
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39223158
66991
10.1038/s41598-024-66991-1
Article
Single photon detection up to 2 µm in pair of parallel microstrips based on NbRe ultrathin films
http://orcid.org/0000-0001-8755-4484
Cirillo C. carla.cirillo@spin.cnr.it

1
Ejrnaes M. 2
Ercolano P. 3
Bruscino C. 3
Cassinese A. 36
Salvoni D. 4
http://orcid.org/0000-0002-3848-9169
Attanasio C. 5
Pepe G. P. 3
Parlato L. 3
1 https://ror.org/0192m2k53 grid.11780.3f 0000 0004 1937 0335 CNR-SPIN, c/o Università Degli Studi Di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano (Sa), Italy
2 grid.482259.0 0000 0004 1774 9464 CNR-SPIN, Via Campi Flegrei, 34, 80078 Pozzuoli (Na), Italy
3 https://ror.org/05290cv24 grid.4691.a 0000 0001 0790 385X Dipartimento Di Fisica “E. Pancini”, Università Degli Studi Di Napoli Federico II, 80125 Napoli, Italy
4 Photon Technology Italy Srl, Via Giacinto Gigante 174, 80128 Napoli, Italy
5 https://ror.org/0192m2k53 grid.11780.3f 0000 0004 1937 0335 Dipartimento Di Fisica “E. R. Caianiello”, Università Degli Studi Di Salerno, 84084 Fisciano (Sa), Italy
6 https://ror.org/005ta0471 grid.6045.7 0000 0004 1757 5281 Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, 80125, P.le Tecchio, 80, Napoli, Italy
2 9 2024
2 9 2024
2024
14 2034517 4 2024
8 7 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Superconducting microstrip single photon detectors (SMSPDs) are increasingly attracting the interest of the scientific community as a new platform for large area detectors with unprecedented advantaged in terms of fabrication. However, while their operativity at the telecommunication wavelength was achieved, working beyond 1.55 µm is challenging. Here, we experimentally demonstrate single-photon operation of NbRe microstrips at wavelengths of 1.55 and 2 µm. The devices are structured as pairs of parallel microstrips with widths ranging from 1.4 to 2.2 μm and lengths from 5 to 10 μm. This innovative design may assure large sensitive areas, without affecting the kinetic inductance, namely the time performance of the detectors. The results are discussed in the framework of the hot-spot two-temperature model.

Keywords

NIR single photon detectors
Superconducting detectors
Microstrips
Subject terms

Superconducting properties and materials
Superconducting devices
Ministero Università e Ricerca (MUR), Grant number 2014–2020 ARS01_00734issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcIntroduction

Twenty years after their introduction1, single photon detectors based on superconducting materials are still the state of the art technology due to their unprecedented performances2–4. Despite being the core of photon-based quantum technology, such as communication, computation and sensing, they represent an active field of research5. Many challenges are still open in order to optimize the performance of these devices for specific fields. For example, different applications require large area coverage, such as dark matter research or light detection and ranging (LIDAR)6–9. For these reasons, efforts are made to increase the widths of the superconducting wires responsible of the detection from the nanoscale, as in superconducting nanowire single photon detectors (SNSPDs)3, to micrometric scale, as in the recently proposed superconducting microstrips single photon detectors (SMSPDs)10. Both devices are based on ultrathin superconducting films typically patterned in forms of meanders, with thickness (d) of the order of the superconducting coherence length (ξ) operating below the critical temperature (Tc) and at bias currents very close to the critical current density (Jc). SNSPDs consist of wires of width in the 30–100 nm range. They were the first to be proposed and they currently are the state-of-the-art devices. Several mechanisms were proposed to model the detection process in SNSPD11. In the very first picture12, an absorbed photon locally heats and thus destroys the superconducting state, creating a normal region, called hot-spot (HS). The HS expands in the nanowire with a dynamics that depends on the microscopical material parameters, until the bias current density is forced to flow in a such reduced area that Jc is overcome and the device switches to the normal state. Summarising, a voltage pulse is produced by an absorbed photon. However, this picture is oversimplified, since in a more realistic refined model13, the HS is replaced by a finite region of weakened superconductivity, in which less Cooper pairs should carry the same current. As a result their velocity can overcome the critical one, and, as a result, the superconducting state can collapse. Both these models account for the dependence of the efficiency on the bias current, since for a given photon energy the number of quasiparticles present in the nanowire increases with increasing J. Therefore, operating at larger J, makes the system closer to the transition point, and consequently more sensitive. However, to account for other experimental observations, such as the dependence of the efficiency on the bias current, or on the position of the incident photon, the role of superconducting vortices, both single ones14,15 and vortex–antivortex pairs (VAP)16 was invoked. In particular, it was suggested that the arrival of a photon may either decrease the energy barrier for vortex entry or may lead to the formation and subsequent breaking of a VAP due to the Lorentz force generated by the bias current. Moreover, different processes can take place at the same time. The study of the dark count rate, namely events not generated by an arriving photon, as a function of the bias current can shed a light on the processes involved17. On top of that, as discussed in several works, one should mention that the material parameters, as well as the device design, play a key role in the determination of the dominant detection mechanism45. In this sense, a paradigm shift is represented by the work of Vodolazov10, where it was suggested that micrometric strips can in principle work in the single photon regime as long as the bias current is uniformly distributed and the energy transfer from the photon to the electronic system is efficient and confined in a small region. These requirements set specific constraints to different microscopical parameters such as resistivity, penetration depth, electronic heat capacity, relaxation rates. In the case of SMSPDs, operativity as single photon detector at 1.55 μm18–21, and only recently, up to 2 μm22 was demonstrated. This has renewed the interest in the realization of detectors based on high-temperature superconductors, such as YBCO and MgB223–26. In fact, while these materials can help to increase the operation temperature of the detectors, their superconducting properties typically suffer from the nanopatterning procedure. Moreover, there is an increasing demand of devices capable of detecting low-energy photons27. In fact, working beyond 1.55 µm opens the path to a wide range of applications, as in the atmosphere monitoring of pollutants and greenhouse gases with LIDARs16,28, in free space communications, or in the space-ground integrated quantum network29. However, this frequency range requires the use of low-gap superconductors such as amorphous ones28,30–32, but with the drawback of operation temperatures in the mK regime. Alternatively, crystalline superconductors were also employed, such as NbTiN, with extremely reduced thickness and width, demanding high-resolution nanopattering33, or by changing the phase of NbN34 or irradiating it32. It is therefore clear that a material-oriented research is crucial for obtaining devices with these demanding performances. For all the reasons previously discussed, the realisation of large-area detectors based on nanowires working at wavelengths longer than 1.55 μm and temperatures accessible by standard cryocooler is desirable, but still challenging.

