Berezinskii-Kosterlitz-Thouless transition in disordered superconducting films

In this Thesis, I investigated the effects of intrinsic electron inhomogeneity on the Berezinskii-Kosterlitz-Thouless (BKT) transition in thin superconducting (SC) films. Using both Monte Carlo numerical simulations and analytical calculations, I studied a two-dimensional XY model with different realizations of quenched disorder. This study revealed that spatially uncorrelated quenched disorder does not modify the key features of the BKT transition, leaving the whole temperature dependence of the superfluid stiffness almost unchanged. In contrast, quenched disorder with strong spatial correlations induces anomalous nucleation of topological phase excitations, i.e. vortices, leading to significant smearing of the universal superfluid-stiffness jump at the critical temperature. This is a key finding for understanding the broad BKT transition observed in several ultrathin SC films and underdoped cuprate superconductors, where spatial inhomogeneity of the SC order parameter may arise either from proximity to the superconductor-insulator transition or competition with other electronic orders. Finally, I investigated the effect of quenched disorder on the two-dimensional vortex lattice that forms when a transverse magnetic field is applied to the film. I showed that, while disorder disrupts the vortex lattice, it can enhance vortex pinning and strengthen the superconducting phase.