  We argue that photon counts in a superconducting nanowire single-photon
detector (SNSPD) are caused by the transition from a current-biased metastable
superconducting state to the normal state. Such a transition is triggered by
vortices crossing the thin film superconducting strip from one edge to another
due to the Lorentz force. Detector counts in SNSPDs may be caused by three
processes: (a) a single incident photon with energy sufficient to break enough
Cooper pairs to create a normal-state belt across the entire width of the strip
(direct photon count), (b) thermally induced single-vortex crossing in the
absence of photons (dark count), which at high bias currents releases the
energy sufficient to trigger the transition to the normal state in a belt
across the whole width of the strip, and (c) a single incident photon with
insufficient energy to create a normal-state belt but initiating a subsequent
single-vortex crossing, which provides the rest of the energy needed to create
the normal-state belt (vortex-assisted single photon count). We derive the
current dependence of the rate of vortex-assisted photon counts. The resulting
photon count rate has a plateau at high currents close to the critical current
and drops as a power-law with high exponent at lower currents. While the
magnetic field perpendicular to the film plane does not affect the formation of
hot spots by photons, it causes the rate of vortex crossings (with or without
photons) to increase. We show that by applying a magnetic field one may
characterize the energy barrier for vortex crossings and identify the origin of
dark counts and vortex-assisted photon counts.