In this work, we show that NbRe-based superconducting detectors35–37 can meet all the-above-mentioned requirements. At this purpose we realized devices with an innovative microstrip layout which consists of a pair of parallel strips, 1.4–2.2 μm wide. This design can be considered as the building block for the realization of more complex structures based on short microstrips arranged in a parallel/series configuration. This solution combines the possibility of having large-area detectors, while using relatively short strips, thus strongly reducing the kinetic inductance, LK, of the device. The superconducting single photon detector (SSPD) is inserted into a bias and readout circuit with a load resistance RL placed in parallel to the device. The electrical equivalent of the SSPD is an inductor with kinetic inductance Lk, in series with a parallel block made of a resistor, Rn, the resistance of the normal domain and a switch. When the strip is in the superconducting state, the switch is closed and shunts the resistor; after the arrival of a photon, the switch opens and adds the resistance Rn in series to the kinetic inductance. Lk depends on the geometry of the device, namely width (w), length (l) and thickness (d), and on the material parameter through the London penetration depth: λLLK=μ0λL2lwd. Moreover, the rise time, τrise, and the decay time, τdecay, of the output voltage pulse are both proportional to the kinetic inductance of the strip38 as τrise=LkRN+RL and τdecay=LkRL. A decrease of LK produces a reduction of the recovery time and an increase of the maximum count rate of the detector. The dark count rates and mechanisms involved in the detection process in this kind of structures were preliminarily studied in a previous work37. Here, we demonstrate that the devices can operate in the single photon regime at λ larger than telecom wavelength, up to 2 μm, and at temperatures of 1.6 K, easily achievable by commercial cryocooler systems. These results represent a significant progress for the realisation of large-area detectors working beyond the telecommunication wavelength at a relatively high temperature. The potential of NbRe ultrathin films for the realisation of SMSPDs with improved performances are delineated in the discussion, where also the perspectives of this work are reported.

Experiment

Nb0.18Re0.82 (hereafter NbRe) ultrathin films with thickness of 4 nm have been deposited on Si/SiOx substrates by DC magnetron sputtering in ultra-high vacuum (P ~ 10−8 mbar) at room temperature. The deposition was performed in an Ar pressure of 4 × 10−3 mbar at a growth rate of 0.3 nm/s39. The NbRe surface was then protected by a 2 nm-thick Al cap layer. The samples were patterned through optical lithography by using a microprinter. Devices with different nominal widths ranging from 1.4 to 2.2 µm, and lengths from 5 to 12.5 µm were fabricated. The devices are pairs of parallel strips, a test geometry that can be replicated in the future to realize series of pairs of parallel strips in order to gradually increase the detection area without affecting the values of the kinetic inductance. All the corners of the devices are rounded to reduce the current crowding effect. All the fabricated devices, their names and geometrical characteristics, as well as their superconducting properties are summarized in Table 1. In Fig. 1a  the layout and a microscope photograph of the device D1 are shown. Table 1 Fabricated devices based on a pair of parallel strips, their geometrical characteristics, along with their transport and superconducting properties.

Device	w (µm)	L (µm)	A (µm2)	Ic-Ir (μA)	Jc (MA/cm2)	
D1	1.4	5	14	6.2	0.30	
D2	2.2	7.5	33	19.2	0.14	
D3	2.1	10	42	8.2	0.27	
Ic and Ir, are the switching and the retrapping current, respectively, as shown in Fig. 2. All values refer to T = 4.2 K.

Figure 1 Layout (a) and microscope photograph (b) of the device D1, consisting in a single pair of parallel strips. The black arrows indicate the length, L, and the width, w, of the strips at the narrowest point. The red arrows indicate the direction of the current flow.

Electrical transport measurements were performed in a liquid 4He cryostat with the samples mounted on a dipstick equipped with a calibrated thermometer, by using a standard four-wire configuration. The superconducting critical temperature, Tc, was resistively measured and defined at the midpoint of the resistive transition. For all devices, we estimated Tc = 5.15 K, in agreement with the results reported on unstructured films40. A typical current–voltage (I–V) characteristic measured at T = 4.2 K on the device D1 is shown in Fig. 2.Figure 2 I-V curve at T = 4.2 K for the device D1. Ic and Ir, are the switching and the retrapping current, respectively. Inset: temperature dependence of the critical current, Ic(T). The red line is the fitting curve obtained by using the Bardeen expression.

As the bias current, Ib, is swept from zero to higher values, the strip exhibits an abrupt transition from the superconducting (zero voltage) to the normal (finite voltage) state at the switching current, Ic. The strip persist in the normal state until the current is reduced below the re-trapping current, Ir, when the strip becomes again superconducting. This gives rise to a hysteretic current–voltage characteristic, that is a fingerprint of the presence of a hot-spot in the superconducting strip. Moreover, it assures a clear bistable switching from the superconducting to the dissipative state, which is crucial for the operation of the strip as a SMSPD. In Table 1, we report the difference between the switching and the retrapping currents (Ic − Ir) as a quality parameter.

