Vortex jets generated by edge defects in current-carrying superconductor thin strips

TL;DR

This paper develops a theoretical model for vortex jet formation caused by edge defects in superconducting strips, predicts measurable voltage signatures, and validates findings with experiments and simulations, enhancing understanding of vortex dynamics in superconductors.

Contribution

It introduces a comprehensive analytical framework for vortex jet shapes in narrow and wide superconducting strips, supported by experimental data and time-dependent Ginzburg-Landau simulations.

Findings

Predicted nonmonotonic transverse voltage dependence on current.

Experimental validation with MoSi strips showing vortex jet behavior.

Simulations reveal vortex jets evolve into vortex rivers at high currents.

Abstract

At sufficiently large transport currents $I_\mathrm{tr}$, a defect at the edge of a superconducting strip acts as a gate for the vortices entering into it. These vortices form a jet, which is narrow near the defect and expands due to the repulsion of vortices as they move to the opposite edge of the strip, giving rise to a transverse voltage $V_\perp$. Here, relying upon the equation of vortex motion under competing vortex-vortex and $I_\mathrm{tr}$-vortex interactions, we derive the vortex jet shapes in narrow ($\xi\ll w\lesssim\lambda_\mathrm{eff}$) and wide ($w\gg\lambda_\mathrm{eff}$) strips [$\xi$: coherence length, $w$: strip width, $\lambda_\mathrm{eff}$: effective penetration depth]. We predict a nonmonotonic dependence $V_\perp(I_\mathrm{tr})$ which can be measured with Hall voltage leads placed on the line $V_1V_2$ at a small distance $l$ apart from the edge defect and which changes its sign upon $l\rightarrow -l$ reversal. For narrow strips, we compare the theoretical predictions with experiment, by fitting the $V_\perp(I_\mathrm{tr},l)$ data for $1\,\mu$m-wide MoSi strips with single edge defects milled by a focused ion beam at distances $l = 16$-$80$\,nm from the line $V_1V_2$. For wide strips, the derived magnetic-field dependence of the vortex jet shape is in line with the recent experimental observations for vortices moving in Pb bridges with a narrowing. Our findings are augmented with the time-dependent Ginzburg-Landau simulations which reproduce the calculated vortex jet shapes and the $V_\perp(I_\mathrm{tr},l)$ maxima. Furthermore, with increase of $I_\mathrm{tr}$, the numerical modeling unveils the evolution of vortex jets to vortex rivers, complementing the analytical theory in the entire range of $I_\mathrm{tr}$.