Complete Population Inversion between Ying-Ying flat bands

Using exact diagonalization methodology, we solve a many-body problem of electrons and holes in the flat conduction and valence band respectively of opposite chirality, namely the Ying-Yang flat bands, as hosted in a diatomic Kagome lattice. We first benchmark the results of single exciton formation with those obtained using DFT-GW methodology [Sethi, et. al., PRL 126, 196403], and then solve the many-exciton problem for the possibility of complete population inversion between the Ying-Yang flat bands. Our calculations show that the completely population inverted pair of flat bands can be stabilized by direct and exchange Coulomb interactions between electrons and holes, which are significantly enhanced by their vanishing kinetic energy. Our findings offer new insights on the nature of flat-band-enabled exciton-exciton interactions, leading to exotic quantum phenomenon, such as excited quantum Hall effects, excitonic insulator state, and topological flat-band laser.