Superconductivity and disorder in topological flat bands

The geometry of the single-particle wave function can have a profound impact on the phases emerging upon the inclusion of interactions and disorder, especially in dispersionless bands. Here, we show via auxiliary-field Monte Carlo simulations how the non-trivial geometry enhances the superfluid weight and hence the superconducting critical temperature in flat-band systems. We further show how fragile and obstructed flat bands possess different properties upon the inclusion of weak disorder. Therefore, we establish the superfluid weight and the eigenstate localization as nontrivial bulk properties that distinguish among fragile topological, obstructed, and trivial flat bands in the presence of interactions and disorder.