Theory for exciton polarization and confinement in moiré domains

Two-dimensional van-der-Waals materials are a promising platform for exciton state engineering. We present a k·p theory to model exciton moiré bands formed by applying a periodic external electrostatic potential to a two-dimensional semiconductor. We treat electrons and holes as separate fermionic degrees of freedom, thus allowing excitons to be polarized by electrostatic potential gradients, leading to confinement of dipolar excitons. Such excitonic states notably form at the domain boundaries in strongly-reconstructed moiré lattices. We apply our theory to explain the role of e-h exchange interaction and symmetry of the electrostatic potential in lifting valley degeneracy. In contrast, higher-energy excitons in this system are unpolarized and have been observed to be confined within the domain interiors. We interpret these states as nearly-free excitons that are trapped by exciton exchange repulsion with the dipolar excitons at the boundary, which represent the lowest-energy excitations and hence are always populated first.