Superfluidity in topologically nontrivial flat bands

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 Ds 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 Ds⩾|C|. Thus, even a flat band can carry finite superfluid current,…

• AO
  Academy of Finland

  Awards: 2012-2017, 263347, 272490, 251748