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Motivated by the experimental progress in controlling the properties of theenergy bands in superconductors, significant theoretical efforts have beendevoted to study the effect of the quantum geometry and the flatness of thedispersion on the superfluid weight. In conventional superconductors, where theenergy bands are wide and the Fermi energy is large, the contribution due tothe quantum geometry is negligible, but in the opposite limit of flat-bandsuperconductors the superfluid weight originates purely from the quantumgeometry of Bloch wave functions. Here, we study how the energy band dispersionand the quantum geometry affect the disorder-induced suppression of thesuperfluid weight. Surprisingly, we find that the disorder-dependence of thesuperfluid weight is universal across a variety of models, and independent ofthe quantum geometry and the flatness of the dispersion. Our results suggestthat a flat-band superconductor is as resilient to disorder as a conventionalsuperconductor.

Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion