Superfluid weight bounds from symmetry and quantum geometry in flat bands

TL;DR

This paper establishes bounds on superfluid weight in flat bands using symmetry and quantum geometry, demonstrating that obstructed Wannier centers can support superconductivity even with zero Berry curvature.

Contribution

It derives new lower bounds for superfluid weight based on symmetry and quantum geometry, extending topological quantum chemistry to superconducting states.

Findings

Superfluid weight bounds are nonzero in obstructed flat bands.

Superconductivity can occur in flat bands with obstructed Wannier centers.

Monte Carlo simulations confirm the theoretical bounds in a model with local interactions.

Abstract

Flat-band superconductivity has theoretically demonstrated the importance of band topology to correlated phases. In two dimensions, the superfluid weight, which determines the critical temperature through the Berezinksii-Kosterlitz-Thouless criteria, is bounded by the Fubini-Study metric at zero temperature. We show this bound is nonzero within flat bands whose Wannier centers are obstructed from the atoms - even when they have identically zero Berry curvature. Next, we derive general lower bounds for the superfluid weight in terms of momentum space irreps in all 2D space groups, extending the reach of topological quantum chemistry to superconducting states. We find that the bounds can be naturally expressed using the formalism of real space invariants (RSIs) that highlight the separation between electronic and atomic degrees of freedom. Finally, using exact Monte Carlo simulations on a model with perfectly flat bands and strictly local obstructed Wannier functions, we find that an attractive Hubbard interaction results in superconductivity as predicted by the RSI bound beyond mean-field. Hence, a nonzero superfluid weight constitutes a nontrivial bulk property that distinguishes obstructed bands from trivial bands in the presence of interactions.