Theoretical analysis of photon detection mechanism in superconducting single-photon detectors

TL;DR

This paper addresses how photons are detected in superconducting single-photon detectors by solving the two-dimensional time-dependent Ginzburg–Landau equations coupled to Maxwell equations, with photon absorption modeled as a local temperature rise inside a circular hotspot of radius $R_{\mathrm{init}}$. It shows that detection can proceed via two mechanisms: a hotspot-like expansion when $R_{\mathrm{init}}$ is large, and vortex–antivortex pair generation near a threshold radius, whose dynamics—and the resulting voltage signal—explain oscillations observed in $\Delta V$ as vortices penetrate from the sample edges. Near the transition between type-II and type-I (small $κ$), oscillatory behavior persists due to edge penetrations, indicating alternative dynamical pathways. The work demonstrates threshold behavior, provides quantitative energy estimates for incident photons, and offers design guidelines for wide-strip superconducting detectors, with results qualitatively consistent with experimental scales.

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 amount of injection 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 certain parameter ranges can be explained by the traditionally considered hotspot model, while other parameter ranges are governed by the generation and annihilation 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 comprehensive examination provides useful guidelines for flexible design of device structures.

Figures (12)

• Figure 1: Illustration of our system. The red and blue areas correspond to superconductor and metallic electrodes, respectively. The system size and current-flow direction are indicated, respectively. The superconducting region is given by $0\le x\le L_{x}$ and $0\le y\le L_{y}$. The center of the initial hotspot with radius $R_{\mathrm{init}}$ is set to the center of the superconductor.
• Figure 2: Time evolution of voltage change $\Delta V$. Various lines present the profiles with different values of $R_{\mathrm{init}}/\xi_0$. We take $j_{\mathrm{bias}}/j_{0}=0.28$ and $\kappa=10$.
• Figure 3: Voltage change $\Delta V$ at $t/t_{0}=400$ (open squares) and $t/t_0 = 800$ (filled squares) as a function of the initial hotspot radius $R_{\mathrm{init}}$. We take $j_{\mathrm{bias}}/j_{0}=0.28$ and $\kappa=10$.
• Figure 4: Schematic view of a vortex--antivortex pair generated inside of the hotspot region as well as a penetrating vortex and a penetrating antivortex from outside the superconductor. Cross symbols inside circles indicate the current flow direction.
• Figure 5: Time evolution of spacetime profile of $\left|\tilde{\Delta}\left(x=L_{x}/2,y\right)\right|$ [(a) upper panel] and that of $\Delta V$ [(b) lower panel] for $R_{\mathrm{init}}/\xi_0=3.0$, $j_{\mathrm{bias}}/j_0=0.28$, $\kappa=10$, and $200\le t/t_{0}\le 350$. Panel (b) is a magnified view of Fig. \ref{['SSPDfig2']} for $R_{\mathrm{init}}/\xi_0 = 3.0$. The blight region in panel (a) corresponds to stable superconducting state. The position, $y/\xi_0=10$, corresponds to the hotspot center.