Use of a generalized thouless energy in describing transport properties of Josephson junctions

The concept of a Thouless energy, introduced originally in the context of Anderson localization (as the inverse diffusion time through a finite-size disordered conductor), has turned out to be an essential energy scale for understanding proximity-induced superconductivity in a normal metal connected to a superconductor; in particular, it has had significant success in the quasiclassical description of phenomena in superconductor-normal-metal-superconductor Josephson junctions. We generalize the concept of a Thouless energy to include transport through strongly correlated insulators, and show how it provides a unified description of transport and indicates how the quasiclassical picture breaks down as we turn on electron-electron correlations in the normal metal layer of a Josephson junction to tune it through the Mott metal-insulator transition.