Vortex Counting and Velocimetry for Slitted Superconducting Thin Strips

Abstract

The maximal speed ${v}^{\ensuremath{\ast}}$ for magnetic flux quanta is determined by the energy relaxation of unpaired electrons and is thus essential for superconducting microstrip single-photon detectors (SMSPDs). However, the deduction of ${v}^{\ensuremath{\ast}}$ from the current-voltage ($I$-$V$) curves at zero magnetic field is hindered by the unknown number of vortices, ${n}_{v}$, as a small number of fast-moving vortices can induce the same voltage as a large number of slow-moving ones. Here, we introduce an approach for the quantitative determination of ${n}_{v}$ and ${v}^{\ensuremath{\ast}}$. The idea is based on the Aslamazov and Larkin prediction of kinks in the $I$-$V$ curves of wide and short superconducting constrictions when the number of fluxons crossing the constriction is increased by one. We realize such conditions in wide $\mathrm{Mo}\mathrm{Si}$ thin strips with slits milled by a focused ion beam and reveal quantum effects in a macroscopic system. By observing kinks in the $I$-$V$ curves with increase of the transport current, we evidence a crossover from a single- to multifluxon dynamics and deduce ${v}^{\ensuremath{\ast}}\ensuremath{\simeq}12$ km/s. Our experimental observations are augmented with numerical modeling results, which reveal a transition from a vortex chain over a vortex jet to a vortex river with increase of ${n}_{v}$ and $v$. Our findings are essential for the development of one-dimensional and two-dimensional few-fluxon devices and provide a demanded approach for the deduction of maximal vortex velocities at the SMSPD operation conditions.