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

Abstract

Dependence of the critical current Ic on the applied magnetic field Ha 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 λ is essentially less than the thickness d of the strip. To investigate the effect of these barriers on Ic 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 Ic(Ha) is calculated for the fields Ha not exceeding the lower critical field. This calculation reveals that the following two situations are possible: i) The critical current Ic(Ha) is determined by the Bean-Livingston barrier in the corners of the strip. ii) The geometrical barrier prevails at low Ha, 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 λ/d.