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

Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geometry is negligible, but in the opposite limit of flat-band superconductors the superfluid weight originates purely from the quantum geometry of Bloch wave functions. Here, we study how the energy band dispersion and the quantum geometry affect the disorder-induced suppression of the superfluid weight. Surprisingly, we find that the disorder-dependence of the superfluid weight is universal across a variety of models, and independent of the quantum geometry and the flatness of the dispersion. Our results suggest that a flat-band superconductor is as resilient to disorder as a conventional superconductor. The provided repository contains all code and data to reproduce the results of this study.The research was partially supported by the Foundation for Polish Science through the IRA Programme co-financed by EU within SG OP. A. L. acknowledges support from a Marie Skłodowska-Curie Individual Fellowship under grant MagTopCSL (ID 101029345). E.R. acknowledge support from DOE, Grant No. DE-SC0022245. We acknowledge the access to the computing facilities of the Interdisciplinary Center of Modeling at the University of Warsaw, Grant No. G84-4, G87-1135, and G88-1203