Confinement of superconducting fluctuations due to emergent electronic inhomogeneities in ultrathin films

The question of homogeneity, granularity, or glassiness of materials on the verge of a superconductor/insulator transition is fundamental and hotly debated. Here, by combining macroscopic and nano-scale studies of superconducting ultrathin NbN films, we reveal some nanoscopic electronic inhomogeneity that emerges when the film thickness is reduced. While thicker films display a purely two-dimensional behavior in electrical transport measurements, we demonstrate a seemingly zero-dimensional regime in the superconducting thermal fluctuations for the thinner samples. This regime corresponds to a longer survival and anomalous local diffusion of the Cooper pair fluctuations. Remarkably, the typical length scale, 20-40 nm, extracted from the fluctuation conductivity coincides with the correlation length of the electronic inhomogeneities directly revealed by local scanning tunneling spectroscopy.