According to Anderson's theorem, the gap of a time-reversal symmetric weak-coupling superconductor is unaffected by nonmagnetic disorder. However, the superfluid weight (stiffness) is reduced in the disordered limit by a factor of $\mathrm{\Delta }\tau$, a product of the scattering time $\tau$ and the superconducting order parameter $\mathrm{\Delta }$. Here, we show that the opposite holds true in flat-band superconductors. While nonmagnetic disorder does reduce the order parameter, we find that its direct effect on superfluid weight is mostly negligible. We show analytically that the effect of disorder is to lowest order given in terms of the difference between the intraband and interband parts of the localization functional of impurity wave functions, finding it to be typically vanishing.

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• Flat bands
• Impurities in superconductors
• Multiband superconductivity
• Superconductivity
• Superfluid density
• Unconventional superconductors
• BCS theory
• Bogoliubov-de Gennes equations
• Mean field theory