27 2001 96 102 10.1063/1.1353699
214 Ohmukai M. Fujita T. Ohno T. The temperature dependence of critical current in YBa2Cu3O7-d thin films deposited on MgO by an eclipse PLD Braz. J. Phys. 31 2001 511 513 10.1590/S0103-97332001000300027
215 Borsoi F. Magnetic Field Resilient Superconducting Circuit Elements for Majorana Parity Detection 2015 Delft University of Technology Master Thesis
216 Datesman A.M. Schultz J.C. Cecil T.W. Lyons C.M. Lichtenberger A.W. Gallium ion implantation into niobium thin films using a focused-ion beam IEEE Trans. Appl. Supercond. 15 2005 3524 3527 10.1109/TASC.2005.849029
217 Matsumoto K. Mele P. Artificial pinning center technology to enhance vortex pinning in YBCO coated conductors Supercond. Sci. Technol. 23 2009 14001 10.1088/0953-2048/23/1/014001
218 Barnes P.N. Kell J.W. Harrison B.C. Haugan T.J. Varanasi C.V. Rane M. Ramos F. Minute doping with deleterious rare earths in YBa2Cu3O7− δ films for flux pinning enhancements Appl. Phys. Lett. 89 2006 012503 10.1063/1.2219391
219 Birlik I. Erbe M. Freudenberg T. Celik E. Schultz L. Holzapfel B. Flux pinning improvement of YBCO superconducting films with BaZrO3 nanoparticles prepared by chemical solution deposition method J. Phys, Conf. Ser. 234 2010 12004 10.1088/1742-6596/234/1/012004
220 Maeda H. Tanaka Y. Fukutomi M. Asano T. A new high-Tc oxide superconductor without a rare earth element Jpn. J. Appl. Phys. 27 1988 L209 10.1143/JJAP.27.L209
221 Hegmann F. Preston J. Origin of the fast photoresponse of epitaxial YBa2Cu3O7−δ thin films Phys. Rev. B 48 1993 16023 16039 10.1103/PhysRevB.48.16023
222 Sobolewski R. New Developments in High Temperature Superconductivity: Proceedings of the 2nd Polish-US Conference Held a Wrocław and Karpacz, Poland, 17–21 August 1998 1998 Springer 100 122
223 Haldar S. Sehrawat A. Balasubramanian K.B. Modelling Response Time Contrasts in Superconducting Nanowire Single Photon Detectors 2024 10.48550/arXiv.2403.07299
224 Rall, D. in Journal of Physics: Conference Series. 042029 (IOP Publishing).
225 Chang J. Esmaeil Zadeh I. Superconducting single-photon detectors get hot Nat. Nanotechnol. 18 2023 322 323 10.1038/s41565-023-01334-1 36941358
226 Bo H. Ren T. Chen Z. Zhang M. Xie Y. Enhancing superconductivity of ultrathin YBa2Cu3O7-δ films by capping non-superconducting oxides Chin. Phys. B 28 2019 067402 10.1088/1674-1056/28/6/067402
