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arXiv:2511.02466 · Journal of the Physical Society of Japan

Theoretical Analysis of Photon Detection Mechanism in Superconducting Single-Photon Detectors

Yusuke Masaki, Hiroaki Matsueda

Published Aug 31, 2026• 0 citations

Abstract

To elucidate the photon detection mechanism of superconducting single-photon detectors, we theoretically examine the dynamics of type-II superconductors with a bias current using the two-dimensional time-dependent Ginzburg–Landau and the Maxwell equations. The photon injection that weakens the superconducting order parameter is treated phenomenologically as a local temperature increase, and the injected energy is controlled by the initial hotspot radius. The photon is detected by the voltage change between two electrodes attached to the left and right edges of the superconductor. We find that the detection dynamics in certain parameter ranges can be explained by the conventional hotspot model, whereas those in other parameter ranges are governed by the formation and subsequent dynamics of superconducting vortex and antivortex pairs. The photon detection is possible for an initial hotspot radius that exceeds a threshold value. We find that the generation of a vortex–antivortex pair occurs near the threshold. The flow of the pair perpendicular to the current direction finally creates a normal region for the photon detection. The voltage change for the Ginzburg–Landau parameter close to the transition point from type-II to type-I superconductor shows anomalous behavior that is not associated with the dynamics of the vortex–antivortex pair. We also examine the effects of spatially non-uniform current density on the voltage change and the superconducting order parameter to provide a hint to understand the behavior of wide-strip single-photon detectors. The estimated values of incident photon energy and response time for photon detection are reasonable in comparison with experiments. The present analysis provides useful guidelines for flexible design of device structures.

DOI: 10.7566/jpsj.95.094703

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A theoretical model with experimental verification is presented to enhance the quantum efficiency of a superconducting single-photon detector without increasing the length or thickness of the active element. The basic enhancement framework is based on: (1) Utilizing the plasmonic nature of a superconducting layer to increase the surface absorption of the input optical signal. (2) Enhancing the critical current of the nanowires by reducing the current crowding at the bend areas through optimally rounded-bend implementation. The experimental system quantum efficiency and fluctuation rates per second are assessed and compared to the proposed theoretical model. The model originated from an accurate description of the different liberation mechanisms of the nano-patterned superconducting films (vortex hopping and vortex-antivortex pairing). It is built complimentary to the existing, well-established models by considering the effects of quantum confinement on the singularities' energy states. The proposed model explains the dynamics of singularities for a wide range of temperatures and widths and describe an accurate count rate behavior for the structure. Furthermore, it explains the abnormal behaviors of the measured fluctuation rates occurring in wide nano-patterned superconducting structures below the critical temperature. In accordance to this model, it has been shown that for a typical strip width, not only is the vortex-antivortex liberation higher than the predicted rate, but also quantum tunneling is significant in certain conditions, and cannot be neglected as it has been in previous models. Also it is concluded that to satisfy both optical guiding and photon detection considerations of the design, the width and the thickness of the superconducting wires should be carefully determined in order to maintain the device sensitivity while crossing over from the current crowding to vortex-based detection mechanisms.

The microscopic mechanism of photon detection in superconducting nanowire single-photon detectors is still under debate. We present a simple but powerful theoretical model that allows us to identify essential differences between competing detection mechanisms. The model is based on quasi-particle multiplication and diffusion after the absorption of a photon. We then use the calculated spatial and temporal evolution of this quasi-particle cloud to determine detection criteria of three distinct detection mechanisms, based on the formation of a normal conducting spot, the reduction of the effective depairing critical current below the bias current, and a vortex-crossing scenario, respectively. All our calculations as well as a comparison to experimental data strongly support the vortex-crossing detection mechanism by which vortices and antivortices enter the superconducting strip from the edges and subsequently traverse it thereby triggering the detectable normal conducting domain. These results may therefore help to reveal the microscopic mechanism responsible for the detection of photons in superconducting nanowires.

We have studied electrical noise of photon detectors representing long and narrow superconducting strips. For large bias currents close to the critical current fluctuations lead to localized, temporary transitions into the normal conducting state, which can be detected as voltage transients developing between the strip ends. We present models based on fluctuations of the chemical potential and current-assisted thermal-unbinding of vortex-antivortex pairs, which explain the current and temperature-dependence of the detector noise.

We experimentally study timing jitter of single-photon detection by NbN superconducting strips with width

w

ranging from 190 nm to $3\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{m}$. We find that timing jitter of both narrow (190 nm) and micron-wide strips is about 40 ps at currents where internal detection efficiency $\ensuremath{\eta}$ saturates and it is close to our instrumental jitter. We also calculate intrinsic timing jitter in wide strips using the modified time-dependent Ginzburg-Landau equation coupled with a two-temperature model. We find that with increasing width the intrinsic timing jitter increases and the effect is most considerable at currents where a rapid growth of $\ensuremath{\eta}$ changes to saturation. We relate it with complicated vortex and antivortex dynamics, which depends on a photon's absorption site across the strip and its width. The model also predicts that at current close to depairing current the intrinsic timing jitter of a wide strip could be about $\ensuremath{\hbar}/{k}_{B}{T}_{c}$ (

{T}_{c}

is a critical temperature of superconductor), i.e., the same as for a narrow strip.

We argue that photon counts in a superconducting nanowire single-photon detector (SNSPD) are caused by the transition from a current-biased metastable superconducting state to the normal state. Such a transition is triggered by vortices crossing the thin and narrow superconducting strip from one edge to another due to the Lorentz force. Detector counts in SNSPDs may be caused by three processes: (a) a single incident photon with sufficient energy to break enough Cooper pairs to create a normal-state belt across the entire width of the strip (direct photon count), (b) thermally induced single-vortex crossing in the absence of photons (dark count), which at high-bias currents releases the energy sufficient to trigger the transition to the normal state in a belt across the whole width of the strip, and (c) a single incident photon of insufficient energy to create a normal-state belt but initiating a subsequent single-vortex crossing, which provides the rest of the energy needed to create the normal-state belt (vortex-assisted single-photon count). We derive the current dependence of the rate of vortex-assisted photon counts. The resulting photon count rate has a plateau at high currents close to the critical current and drops as a power law with high exponent at lower currents. While the magnetic field perpendicular to the film plane does not affect the formation of hot spots by photons, it causes the rate of vortex crossings (with or without photons) to increase. We show that by applying a magnetic field one may characterize the energy barrier for vortex crossings and identify the origin of dark counts and vortex-assisted photon counts.