Superconductivity in a disordered vortex lattice

Orbital magnetic field, as well as disorder, weaken superconductivity of a type-II superconducting film when acting individually. The Abrikosov vortex lattice, resulting from magnetic field, melts with the increasing field strength turning the superconductor into a metal. On the other hand, disorder causes a two-dimensional superconducting film to undergo a transition to an insulating state beyond a critical strength of disorder. Here we show that the simultaneous presence of these perturbations leads to an interesting evolution of superconductivity. We demonstrate that the local superconductivity strengthen due to a self-consistent spatial reorganization of order parameters. At weak disorder strengths, the same critical field that collapses the superconducting energy gap which is also responsible for the vanishing of the superfluid density. However, these two critical fields diverge from one another at large disorder strengths. In addition, disorder is found to distort the Caroli-de Gennes-Matricon bound state, which in the clean system features a strong zero-bias peak in the local density of states (LDOS) at the vortex-core. This peak disappears featuring a dip in LDOS at core, even for weak disorders. We comprehend such behavior and discuss possible experimental signatures.