Vortex-induced dissipation in narrow current-biased thin-film superconducting strips

Abstract

A vortex crossing a thin-film superconducting strip from one edge to the other, perpendicular to the bias current, is the dominant mechanism of dissipation for films of thickness $d$ on the order of the coherence length $\ensuremath{\xi}$ and of width $w$ much narrower than the Pearl length $\ensuremath{\Lambda}\ensuremath{\gg}w\ensuremath{\gg}\ensuremath{\xi}$. At high bias currents ${I}^{*}<I<{I}_{c}$ the heat released by the crossing of a single vortex suffices to create a belt-like normal-state region across the strip, resulting in a detectable voltage pulse. Here ${I}_{c}$ is the critical current at which the energy barrier vanishes for a single vortex crossing. The belt forms along the vortex path and causes a transition of the entire strip into the normal state. We estimate ${I}^{*}$ to be roughly ${I}_{c}/3$. Furthermore, we argue that such ``hot'' vortex crossings are the origin of dark counts in photon detectors, which operate in the regime of metastable superconductivity at currents between ${I}^{*}$ and ${I}_{c}$. We estimate the rate of vortex crossings and compare it with recent experimental data for dark counts. For currents below ${I}^{*}$, that is, in the stable superconducting but resistive regime, we estimate the amplitude and duration of voltage pulses induced by a single vortex crossing.