Excited quantum anomalous (spin) Hall effect: enantiomorphic flat bands in a diatomic Kagome lattice

Quantum anomalous Hall effect (QAHE) and quantum spin Hall effect (QSHE) are ground-state equilibrium properties characterized by Fermi level lying in a topological gap, below which all the occupied bands are summed to a non-zero Chern and Z2 number for the QAHE and QSHE, respectively. Here, we propose theoretical concepts and models of non-equilibrium excited-state QAHE (EQAHE) and QSHE (EQSHE) generated by photoexcited singlet and triplet excitonic states, respectively, between two enantiomorphic flat bands (FBs) of opposite chirality hosted in a diatomic Kagome lattice. The two FBs have a trivial gap in between, i.e., the system is a trivial insulator in the ground-state; but nontrivial gaps above and below, so that upon excitation, the quasi-Fermi levels of both electrons and holes will lie in a nontrivial gap, when complete population inversion is achieved as in an excitonic insulator. Then dissociation of singlet and triplet excitons will lead to EQAHE and EQSHE, respectively, with the former breaking and the latter preserving the time-reversal symmetry. Implications and realization of enantiomorphic FBs in real materials are also discussed.