For all the investigated devices the values the critical current density, Jc = Ic/wd = Ic/A at T = 4.2 K are in the range 0.1–0.4 MA/cm2. The behaviour of Ic as a function of the temperature for the device D1 is reported in the inset of Fig. 2. The experimental data are fitted according to the Bardeen expression 41 IcT=I01-TTc23/2, with I0=360±10 μA and Tc=4.8±0.1 K. The value of Tc is slightly lower than the measured value, probably due to the fact the previous formula does not reproduce the critical current values at higher temperatures, when vortex and antivortex pairs start to dissociate37. Moreover, at the lowest temperature reachable with our experimental set-up, approximatively 1.6 K, Ic is not yet saturated. We will come back to this point and to the related consequences when analysing the detection performances of the devices.

In the following, we focus on the device showing the larger critical current values, namely D1 (see Table 1). In fact, it is known that the single photon regime in microstrips can be obtained only if the ratio between the Jc and the depairing current, Jdp, is beyond a specific threshold which depends on the parameter γ = (8π2/5) Ce/Cp10. γ measures the ability of the material to maintain as much as possible the photon energy in a spatially confined region of excitations in the electron system (here Ce and Cp are heat capacities of the electron and photon system, respectively). For our NbRe films at T = Tc it is γ ≈ 1542 and we estimated that single photon regime was achieved only if the ratio Jc/Jdp was above 0.2136.

The devices were illuminated through a multimode fiber that couples light from room temperature to the refrigerated part where it ends 52 mm above the SMSPDs and emits a cone of light to ensure uniform illumination. The stripes are electrically connected through a small printed circuit to a coaxial cable that goes up to room temperature where a bias-tee (mini-circuits ZFBT-6GWþ) allows to apply a noise filtered DC bias from custom low-noise electronics. It also amplifies the SMSPD signal pulses using an RF amplifier (mini-circuits ZFL-1000LN) before registering them on an oscilloscope or counting them. In order to avoid latching, which could affect our microstrips due to their short length, we inserted a 470 nH series inductance and a 333 Ω parallel resistor in the measurement circuit43. Two diode lasers at different wavelengths, λ, were used. The light emitted from the first laser has λ = 1550 nm and a continuous power of 1 mW. In this case, to obtain a pulsed beam, the pulse/pattern generator mod.81104A by Hewlett–Packard has been used. The laser is fiber coupled and attenuated in two stages, the first one using an electronic variable optical attenuator by Thorlabs and the second stage of attenuation is done using a section of free space beam propagation where we can insert neutral density filters in the beam path. The other laser (FPL2000S by Thorlabs) with λ = 2 µm has a control unit which allows the setting of the operation current flowing through it, and then of the output power. However, these values are an overestimation of the power that actually reaches the sample, since losses take place at the FC/PC connectors between the fiber and the insert.

A typical photon response pulse for the detector D1 at T = 1.57 K, Ib = 200 µA, and at 1.5 µm is reported in Fig. 3a. The main goal of this work is to demonstrate the single-photon sensitivity of NbRe microwires beyond the telecommunication wavelength, up to 2 µm. The results in terms of the photon count rate (PCR, left scale) and the dark count rate (DCR, right scale) at T = 1.57 K (T/Tc = 0.31) using laser pulses at 1.55 µm (2 µm) are shown in Fig. 3b by red (blue) symbols, and black circles, respectively, for the device D1. A nearly saturated PCR is obtained at both wavelengths, probably due to the geometry of the samples, since the region sensitive to light can expand into the tapered edges at higher bias current. Better performances in this sense could in principle be achieved by reducing the operation temperature, since working below 1 K can assure higher Ic values (see inset of Fig. 2), with obvious benefits in terms of PCR and DCR45. Similar results can be achieved by further reducing the films thickness, which will also require measuring at lower temperatures. Concerning false events, the dark count rates show an exponentially increase with Ib. A change in the DCR slope at Ib/Ic = 0.94, related to the background and the intrinsic contribution, is clearly visible.Figure 3 (a) Typical photon response pulse for the detector D1 at T = 1.57 K and Ib = 200 μA at 1.5 µm. (b) Dark count rate (black circles) and photon count rate at 1.55 μm (red circles) and at 2.00 μm (blue triangles) for the device D1 at T = 1.57 K.

Finally, by measuring the PCR as a function of the light attenuation for both the analysed wavelengths, we verified that the devices were working in the single-photon counting regime.

By assuming that the photon statistics has a Poissonian distribution, for a mean number of m photons per pulse, the probability P(n) of detecting n photons from a given pulse is proportional to P(n) ≅ e−m(m)n/n! By attenuating the radiation fluence to reduce the total number of incident photons on the detector the condition m « 1 (corresponding to having on average much less than one photon per pulse) is achieved. In this case it is: P(n) ≅ mn/n! Since the energy of the pulse is proportional to m, the photon count rate in the detection regime of n-photons exhibits a power-law dependence on the mean pulse energy where the exponent is n. Therefore, if the detection process is of the single-photon type, the photon count rate is linearly proportional to the photon flux1. In Fig. 4a, the result obtained as a function of the ratio Ib/Ic is reported at λ = 1.55 μm. The experimental data, which spread over two orders of magnitude in a wide range of Ib, were successfully fitted by the dependence P =a·Pb , where a and b are free fitting parameters (see lines in Fig. 4a). The same analysis was performed at λ = 2.0 μm by fixing Ib/Ic = 0.90, as shown in Fig. 4b. Also in this case the data are satisfactory reproduced by a linear fit. As reported in Table 2, the value of b is very close to unity for all the analysed currents and at both wavelengths, demonstrating that the detection probability linearly depends on the average number of incident photons. Therefore, we can conclude that the device works in the single photon regime at λ = 1.55 μm as well as at λ = 2.0 μm.Figure 4 Photon count rate as a function of light intensity for the device D1 at T = 1.57 K. The lines represent the fitting curves of the experimental data at (a) 1.55 μm as a function of the bias current, and at (b) 2.0 μm for Ib/Ic = 0.90.

