Topological exciton superfluidity in driven quantum anomalous Hall insulators: Application to twisted bilayer graphene

Exciton states of interacting quantum anomalous Hall (QAH) insulators may inherit nontrivial Berry phases from the underlying electron bands. We investigate the possible onset of topological exciton superfluidity in the case of a two-band QAH insulator driven by a continuous wave laser of a resonant frequency, exploiting the Floquet-Keldysh formalism. We analyze the superfluid weight and the critical temperature in the steady state, focusing on the effects of the quantum metric of the electron bands, in analogy to those in flat-band superconductivity. We propose that the nonlinear optical current can reveal signatures of the topology of the exciton bands as well as the exciton condensate. We apply the theory to the magic-angle twisted bilayer graphene near the chiral limit, in which the flat bands may host ideal quantum geometry for realizing the topological exciton superfluid.