  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 vorticity of excitons. We propose that the exciton vorticity
can also be experimentally measured by the nonlinear anomalous Hall effect,
whereas the exciton superfluidity can be detected by voltage-drop quantization
through a combination of the quantum geometry and the Aharonov-Casher effect.
Topological excitons and their superfluid phase could be realized in flat bands
of twisted Van der Waals heterostructures.
