Superfluid density of a pseudogapped superconductor near SIT

We analyze critical behavior of superfluid density $\rho_s$ in strongly disordered superconductors near superconductor-insulator transition and compare it with the behavior of the spectral gap $\Delta$ for collective excitations. We show that in contrast to conventional superconductors, the superconductors with preformed pairs display unusual scaling relation $\rho_s \propto \Delta^2$ close to superconductor-insulator transition. This relation have been reported in very recent experiments.