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 MoS$_2$ or WSe$_2$ 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 WSe$_2$ monolayer by three sheets of hBN (around 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 WSe$_2$ monolayer deposited on stacked hBN layers. These results are compared to the recently proposed Quantum Electrostatic Heterostructure approach.