Current dependence of the 'red' boundary of superconducting single photon detectors in the modified hot spot model

Abstract

We find the relation between the energy of the absorbed photon and the threshold current at which the resistive state appears in the current-carrying superconducting film with the probability about unity. In our calculations we use the modified hot spot model, which assumes different strength of suppression of the superconducting order parameter in the finite area of the film around the place where the photon is absorbed. To find the threshold current we solve the Ginzburg-Landau equation for superconducting order parameter, which automatically includes the current continuity equation and it allows us to consider the back effect of current redistribution near the hot spot on the stability of the superconducting state. We find quantitative agreement with the recent experiments, where we use the single fitting parameter which describes what part of the energy of the photon goes for the local destruction of the superconductivity in the film.