Table 2 Values of the exponent b extracted from the fitting procedure of the count rate as a function of the normalized light intensity for different current bias and wavelengths.

λ (μm)	Ib/Ic	b	
1.55	0.85	1.11 ± 0.02	
1.55	0.90	1.13 ± 0.06	
1.55	0.95	0.93 ± 0.09	
2.0	0.90	0.99 ± 0.01	

Discussion

Before commenting on the results obtained for device D1 under illumination, it is worth to review a representative of the data on SMSPDs available in the literature. Table 3 lists the superconductors used to fabricate these devices and compares their geometrical characteristics, operation temperatures, and efficiency (when not available, the presence/absence of the saturation in the PCR is reported) at a specified wavelength. Different materials were tested, from nitrides to amorphous superconductors, all of them intensively investigated to realize high-performing SNSPDs3,45. However, to date, a saturated single photon response in microstrips at 1.55 μm above 1 K was reported only for NbN18, while WSi20 and MoSi19 required to work below this temperature. Moreover, single photon regime was demonstrated at the same wavelength only for NbN18, and WSi20. Notably, He-irradiated NbN devices, shunted with a proper resistance, demonstrated saturated internal detection efficiency at λ = 2 μm22. As shown in Table 3, a meander geometry is commonly used to guarantee a large effective detection area, but at the price of increasing the values of LK. Table 3 Overview of the main characteristics of a representative of SMSPDs based on different superconductors.

Material	Geometry	Width (μm)	Thickness (nm)	Operation temperature (K)	Wavelength (μm)	Efficiency/count rate	Single-photon regime	
NbN18	Constriction-type bridge	2.12	5.8	1.7	1.55	10%	Yes	
NbN21	Meander	1	7	0.84 (2.1)	1.55	92.2% (70%)	Not available	
He irradiated NbN22	Double-spiral	1	7	0.85	1.55 (2.0)	Saturated (saturated)	Not available	
NbTiN44	Meander	1	6	2.2	1.55 (0.85)	Not saturated (saturated)	Not available	
MoSi19	Meander	1–3	3–5	0.3	1.55	Not available (saturated)	Not available	
MoSi46	Meander	1	2	0.8	1.065	Not available (saturated)	Not available	
WSi20	Meander	1–3	2.1–2.8	0.8	1.55	Not available (saturated)	Yes	
WSi46	Meander	1	2.2–5.1	0.8	1.065	Not available (saturated)	Not available	

Here, we demonstrated single photon sensitivity at λ = 1.5 and 2 μm in pairs of short parallel microstrips made of NbRe films at about 1.6 K. We believe that our findings are, on one hand, a consequence of the properties of the electronic system, and, in particular, its higher capability of retaining the photon energy compared to the phonon system, which makes NbRe competitive with amorphous superconductors in the detection at high wavelengths. This occurrence is measured by the parameter γ, as extensively explained in10. On the other hand, the value of the superconducting order parameter in NbRe, which is intermediate between NbN and amorphous superconductors, may, in principle assure an operation temperature easily accessible by cryogen-free technology. Moreover, this work is an important milestone towards the realization of large area detectors with low LK, since the device design can be extended from a single pair to a series of parallel microstrips, or to even more complex geometries.

Finally, our efforts are now towards a saturated photo response regime and the extension of the detection wavelength. Both these targets can be in principle achieved by reducing the film thickness and the operation temperature.

Conclusions

In conclusion, this work demonstrates the suitability of NbRe for the realization of SMSPDs working beyond 1.55 μm at a relatively high temperature. Single-photon regime operation was clearly demonstrated up to 2 μm on a pair of parallel strips, a geometry never explored before. This innovative layout can be considered the building block of more complex designs which may result in large detection area and low kinetic inductance. Future experiments aim at optimizing the detectors for specific applications and to extend the detection capability even further into longer wavelengths.

Methods

Device patterning

The SMSPDs were optically patterned by direct writing using a smart print (Microlight3D) starting from the as-deposited NbRe films. The AZ1505 positive resist has been spanned at 4000 rpm for 60 s on the films, to obtain a resist layer with a nominal thickness of 600 nm. This guarantees the realization of strips of reduced widths with a high degree of resolution and reproducibility. Subsequently, the samples have been illuminated by blue (430 nm) light for an exposure time of 0.3 s and then developed for 30 s in AZ351B, which has been diluted in distilled water according to a 1:4 ratio. Great care has been paid to the films exposure due to the reduced working area of the microprinter. In fact, the system can exposure areas of 1920 × 1080 pixels, where one pixel corresponds to 704 nm. Therefore, the realization of large patterns requires the consecutive exposure of the different areas in which the main geometry can be divided. During this process, the movement of the projector from one point of the surface to the other is automatically implemented by a micromanipulator, allowing a shift along the horizontal direction, x, and the vertical direction, y, by following a path that includes all the dowels. In order to overcome any problems in the connection between the different parts of the drawing, the stitching technique (i.e., the partial overlapping of the adjacent pieces) is used. In the case of series of pairs of parallel microstrips the stitching used introduces a proximity effect with regions which are more exposed with respect to others.

Finally, a purely physical process based on Ar ion etching has been used to remove the NbRe film not exposed. The process is realized at an Ar ion pressure of 5.1 × 10−4 kPa, at a power of 4.5 W, and with a cathode current of about 2.2 A. With these parameters the etching rate is of 1 nm/min. The poor selectivity of the process is overcome by the large thickness of the resist layer, which is much thicker than the one of the material to be removed. By using this technique, strips with well-defined profiles can be obtained.

