Bandstructure and excitons in WSe₂ as a function of the inter-layer distance.

The band structure of monolayer WSe₂ is studied at various levels of approximation, from density functional theory (DFT) to quasi-particle self-consistent GW (QSGW) with and without vertex contributions (Ladder Diagrams) and with and without spin-orbit coupling (SOC) as a function of the distance between the layers. The dielectric function is also studied within random phase approximation (RPA) and the Bethe-Salpeter equation (BSE). Our results show that the QSGW gap scales linearly with the inter-layer distance. At infinite distance, we extrapolate the gap to be ∼ 3.7 (eV), which decreases to ∼ 3.5 (eV) after including ladder diagrams. We also find two excitons for the in-plane wavevector using the BSE method, where the first has a binding energy of ∼ 1 (eV). Unlike the QSGW gap, the position of the first exciton peak does not noticeably change with the inter-layer distance, suggesting that the long range effects on the screened Coulomb interaction in QSGW and BSE cancel out. Symmetry labeling of the bands near the gap is also carried out showing allowed transitions in an optical process presented along with the transition rates.