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Recent experiments on disordered superconductors find that the superfluiddensity $n_s(T)$ decreases dramatically and characteristically with disorder,differently from what is expected for a mean order parameter field or BCS,amplitude only, picture for the superconductor. We describe here a newmicroscopic free energy functional which explicitly describes its dependence onboth the amplitude and phase of superconducting order, in a gauge invariantmanner. We use this here in an approximation of noninteracting phasefluctuations (Gaussian or harmonic approximation) to obtain $n_s(T)$ in thepresence of (static) disorder. We compare our results successfully withexperiment.

Microscopic free energy functional of superconductive amplitude and phase: Superfluid density in disordered superconductors