Acknowledgements

The authors wish to thank M. Casalino for the availability of the laser source at 2.0 μm. This research was supported by the QUANCOM Project 225521 (MUR PON Ricerca e Innovazione No. 2014–2020 ARS01_00734) and by the "Quantum Italy Deployment (QUID)" Project n°101091408 (Digital Europe Programme).

Author contributions

C. C. conceived and conducted the experiment, wrote and edited the manuscript; M. E. conceived and conducted the experiment, analysed the results; P. E. conducted the experiment and analysed the results; C. B. conducted the experiment; D. S. conceived and conducted the experiment; A. C. conceived the experiment; C.A. conceived the experiment, G.P. Pepe conceived the experiment; L. Parlato conceived and conducted the experiment, analysed the results, wrote and edited the manuscript. All authors reviewed the manuscript.

Funding

This work was supported by Ministero Università e Ricerca (MUR), Grant number 2014–2020 ARS01_00734, Carla Cirillo, Mikkel Ejrnaes, Giovanni Piero Pepe.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
==== Refs
References

1. Goltsman GN 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. 2001 79 705 10.1063/1.1388868
Goltsman, G. N. et al. Picosecond superconducting single-photon optical detector. Appl. Phys. Lett. 79, 705 (2001).10.1063/1.1388868
2. Chang J Los JWN Tenorio-Pearl JO Noordzij N Gourgues R Guardiani A Zichi JR Pereira SF Urbach HP Zwiller V Dorenbos SN Esmaeil ZI Detecting telecom single photons with 99.5−2.07+0.5% system detection efficiency and high time resolution APL Photonics 2021 6 036114 10.1063/5.0039772
Chang, J. et al. Detecting telecom single photons with 99.5−2.07+0.5% system detection efficiency and high time resolution. APL Photonics 6, 036114 (2021).10.1063/5.0039772
3. Esmaeil Zadeh I Chang J Los JWN Gyger S Elshaari AW Steinhauer S Dorenbos SN Zwiller V Superconducting nanowire single-photon detectors: A perspective on evolution, state-of-the-art, future developments, and applications Appl. Phys. Lett. 2021 118 190502 10.1063/5.0045990
Esmaeil Zadeh, I. et al. Superconducting nanowire single-photon detectors: A perspective on evolution, state-of-the-art, future developments, and applications. Appl. Phys. Lett. 118, 190502 (2021).10.1063/5.0045990
4. Hadfield RH Leach J Fleming F Paul DJ Tan CH Shien Ng J Henderson RK Buller GS Single-photon detection for long-range imaging and sensing Optica 2023 10 1124 10.1364/OPTICA.488853
Hadfield, R. H. et al. Single-photon detection for long-range imaging and sensing. Optica 10, 1124 (2023).10.1364/OPTICA.488853
5. Chang J Gao J Esmaeil Zadeh I Elshaari AW Zwiller V Nanowire-based integrated photonics for quantum information and quantum sensing Nanophotonics 2023 12 339 10.1515/nanoph-2022-0652
Chang, J., Gao, J., Esmaeil Zadeh, I., Elshaari, A. W. & Zwiller, V. Nanowire-based integrated photonics for quantum information and quantum sensing. Nanophotonics 12, 339 (2023).10.1515/nanoph-2022-0652
6. Li M Wu Y Yuan J Zhao L Tang D Dong J Xia H Dou X Stratospheric aerosol lidar with a 300 µm diameter superconducting nanowire single-photon detector at 1064 nm Opt. Express 2023 31 2768 10.1364/OE.475124 36785283
Li, M. et al. Stratospheric aerosol lidar with a 300 µm diameter superconducting nanowire single-photon detector at 1064 nm. Opt. Express 31, 2768 (2023).36785283 10.1364/OE.475124
7. Chiles J Charaev I Lasenby R Baryakhtar M Huang J Roshko A Burton G Colangelo M Van Tilburg K Arvanitaki A Nam SW Berggren KK New constraints on dark photon dark matter with superconducting nanowire detectors in an optical haloscope Phys. Rev. Lett. 2022 128 231802 10.1103/PhysRevLett.128.231802 35749181
Chiles, J. et al. New constraints on dark photon dark matter with superconducting nanowire detectors in an optical haloscope. Phys. Rev. Lett. 128, 231802 (2022).35749181 10.1103/PhysRevLett.128.231802
8. Steinhauer S Gyger S Zwiller V Progress on large-scale superconducting nanowire single-photon detectors Appl. Phys. Lett. 2021 118 100501 10.1063/5.0044057
Steinhauer, S., Gyger, S. & Zwiller, V. Progress on large-scale superconducting nanowire single-photon detectors. Appl. Phys. Lett. 118, 100501 (2021).10.1063/5.0044057
9. Salvoni D Parlato L Ejrnaes M Mattioli F Gaggero A Martini F Boselli A Sannino A Amoruso S Cristiano R Pepe GP Large area SNSPD for lidar measurements in the infrared IEEE Trans. Appl. Supercond. 2022 32 2200304 10.1109/TASC.2022.3146099
Salvoni, D. et al. Large area SNSPD for lidar measurements in the infrared. IEEE Trans. Appl. Supercond. 32, 2200304 (2022).10.1109/TASC.2022.3146099
10. Vodolazov DYu Single-photon detection by a dirty current-carrying superconducting strip based on the kinetic-equation approach Phys. Rev. Appl. 2017 7 034014 10.1103/PhysRevApplied.7.034014
