Microscopic equivalence of the vortex-entry current and the depairing current in a superconducting thin-film strip

Abstract

The current at which vortices enter a superconducting strip is usually identified in Pearl--London theory with the disappearance of an edge barrier. This work reformulates the same question microscopically as the loss of local stability of the vortex-free current-carrying state, using the fixed-current Gibbs functional of dirty-limit Usadel theory, which is valid at arbitrary temperatures. For an ideal homogeneous thin-film strip at zero applied field, with self-field effects neglected, the stability of the vortex-free state is examined against both spatially uniform and nonuniform perturbations. The barrier-disappearance current is shown to be set by the uniform perturbation and to coincide exactly with the depairing current.