Island formation in disordered superconducting thin films at finite magnetic fields

It has been predicted theoretically and observed experimentally that disorder leads to spatial fluctuations in the superconducting (SC) gap. Areas where SC correlations are finite, coined SC islands, were shown experimentally to persist into the insulating side of the superconductor-insulator transition. The existence of such (possibly weakly coupled) SC islands in amorphous thin films of superconducting material accounts for numerous experimental findings related to superconductor-insulator transition and nonmonotonic magnetoresistance behavior in the insulating region. In this work, a detailed analysis pertaining to the occurrence of SC islands in disordered two-dimensional superconductors is presented. Using a locally self-consistent numerical solution of the Bogoliubov-de Gennes equations, the formation of SC islands is demonstrated, and their evolution with an applied perpendicular magnetic field is studied in some detail, along with the disorder-induced vortex pinning. While mean-field theory cannot, in principle, explore phase correlations between different islands, it is demonstrated that, by inspecting the effect of a parallel magnetic field, one can show that the islands are indeed uncorrelated SC domains. Experimental predictions based on this analysis are presented.