Vodolazov, DYu. Single-photon detection by a dirty current-carrying superconducting strip based on the kinetic-equation approach. Phys. Rev. Appl. 7, 034014 (2017).10.1103/PhysRevApplied.7.034014
11. Engel A Renema JJ Ilin K Semenov A Detection mechanism of superconducting nanowire single-photon detectors Supercond. Sci. Technol. 2015 28 114003 10.1088/0953-2048/28/11/114003
Engel, A., Renema, J. J., Ilin, K. & Semenov, A. Detection mechanism of superconducting nanowire single-photon detectors. Supercond. Sci. Technol. 28, 114003 (2015).10.1088/0953-2048/28/11/114003
12 Semenov AD Goltsman GN Korneev AA Quantum detection by current carrying superconducting film Phys. C 2001 351 349 10.1016/S0921-4534(00)01637-3
Semenov, A. D., Goltsman, G. N. & Korneev, A. A. Quantum detection by current carrying superconducting film. Phys. C 351, 349 (2001).10.1016/S0921-4534(00)01637-3
13. Semenov A Engel A Hübers HW Spectral cut-off in the efficiency of the resistive state formation caused by absorption of a single-photon in current-carrying superconducting nano-strips Eur. Phys. J. B 2005 47 495 10.1140/epjb/e2005-00351-8
Semenov, A. et al. Spectral cut-off in the efficiency of the resistive state formation caused by absorption of a single-photon in current-carrying superconducting nano-strips. Eur. Phys. J. B 47, 495 (2005).10.1140/epjb/e2005-00351-8
14. Casaburi A Heath RM Ejrnaes M Nappi C Cristiano R Hadfield RH Experimental evidence of photoinduced vortex crossing in current carrying superconducting strips Phys. Rev. B 2015 92 214512 10.1103/PhysRevB.92.214512
Casaburi, A. et al. Experimental evidence of photoinduced vortex crossing in current carrying superconducting strips. Phys. Rev. B 92, 214512 (2015).10.1103/PhysRevB.92.214512
15. Jahani S Yang L-P BuganzaTepole A Bardin JC Tang HX Jacob Z Probabilistic vortex crossing criterion for superconducting nanowire single-photon detectors J. Appl. Phys. 2020 127 143101 10.1063/1.5132961
Jahani, S. et al. Probabilistic vortex crossing criterion for superconducting nanowire single-photon detectors. J. Appl. Phys. 127, 143101 (2020).10.1063/1.5132961
16. Renema JJ Gaudio R Wang Q Zhou Z Gaggero A Mattioli F Leoni R Sahin D de Dood MJA Fiore A van Exter MP Experimental test of theories of the detection mechanism in a nanowire superconducting single photon detector Phys. Rev. Lett. 2014 112 117604 10.1103/PhysRevLett.112.117604 24702419
Renema, J. J. et al. Experimental test of theories of the detection mechanism in a nanowire superconducting single photon detector. Phys. Rev. Lett. 112, 117604 (2014).24702419 10.1103/PhysRevLett.112.117604
17. Bartolf A Engel A Schilling A Ilin K Siegel M Hübers H-W Semenov A Current-assisted thermally activated flux liberation in ultrathin nanopatterned NbN superconducting meander structures Phys. Rev. B 2010 81 024502 10.1103/PhysRevB.81.024502
Bartolf, A. et al. Current-assisted thermally activated flux liberation in ultrathin nanopatterned NbN superconducting meander structures. Phys. Rev. B 81, 024502 (2010).10.1103/PhysRevB.81.024502
18. Korneeva YuP Vodolazov DYu Semenov AV Florya IN Simonov N Baeva E Korneev AA Goltsman GN Klapwijk TM Optical single-photon detection in micrometer-scale NbN bridges Phys. Rev. Appl. 2018 9 064037 10.1103/PhysRevApplied.9.064037
Korneeva, Yu. P. et al. Optical single-photon detection in micrometer-scale NbN bridges. Phys. Rev. Appl. 9, 064037 (2018).10.1103/PhysRevApplied.9.064037
19. Charaev I Morimoto Y Dane A Agarwal A Colangelo M Berggren KK Large-area microwire MoSi single-photon detectors at 1550 nm wavelength Appl. Phys. Lett. 2020 116 242603 10.1063/5.0005439
Charaev, I. et al. Large-area microwire MoSi single-photon detectors at 1550 nm wavelength. Appl. Phys. Lett. 116, 242603 (2020).10.1063/5.0005439
20. Chiles J Mirin RP Buckley SM Lita A Verma VB Allmaras J Nam SW Superconducting microwire detectors based on WSi with single-photon sensitivity in the near-infrared Appl. Phys. Lett. 2020 116 242602 10.1063/5.0006221
Chiles, J. et al. Superconducting microwire detectors based on WSi with single-photon sensitivity in the near-infrared. Appl. Phys. Lett. 116, 242602 (2020).10.1063/5.0006221
21. 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 Wang Z Xie X-M Superconducting microstrip single-photon detector with system detection efficiency over 90% at 1550 nm Photonics Res. 2021 9 958 10.1364/PRJ.419514
Xu, G.-Z. et al. Superconducting microstrip single-photon detector with system detection efficiency over 90% at 1550 nm. Photonics Res. 9, 958 (2021).10.1364/PRJ.419514
22. Wang Y-Z Zhang W-J Xu G-Z Xiong J-M Fan D-H Chen Z-G Zhang X-Y Wang Z You L-X Characterization of a superconducting microstrip single-photon detector shunted with an external resistor Supercond. Sci. Technol. 2023 36 065004 10.1088/1361-6668/acce74
Wang, Y.-Z. et al. Characterization of a superconducting microstrip single-photon detector shunted with an external resistor. Supercond. Sci. Technol. 36, 065004 (2023).10.1088/1361-6668/acce74
