Single-Photon Detection by a Dirty Current-Carrying Superconducting Strip Based on the Kinetic-Equation Approach

Using a kinetic-equation approach, we study the dynamics of electrons and phonons in current-carrying superconducting nanostrips after the absorption of a single photon of the near-infrared or optical range. We find that the larger the C-e/C-ph|(Tc) ratio (where T-c is the critical temperature of a superconductor and C-e and C-ph are specific heat capacities of electrons and phonons, respectively), the larger the portion of the photon's energy goes to electrons. The electrons become more strongly heated and hence can thermalize faster during the initial stage of hot-spot formation. The thermalization time tau(th) can be less than 1 ps for superconductors with C-e/C-ph|(Tc) >> 1 and a small diffusion coefficient of D similar or equal to 0.5 cm(2)/s when thermalization occurs, mainly due to electron-phonon and phonon-electron scattering in a relatively small volume of approximately xi(2)d (xi is a superconducting coherence length, while d < xi is a thickness of the strip). For longer time spans, due to diffusion of hot electrons' effective temperature inside the hot spot decreases, the size of the hot spot increases, the superconducting state becomes unstable, and the normal domain spreads in the strip at a current larger than the so-called detection current. We find the dependence of the detection current on the photon's energy, the location of its absorption in the strip, the width of the strip, and the magnetic field, and we compare this dependence with existing experiments. Our results demonstrate that materials with C-e/C-ph|(Tc) << 1 are bad candidates for single-photon detectors due to a small transfer of the photon's energy to electronic system and a large tth. We also predict that even a several-micron-wide dirty superconducting bridge is able to detect a single near-infrared or optical photon if its critical current exceeds 70% of the depairing current and Ce/C-ph|(Tc) greater than or similar to 1.