Superfluidity in topologically nontrivial flat bands

TL;DR

This paper demonstrates that topologically nontrivial flat bands can support finite superfluid weight due to their nonzero Chern number, potentially leading to higher critical temperatures in superconductors.

Contribution

It provides a general formula linking the superfluid weight to the quantum metric and Chern number in topologically nontrivial flat bands, a novel theoretical insight.

Findings

Superfluid weight in flat bands is bounded below by the Chern number magnitude.

Quantum metric integral determines superfluid weight in topologically nontrivial flat bands.

Example calculation for the Harper-Hubbard model suggests experimental testability.

Abstract

Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here, we provide a general result for the superfluid weight $D_{\rm s}$ of a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern number $C$. We find that the integral over the Brillouin zone of the quantum metric, an invariant calculated from the Bloch functions, gives the superfluid weight in a flat band, with the bound $D_{\rm s} \geq |C|$. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide $D_{\rm s}$ for the time-reversal invariant attractive Harper-Hubbard model that can be experimentally tested in ultracold gases. In general, our results establish that a topologically nontrivial flat band is a promising concept for increasing the critical temperature of the superconducting transition.