Intrinsic detection efficiency of superconducting single photon detector in the modified hot spot model

We theoretically study the dependence of the intrinsic detection efficiency (IDE) of superconducting single photon detector on the applied current $I$ and magnetic field $H$. We find that the current, at which the resistive state appears in the superconducting film, depends on the position of the hot spot (region with suppressed superconductivity around the place where the photon has been absorbed) with respect to the edges of the film. It provides inevitable smooth dependence IDE(I) when IDE $sim 0.05-1$ even for homogenous straight superconducting film and in the absence of fluctuations. When IDE $lesssim 0.05$ much sharper current dependence comes from the fluctuation assisted vortex entry to the hot spot located near the edge of the film. We find that weak magnetic field strongly affects IDE when the photon detection is connected with fluctuation assisted vortex entry (IDE$ll 1$) and it weakly affects IDE when the photon detection is connected with the current induced vortex entry to the hot spot or nucleation of the vortex-antivortex pair inside the hot spot (IDE$sim 0.05-1$).

Differences in the effects of turns and constrictions on the resistive response in current-biased superconducting wire after single photon absorption

We study how turns and constrictions affect the resistive response of the superconducting wire after instant in time and local in space heating, which models the absorption of the single photon by the wire. We find that the presence of constriction favors detection of photons of various energies but the presence of turn increases only ability to detect relatively low energy photons. The main reason is that in case of constriction the current density is increased over whole length and width of the constriction while in case of the turn the current density is enhanced only near the inner corner of the turn. It results in inhomogeneous Joule heating near the turn and worsens the conditions for appearance of the normal domain at relatively small currents when the high energy photons already could create normal domain in straight part of the wire. We also find that the amplitude of the voltage pulse depends on the place where the photon is absorbed. It is the smallest one when photon is absorbed near the turn and it is the largest one when photon is absorbed near the constriction. This effect comes from the difference in resistance of constriction and the turn in the normal state from the resistance of the rest of the wire.