We study the dynamics of the order parameter in a superconducting film with transport current after absorption of a single photon. The system from the time-dependent Ginszburg-Landau equation, Poisson's equation for an electrical potential, and the heat-diffusion equation were solved numerically. For each photon energy in the absence of fluctuations there exists a corresponding threshold current below which the superconducting state is stable and no voltage appears between the ends of the film. At larger currents, the superconducting state collapses starting from the appearance of a vortex-antivortex pair in the center of the region with suppressed superconducting order parameter, which has been created by the absorbed photon. Lorentz force causes motion of these vortices that heats the film locally and gives rise to a normal domain. When biased with the fixed current, the film latches in the normal state. In the regime when the current via superconductor may change, which is more relevant for experiments, the normal domain exists only for a short time, resulting in the voltage pulse with the duration controlled by the kinetic inductance of the superconducting film.

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 ∼ 0.05 − 1 even for homogenous straight superconducting film and in the absence of fluctuations. When IDE 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≪ 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∼ 0.05 − 1).

Reduction of the critical current in narrow superconducting NbN lines with sharp and rounded bends with respect to the critical current in straight lines was studied at different temperatures. We compare our experimental results with the reduction expected in the framework of the London model and the Ginsburg-Landau model. We have experimentally found that the reduction is significantly less than either model predicts. We also show that in our NbN lines the bends mostly contribute to the reduction of the critical current at temperatures well below the superconducting transition temperature.

We have found experimentally that the rise times of voltage pulses in NbN superconducting single photon detectors increase nonlinearly with increasing detector length. We fabricated superconducting single photon detectors based on NbN thin films with a meander-like sensitive region of area from 2x2 µm 2 to 11x11 µm 2 . The effect is connected with the dependence of the detector resistance, which appears after photon absorption, on its kinetic inductance and hence on detector length. This conclusion is confirmed by our calculations in the framework of the two-temperature model. _____________________________ a) Author to whom correspondence should be addressed. Electronic mail: morozov@scontel.ru