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

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.