Critical current in thin flat superconductors with Bean-Livingston and geometrical barriers

TL;DR

This paper theoretically analyzes how Bean-Livingston and geometrical barriers influence the critical current in thin superconducting strips, revealing conditions under which each barrier dominates based on the ratio of penetration depth to thickness.

Contribution

It provides a rigorous two-dimensional current distribution model considering both barriers, clarifying their interplay and dominance in determining the critical current.

Findings

Critical current depends on the interplay of barriers.

Bean-Livingston barrier dominates at high fields.

Geometrical barrier dominates at low fields.

Abstract

Dependence of the critical current $I_c$ on the applied magnetic field $H_a$ is theoretically studied for a thin superconducting strip of a rectangular cross section, taking an interplay between the Bean-Livingston and the geometric barriers in the sample into account. It is assumed that bulk vortex pinning is negligible, and the London penetration depth $\lambda$ is essentially less than the thickness $d$ of the strip. To investigate the effect of these barriers on $I_c$ rigorously, a two-dimensional distribution of the current over the cross section of the sample is derived, using the approach based on the methods of conformal mappings. With this distribution, the dependence $I_c(H_a)$ is calculated for the fields $H_a$ not exceeding the lower critical field. This calculation reveals that the following two situations are possible: i) The critical current $I_c(H_a)$ is determined by the Bean-Livingston barrier in the corners of the strip. ii) The geometrical barrier prevails at low $H_a$, but with increasing magnetic field, the Bean-Livingston barrier begins to dominate. The realization of one or the other of these two situations is determined by the ratio $\lambda/d$.