Enhanced phase-coherent multifractal two-dimensional superconductivity

We study the interplay of superconductivity and disorder by solving numerically the Bogoliubov-de Gennes equations in a two-dimensional lattice of size 80 x 80, which makes investigating the weak-coupling limit possible. In contrast with results in the strong-coupling region, we observe enhancement of superconductivity and intriguing multifractal-like features such as a broad log-normal spatial distribution of the order parameter, a parabolic singularity spectrum, and level statistics consistent with those of a disordered metal at the Anderson transition. The calculation of the superfluid density, including small phase fluctuations, reveals that, despite this intricate spatial structure, phase coherence still holds for sufficiently weak disorder. It breaks down only for stronger disorder but before the insulating transition takes place.