Emergent inhomogeneity in dirty superconductors: microscopic theory

Superconducting state is known to become inhomogeneous as a material gets closer to the metal-to-insulator transition. The origin of inhomogeneity is naturally attributed to the increase of disorder, but a particular mechanism behind the effect is still unknown. We report on the microscopic theory of the emergent inhomogeneity in moderately disordered superconductors, which takes into account electron scattering on a few impurities located at a distance of the mean free path or closer. The contribution of such processes can parametrically exceed diffusive contribution considered previously. Emergent inhomogeneity is manifested in spatial fluctuations of the superconducting critical temperature and the quasiparticle gap, which can be probed by scanning tunneling measurements. Our findings suggest that with increasing disorder strength the superconducting state first becomes strongly inhomogeneous, and only then the metal-to-insulator transition occurs.