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Tunneling Spectroscopy Across the Superconductor-Insulator Thermal Transition

Advances in scanning tunneling spectroscopy reveal the presence of superconducting nanoregions well past the bulk thermal transition in strongly disordered superconductors. We use a Monte Carlo tool to capture the spatially differentiated amplitude and phase fluctuations in such a material and establish spatial maps of the coherence peak as the superconductor is driven through the thermal transition. Analysis of the local density of states reveals that superconducting regions shrink and fragment with increasing temperature, but survive in small clusters to a temperature $T_{clust} >> T_{c}$ . The gap (or pseudogap) in the spectrum survives in general to another independent scale, $T_{g}$, depending on the strength of interaction. This multiple scale description is consistent with recent measurements and defines the framework for analysing strongly disordered superconductors.