Superfluidity in topologically nontrivial flat bands

Sebastiano Peotta; Päivi Törmä

doi:10.1038/ncomms9944

paper

Superfluidity in topologically nontrivial flat bands

arXiv:1506.02815 · doi:10.1038/ncomms9944

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 $D_{s}$ 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 $D_{s} \geq ∣ C ∣$ . Thus, even a flat band can carry finite superfluid current, provided the Chern number is nonzero. As an example, we provide $D_{s}$ 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.

main text 19 pages, 2 figures; supplementary 19 pages, 3 figures. First version submitted to Nature Communications

Superfluidity in topologically nontrivial flat bands

Abstract

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