Wannier-Hubbard model of excitons in moiré superlattices: competition between exchange and localization.

Atomically thin semiconductors, particularly transition metal dichalcogenides (TMDs), display reduced charge screening that increases the binding energy of excitons. Furthermore, stacked layers of these materials allow for spatially-indirect excitons with exceptionally long lifetimes. However, the lattice stacking introduces reconstruction and mismatch effects that give rise to long-range moiré potential, localizing the excitons and limiting their transport before recombination. We examine the competition between these effects by developing a theory for excitons in an arbitrary continuum moiré potential, including internal excitonic degrees of freedom which expand previous continuum approaches to allow for entanglement of exciton deformation and center of mass (CM) position. We solve numerically for the exciton bands, and then derive an effective exciton Wannier-Hubbard model from them. We illustrate the spatial distribution of exciton states vs. CM position. Comparing representative cases, we show that exchange dominates band dispersion, allowing for hopping between potential minima, and that short-range moiré potentials are more effective at spatially separating the electron and hole.