Superfluidity in topologically nontrivial flat bands

TLDR

Topological invariants of Bloch functions, particularly the Chern number, characterize new phases such as topological insulators and explain the quantized conductance observed in the quantum Hall effect. The study aims to derive a general expression for the superfluid weight \(D_{\rm s}\) in multiband superconductors with nonzero Chern number. The authors obtain \(D_{\rm s}\) from the quantum metric of Bloch functions and demonstrate it with the time‑reversal invariant attractive Harper‑Hubbard model, which can be experimentally tested in ultracold gases. They find that the quantum‑metric integral gives a superfluid weight bounded below by \(|C|\), showing that flat bands with nonzero Chern number can carry finite superfluid current and may raise the superconducting critical temperature.

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.