Geometry-dependent critical currents in superconducting nanocircuits

TL;DR

This paper analyzes how geometry affects the critical currents in superconducting nanocircuits, revealing effects of current crowding and proposing rounded designs to enhance performance and reduce issues like dark counts and heating.

Contribution

It provides a detailed calculation of critical currents in complex geometries, highlighting the impact of curvature and proposing design improvements to mitigate current crowding effects.

Findings

Current crowding reduces critical current at sharp turns.

Rounded corners can mitigate current crowding effects.

Designs with curvature less than the coherence length improve critical current.

Abstract

In this paper we calculate the critical currents in thin superconducting strips with sharp right-angle turns, 180-degree turnarounds, and more complicated geometries, where all the line widths are much smaller than the Pearl length $\Lambda = 2 \lambda^2/d$. We define the critical current as the current that reduces the Gibbs free-energy barrier to zero. We show that current crowding, which occurs whenever the current rounds a sharp turn, tends to reduce the critical current, but we also show that when the radius of curvature is less than the coherence length this effect is partially compensated by a radius-of-curvature effect. We propose several patterns with rounded corners to avoid critical-current reduction due to current crowding. These results are relevant to superconducting nanowire single-photon detectors, where they suggest a means of improving the bias conditions and reducing dark counts. These results also have relevance to normal-metal nanocircuits, as these patterns can reduce the electrical resistance, electromigration, and hot spots caused by nonuniform heating.