Dependence of the hBN Layer Thickness on the Band Structure and Exciton Properties of Encapsulated WSe₂ Monolayers

The optical properties of two-dimensional transition metal dichalcogenide monolayers such as MoS₂ or WSe₂ are dominated by excitons, Coulomb bound electron-hole pairs. Screening effects due the presence of hexagonal-BN surrounding layers have been investigated by solving the Bethe Salpeter Equation on top of GW wave functions in density functional theory calculations. We have calculated the dependence of both the quasi-particle gap and the binding energy of the neutral exciton ground state E_b as a function of the hBN layer thickness. This study demonstrates that the effects of screening at this level of theory are more short-ranged that it is widely believed. The encapsulation of a WSe₂ monolayer by three sheets of hBN (∼ 1 nm) already yields a 20 % decrease of E_b whereas the maximal reduction is 27% for thick hBN. We have performed similar calculations in the case of a WSe₂ monolayer deposited on stacked hBN layers. These results are compared to the recently proposed Quantum Electrostatic Heterostructure approach.