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

We theoretically study the dependence of the intrinsic detection efficiency (IDE) of a superconducting nanowire 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 (a region with suppressed superconductivity around the place where the photon has been absorbed) with respect to the edges of the film. This circumstance leads to inevitable smooth dependence IDE(I) when IDE similar to 0.05 - 1, even for a homogenous straight superconducting film and in the absence of fluctuations. For IDE less than or similar to 0.05, a much sharper current dependence comes from the fluctuation-assisted vortex entry to the hot spot, which is located near the edge of the film. We find that a weak magnetic field strongly affects IDE when the photon detection is connected with fluctuation-assisted vortex entry to the hot spot (IDE << 1), and it weakly affects IDE when the photon detection is connected with the current-induced vortex nucleation in the film with the hot spot (IDE similar to 0.05 - 1).