Fragile topology and flat-band superconductivity in the strong-coupling regime

TL;DR

This paper demonstrates through Monte Carlo simulations that fragile topology in flat bands imposes a lower bound on superfluid weight, influencing the superconducting transition temperature in systems like magic-angle twisted bilayer graphene.

Contribution

It provides the first numerical evidence that fragile topology affects superconductivity beyond mean-field theory in flat-band systems.

Findings

Superconducting transition temperature scales linearly with interaction strength.

Fragile topology imposes a lower bound on superfluid weight beyond mean-field.

Adding trivial bands can affect the topological properties and superconductivity.

Abstract

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a mean-field description, a non-zero Chern number or fragile topology sets a lower bound for $D_s$, which, via the Berezinskii-Kosterlitz-Thouless mechanism, might explain the relatively high superconducting transition temperature measured in magic-angle twisted bilayer graphene (MATBG). For fragile topology, relevant for the bilayer system, the fate of this bound for finite temperature and beyond the mean-field approximation remained, however, unclear. Here, we use numerically exact Monte Carlo simulations to study an attractive Hubbard model in flat bands with topological properties akin to those of MATBG. We find a superconducting phase transition with a critical temperature that scales linearly with the interaction strength. We then investigate the robustness of the superconducting state to the addition of trivial bands that may or may not trivialize the fragile topology. Our results substantiate the validity of the topological bound beyond the mean-field regime and further stress the importance of fragile topology for flat-band superconductivity.