Fano fluctuations in superconducting nanowire single-photon detectors

Because of their universal nature, Fano fluctuations are expected to influence the response of superconducting nanowire single-photon detectors (SNSPDs). We predict that photon counting rate (\(PCR\)) as a function of bias current (\(I_B\)) in SNSPDs is described by an integral over a transverse coordinate-dependent complementary error function. The latter describes smearing of local responses due to Fano fluctuations of the amount of energy deposited into electronic system. The finite width, \(\sigma\), of the \(PCR\) vs \(I_B\) arises from fluctuations in the energy partition between quasiparticles and phonons during the energy down-conversion cascade. In narrow-nanowire SNSPDs the local responses are uniform, and the effect of Fano-fluctuations on \(\sigma\) is dominant. In wide-nanowire SNSPDs with strong coordinate dependence of local responses due to vortex-antivortex unbinding and vortex entry from edges, Fano-fluctuations smear singularities imprinted by vorticity on the transition part of \(PCR\) curve. We demonstrate good agreement between theory and experiments for a series of bath temperatures and photon energies in narrow-wire WSi SNSPDs. The time-resolved hotspot relaxation curves predicted by Fano fluctuations match the Lorentzian shapes observed in experiments over the whole range of bias currents investigated except for their tails.