Theory of topological exciton insulators and condensates in flat Chern bands.

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons are expected to condense and exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate the excitonic bound states and superfluidity in flat-band insulators pumped with light. We find that the exciton wavefunctions exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Moreover, both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the exciton vorticity. We propose that the vorticity can also be experimentally measured via the nonlinear anomalous Hall effect, whereas the exciton superfluidity can be detected by voltage-drop quantization through a combination of quantum geometry and Aharonov-Casher effect. Topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures.