Superfluidity in topologically nontrivial flat bands

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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 weightDsof a multiband superconductor that is applicable to topologically nontrivial bands with nonzero Chern numberC. 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 boundDs⩾|C|. Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provideDsfor 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.

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