Gaplessness from disorder and quantum geometry in gapped superconductors

TL;DR

This paper reveals how quantum geometry influences the localization of low-energy states in disordered gapped superconductors, leading to increased delocalization and gapless excitations similar to dirty nodal superconductors.

Contribution

It introduces a novel mechanism linking the Fubini-Study metric to localization length in disordered superconductors with sign-changing order parameters.

Findings

Fubini-Study metric controls localization length of Andreev bound states

Increased metric leads to more delocalized low-energy states

Results resemble properties of gapless, dirty nodal superconductors

Abstract

It is well known that disorder can induce low-energy Andreev bound states in a sign-changing, but fully gapped, superconductor at $\pi-$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 wavefunctions controls the localization length and the hybridization between bound states localized at distinct $\pi-$junctions. We present results for the inverse participation ratio, superfluid stiffness, site-resolved and disorder-averaged spectral functions as a function of increasing 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 moire graphene superconductors.