23 Ejrnaes M Parlato L Arpaia R Bauch T Lombardi F Cristiano R Tafuri F Pepe GP Observation of dark pulses in 10 nm thick YBCO nanostrips presenting hysteretic current voltage characteristics Supercond. Sci. Technol. 2017 30 12LT02 10.1088/1361-6668/aa94b9
Ejrnaes, M. et al. Observation of dark pulses in 10 nm thick YBCO nanostrips presenting hysteretic current voltage characteristics. Supercond. Sci. Technol. 30, 12LT02 (2017).10.1088/1361-6668/aa94b9
24. Charaev I Bandurin DA Bollinger AT Phinney IY Drozdov I Colangelo M Butters BA Taniguchi T Watanabe K He X Medeiros O Bozovic I Jarillo-Herrero P Berggren KK Single-photon detection using high-temperature superconductors Nat. Nanotechnol. 2023 18 343 10.1038/s41565-023-01325-2 36941357
Charaev, I. et al. Single-photon detection using high-temperature superconductors. Nat. Nanotechnol. 18, 343 (2023).36941357 10.1038/s41565-023-01325-2
25. 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. 2023 122 192604 10.1063/5.0150805
Kumar, A. et al. Ultrafast low-jitter optical response in high-temperature superconducting microwires. Appl. Phys. Lett. 122, 192604 (2023).10.1063/5.0150805
26. Charaev I Batson EK Cherednichenko S Reidy K Drakinskiy V Yu Y Lara-Avila S Thomsen JD Colangelo M Incalza F Ilin K Schilling A Berggren KK Single-photon detection using large-scale high-temperature MgB2 sensors at 20 K Nat. Commun. 2024 10.48550/arXiv.2308.15228 38729944
Charaev, I. et al. Single-photon detection using large-scale high-temperature MgB2 sensors at 20 K. Nat. Commun.10.48550/arXiv.2308.15228 (2024).38729944 10.48550/arXiv.2308.15228
27. Dello Russo S Elefante A Dequal D Pallotti DK Santamaria Amato L Sgobba F Siciliani de Cumis M Advances in mid-infrared single-photon detection Photonics 2022 MDPI 470
Dello Russo, S. et al. Advances in mid-infrared single-photon detection. In Photonics 470 (MDPI, 2022).
28. Taylor G Walter A Korzh B Bumble B Patel S Allmaras J Beyer A O’Brient R Shaw M Wollman E Low-noise single-photon counting superconducting nanowire detectors at infrared wavelengths up to 29 µm Optica 2023 10 1672 10.1364/OPTICA.509337
Taylor, G. et al. Low-noise single-photon counting superconducting nanowire detectors at infrared wavelengths up to 29 µm. Optica 10, 1672 (2023).10.1364/OPTICA.509337
29. Hao H Zhao QY Huang YH Deng J Yang F Ru S-Y Liu Z Wan C Liu H Li Z-J Wang H-B Tu X-C Chen J Kang L Wu P-H A compact multi-pixel superconducting nanowire single-photon detector array supporting gigabit space-to-ground communications Light Sci. Appl. 2024 13 25 10.1038/s41377-023-01374-1 38253520
Hao, H. et al. A compact multi-pixel superconducting nanowire single-photon detector array supporting gigabit space-to-ground communications. Light Sci. Appl. 13, 25 (2024).38253520 10.1038/s41377-023-01374-1
30. Chen Q Ge R Zhang L Li F Zhang B Jin F Han H Dai Y He G Fei Y Wang X Wang H Jia X Zhao Q Tu X Kang L Chen J Wu P Mid-infrared single photon detector with superconductor Mo0.8Si0.2 nanowire Sci. Bull. 2021 66 965 10.1016/j.scib.2021.02.024
Chen, Q. et al. Mid-infrared single photon detector with superconductor Mo0.8Si0.2 nanowire. Sci. Bull. 66, 965 (2021).10.1016/j.scib.2021.02.024
31. Verma VB Korzh B Walter AB Lita AE Briggs RM Colangelo M Zhai Y Wollman EE Beyer AD Allmaras JP Vora H Zhu D Schmidt E Kozorezov AG Berggren KK Mirin RP Nam SW Shaw MD Single-photon detection in the mid-infrared up to 10 μm wavelength using WSi superconducting nanowire detectors APL Photonics 2021 6 056101 10.1063/5.0048049
Verma, V. B. et al. Single-photon detection in the mid-infrared up to 10 μm wavelength using WSi superconducting nanowire detectors. APL Photonics 6, 056101 (2021).10.1063/5.0048049
32. Colangelo A Walter AB Korzh BA Schmidt E Bumble B Lita AE Beyer AD Allmaras JP Briggs RM Kozorezov AG Wollman EE Shaw MD Berggren KK Large-area superconducting nanowire single-photon detectors for operation at wavelengths up to 7.4 μm Nano Lett. 2022 22 5667 10.1021/acs.nanolett.1c05012 35848767
Colangelo, A. et al. Large-area superconducting nanowire single-photon detectors for operation at wavelengths up to 7.4 μm. Nano Lett. 22, 5667 (2022).35848767 10.1021/acs.nanolett.1c05012
33. Chang J Los J Gourgues R Steinhauer S Dorenbos S Pereira S Urbach H Zwiller V EsmaeilZadeh I Efficient mid-infrared single-photon detection using superconducting NbTiN nanowires with high time resolution in a Gifford–McMahon cryocooler Photonics Res. 2022 10 1063 10.1364/PRJ.437834
Chang, J. et al. Efficient mid-infrared single-photon detection using superconducting NbTiN nanowires with high time resolution in a Gifford–McMahon cryocooler. Photonics Res. 10, 1063 (2022).10.1364/PRJ.437834
34. Pan Y Zhou H Zhang L Li H Tang Y Yu H Si M You L Wang Z Superconducting nanowire single-photon detector made of ultrathin γ-Nb4N3 film for mid-infrared wavelengths Supercond. Sci. Technol. 2021 34 074001 10.1088/1361-6668/abf851
