  The interplay of superconductivity and disorder generates a wealth of complex
phenomena. In particular, the peculiar structure of diffusive electronic
wavefunctions 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 homogenous structural disorder as a model
system of a 2D superconductor in the weak-antilocalization regime. Then, we
perform an extensive study of the emergent fluctuations of local density of
states (LDOS) and spectral energy gap in this material and compare them with
both analytical results and numerical solution of the attractive Hubbard model.
We show that mesoscopic LDOS fluctuations allow to probe locally both the
elastic and inelastic scattering rates which are notoriously difficult to
measure in transport measurements.
