Microscopic theory of the field-induced instability of the vortex-free state in superconducting thin-film strips
In the Pearl--London theory, the edge-barrier-disappearance field of a superconducting thin-film strip depends on an arbitrary short-distance core cutoff because the vortex is treated as a point object. The theory does not determine the cutoff or how it depends on temperature $T$, and therefore cannot determine the $T$ dependence of the instability field. Here we formulate the microscopic stability problem directly for the vortex-free superconducting state. This removes the core-cutoff ambiguity and determines the instability field $B_s$ over the full temperature range and across all width regimes considered here. For a homogeneous dirty strip with negligible self-field, three width regimes occur. For $W W_2(T)$, the critical wave number is finite and the unstable mode is localized near an edge. In the wide-strip limit, $B_s\propto1/W$, recovering the Pearl--London scaling. In sufficiently narrow strips, however, the Pearl--London edge-barrier picture fails qualitatively.