Pan, Y. et al. Superconducting nanowire single-photon detector made of ultrathin γ-Nb4N3 film for mid-infrared wavelengths. Supercond. Sci. Technol. 34, 074001 (2021).10.1088/1361-6668/abf851
35. Cirillo C Chang J Caputo M Los JWN Dorenbos S EsmaeilZadeh I Attanasio C Superconducting nanowire single photon detectors based on disordered NbRe films Appl. Phys. Lett. 2020 117 172602 10.1063/5.0021487
Cirillo, C. et al. Superconducting nanowire single photon detectors based on disordered NbRe films. Appl. Phys. Lett. 117, 172602 (2020).10.1063/5.0021487
36. Ejrnaes M Cirillo C Salvoni D Chianese F Bruscino C Ercolano P Cassinese A Attanasio C Pepe GP Parlato L Single photon detection in NbRe superconducting microstrips Appl. Phys. Lett. 2022 121 262601 10.1063/5.0131336
Ejrnaes, M. et al. Single photon detection in NbRe superconducting microstrips. Appl. Phys. Lett. 121, 262601 (2022).10.1063/5.0131336
37. Ercolano P Cirillo C Ejrnaes M Chianese F Salvoni D Bruscino C Satariano R Cassinese A Attanasio C Pepe GP Parlato L Investigation of dark count rate in NbRe microstrips for single photon detection Supercond. Sci. Technol. 2023 36 105011 10.1088/1361-6668/acf24a
Ercolano, P. et al. Investigation of dark count rate in NbRe microstrips for single photon detection. Supercond. Sci. Technol. 36, 105011 (2023).10.1088/1361-6668/acf24a
38. 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. 2009 22 055006 10.1088/0953-2048/22/5/055006
Ejrnaes, M. et al. Characterization of parallel superconducting nanowire single photon detectors. Supercond. Sci. Technol. 22, 055006 (2009).10.1088/0953-2048/22/5/055006
39. Cirillo C Caputo M Divitini G Robinson JWA Attanasio C Polycrystalline NbRe superconducting films deposited by direct current magnetron sputtering Thin Solid Films 2022 758 139450 10.1016/j.tsf.2022.139450
Cirillo, C., Caputo, M., Divitini, G., Robinson, J. W. A. & Attanasio, C. Polycrystalline NbRe superconducting films deposited by direct current magnetron sputtering. Thin Solid Films 758, 139450 (2022).10.1016/j.tsf.2022.139450
40. Cirillo C Carapella G Salvato M Arpaia R Caputo M Attanasio C Superconducting properties of noncentrosymmetric Nb0.18Re0.82 thin films probed by transport and tunneling experiments Phys. Rev. B 2016 94 104512 10.1103/PhysRevB.94.104512
Cirillo, C. et al. Superconducting properties of noncentrosymmetric Nb0.18Re0.82 thin films probed by transport and tunneling experiments. Phys. Rev. B 94, 104512 (2016).10.1103/PhysRevB.94.104512
41. Bardeen J Critical fields and currents in superconductors Rev. Mod. Phys. 1962 34 667 10.1103/RevModPhys.34.667
Bardeen, J. Critical fields and currents in superconductors. Rev. Mod. Phys. 34, 667 (1962).10.1103/RevModPhys.34.667
42. Karki AB Xiong YM Haldolaarachchige N Stadler S Vekhter I Adams PW Young DP Phelan WA Chan JY Physical properties of the noncentrosymmetric superconductor Nb0.18Re0.82 Phys. Rev. B 2011 83 144525 10.1103/PhysRevB.83.144525
Karki, A. B. et al. Physical properties of the noncentrosymmetric superconductor Nb0.18Re0.82. Phys. Rev. B 83, 144525 (2011).10.1103/PhysRevB.83.144525
43. Kerman AJ Dauler EA Keicher WE Yang JKW Berggren KK Goltsman G Voronov B Kinetic-inductance-limted reset time of superconducting nanowire photon counters Appl. Phys. Lett. 2006 88 111116 10.1063/1.2183810
Kerman, A. J. et al. Kinetic-inductance-limted reset time of superconducting nanowire photon counters. Appl. Phys. Lett. 88, 111116 (2006).10.1063/1.2183810
44. Yabuno M China F Miki S Terai H Large-area niobium titanium nitride superconducting microstrip single-photon detector fabricated using a photolithography process IEEE Trans. Appl. Supercond. 2023 53 2200104
Yabuno, M., China, F., Miki, S. & Terai, H. Large-area niobium titanium nitride superconducting microstrip single-photon detector fabricated using a photolithography process. IEEE Trans. Appl. Supercond. 53, 2200104 (2023).
45. Holzman I Yachin Y Superconducting nanowires for single-photon detection: Progress, challenges, and opportunities Adv. Quantum Technol. 2019 2 1800058 10.1002/qute.201800058
Holzman, I. & Yachin, Y. Superconducting nanowires for single-photon detection: Progress, challenges, and opportunities. Adv. Quantum Technol. 2, 1800058 (2019).10.1002/qute.201800058
46. Luskin JS Allmaras JP Schmidt E Walter AB Korzh B Beyer AD Wollman EE Bumble B Narvaez L Nam SW Charaev I Colangelo M Berggren KK Verma VB Pena C Spiropulu M Garcia-Sciveres M Derenzo S Shaw MD Large active-area superconducting microwire detector array with single-photon sensitivity in the near-infrared Appl. Phys. Lett. 2023 122 243506 10.1063/5.0150282
Luskin, J. S. et al. Large active-area superconducting microwire detector array with single-photon sensitivity in the near-infrared. Appl. Phys. Lett. 122, 243506 (2023).10.1063/5.0150282
