Gaplessness from disorder and quantum geometry in gapped superconductors

Abstract

It is well known that disorder can induce low-energy Andreev bound states in a sign-changing, but fully gapped, superconductor at π junctions. Generically, these excitations are localized. Starting from a superconductor with a sign-changing and nodeless order parameter in the clean limit, here we demonstrate a mechanism for increasing the localization length associated with the low-energy Andreev bound states at a fixed disorder strength. We find that the Fubini-Study metric associated with the electronic Bloch wave functions controls the localization length and the hybridization between bound states localized at distinct π junctions. We present results for the inverse participation ratio, superfluid stiffness, site-resolved, and disorder-averaged spectral functions as a function of increasing the Fubini-Study metric, which indicate an increased tendency towards delocalization. The low-energy properties resemble those of a dirty nodal superconductor with gapless Bogoliubov excitations. We place these results in the context of recent experiments in moiré graphene superconductors.

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