Local density of states fluctuations in a two-dimensional superconductor as a probe of quantum diffusion

The interplay of superconductivity and disorder generates a wealth of complex phenomena. In particular, the peculiar structure of diffusive electronic wave functions is predicted to increase the superconducting critical temperature in some range of disorder. In this work, we use an epitaxial monolayer of lead showing a simple band structure and homogeneous structural disorder as a model system of a two-dimensional superconductor in the weak-antilocalization regime. Then, we perform an extensive study of the emergent fluctuations of the local density of states (LDOS) and spectral energy gap in this material and compare them with both analytical results and the numerical solution of the attractive Hubbard model. We show that mesoscopic LDOS fluctuations allow us to probe locally both the elastic and inelastic scattering rates, which are notoriously difficult to measure in transport measurements.