Vortex-assisted mechanism of photon counting in a superconducting nanowire single-photon detector revealed by external magnetic field

We use an external magnetic field to probe the detection mechanism of a superconducting nanowire single-photon detector. We argue that the hot belt model (which assumes partial suppression of the superconducting order parameter $\mathrm{\Delta }$ across the whole width of the superconducting nanowire after absorption of the photon) does not explain observed weak-field dependence of the photon count rate (PCR) for photons with $\lambda =450\mathrm{nm}$ and noticeable decrease of PCR (with increasing the magnetic field) in a range of the currents for photons with wavelengths $\lambda =450–1200\mathrm{nm}$. Found experimental results for all studied wavelengths can be explained by the vortex hot spot model (which assumes partial suppression of $\mathrm{\Delta }$ in the area with size smaller than the width of the nanowire) if one takes into account nucleation and entrance of the vortices to the photon induced hot spot and their pinning by the hot spot with relatively large size and strongly suppressed $\mathrm{\Delta }$.

Figure 1

Current dependence of the normalized photon count rate $[\mathrm{PCR}/{\mathrm{PCR}}_{\text{sat}}(H=0)=\mathrm{IDE}]$ for different wavelengths found for good quality detector NbN1. For $\lambda =1200$ and 1550 nm we find ${\mathrm{PCR}}_{\text{sat}}\left(H=0\right)$ from extrapolation of the experimental results to larger currents and assuming small variation of the shape of dependence $\mathrm{IDE}\left(I\right)$ with change of $\lambda$.

Figure 2

$\mathrm{IDE}\left(I\right)$ of the NbN1 detector at different magnetic fields. In the inset in panel (d) we present experimental field dependence of the critical current of this detector.

Figure 3

Dark count rate in the NbN1 detector at different magnetic fields.

Figure 4

Dark count rate and experimental critical current (in the inset) of the NbN2 detector at different magnetic fields.

Figure 5

Dependence of the detection current $I_{\text{det}}$ (at which the resistive response appears in the SNSPD after photon absorption) on the position of the hot spot across the nanowire, following from the model with a pinned vortex [9] (solid symbols) and the model with an unpinned vortex (empty symbols). The detection current is normalized in units of depairing current $I_{\text{dep}}$ and the origin of the $x$ coordinate is at the left edge of the strip. $I_{\text{det}}^{\text{min}}$ and $I_{\text{det}}^{\text{max}}$ correspond to the minimal and maximal detection current in two models for HS with $R=5\xi$.

Figure 6

Dependence of the detection current $I_{\text{det}}$ on the coordinate of the hot spot (with two radii) at different magnetic fields. Panel (a) corresponds to the model with an unpinned vortex and panel (b) corresponds to the model with a pinned vortex of [9].

Figure 7

Current dependence of IDE at different magnetic fields (from $H=0$ to $0.03H_{c2}$ with step $\delta H=0.005H_{c2}$) following from the vortex hot spot model with an unpinned vortex. Panel (a) corresponds to the hot spot with radius $R=2.5\xi$ while panel (b) corresponds to the hot spot with $R=5\xi$ (in both cases $\alpha =-1$). In the insets similar dependencies are present for the hot spot model with a pinned vortex of [9].

Figure 8

Current dependence of IDE at different magnetic fields following from the vortex hot spot model with an unpinned vortex and “dead” edge layers in the nanowire, where $T_c$ is locally suppressed.

Figure 9

Numerically calculated magnetic field dependence of the critical current $I_c$ of the straight nanowire with $w=20\xi$ (empty squares) and the meander (solid circles) with geometrical parameters shown on the bottom inset. For the meander we take into account the bend where the external magnetic field decreases the critical current. In the insets we show the contour plot of $\left|\mathrm{\Delta }\right|$ for the meander at different magnetic fields and $I\lesssim I_c\left(H\right)$. At $H\le 0.012H_{c2}$ there are no vortices in the meander. In the narrowest place of the meander vortices appear at $H>0.038H_{c2}$.

Figure 10

Dependence of the current, at which experimental IDE reaches 0.9 (squares) and 0.5 (circles), on the energy of the photon (results are obtained for the NbN1 detector). The theoretical curves (solid and dashed) are found in assumption that current $I_{\mathrm{thr}}$ is equal to the detection current for the hot spot located in the center of the nanowire or at its edge (in the last case it has the form of a semicircle). Fitting coefficient $\eta$ describes what part of the photon's energy goes for suppression of $\mathrm{\Delta }$ inside the hot spot [23]. In the inset we show results for the WSi based detector extracted from Fig. 2 of [24].