Charge Dynamics Across the Disorder Driven Superconductor-Insulator Transition

While insensitive to weak non magnetic disorder, an s-wave superconductor can be driven insulating by strong disorder. Using a scheme that captures the correct ground state, and fully retains thermal amplitude and phase fluctuations, we describe the disorder driven superconductor-insulator transition at finite temperature. Our results on the resistivity suggest that beyond moderate disorder the low temperature superconducting state can arise out of an insulating normal state. We also find that the low frequency weight in the density of states and optical conductivity are non monotonic in disorder, with a maximum near critical disorder, and their high temperature value correlate with the superconducting fraction in the disordered ground state.