From moiré electrons and holes to moiré excitons in two-dimensional semiconductor heterobilayers

Abstract Moiré patterns in the crystal structure of twisted or lattice-mismatched semiconductor van der Waals bilayers lead to spatial modulations of conduction and valence bands along the material plane. These modulations play the role of superlattice potentials for electrons and holes in the semiconductor, ultimately resulting in a band structure for moiré quasi-particles. In the case of strong electron–hole interactions, a moiré exciton quasi-particle, whose energy dispersion is controlled by the moiré potential, is formed. However, if the moiré potential is of the same order of magnitude as the electron–hole interaction potential, the exciton center-of-mass coordinates cannot be separated from the relative coordinates, and the concept of a bound electron–hole pair behaving as a single moiré quasi-particle fails. Here, we provide a model that allows one to crossover from moiré electrons and holes (i.e. in-plane spatially indirect excitons) to moiré excitons. We predict that for some combinations of heterobilayer materials, the exciton binding energy and oscillator strength will be strongly dependent on the moiré potential, a feature that the conventional moiré exciton model does not capture.