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

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 $V_1{V}_2$ at a small distance $l$ apart from the edge defect and which changes its sign upon $l\to -l$ 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 $V_1{V}_2$. 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 $I_{\mathrm{tr}}$.

12 pages, 6 figures

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