Quasiparticle and Excitonic Structures of Few-layer and Bulk GaSe: Interlayer Coupling, Self-energy, and Electron-hole Interaction

Metal monochalcogenide GaSe is a classic layered semiconductor that has received increasing research interest due to its highly tunable electronic and optical properties for ultrathin electronics applications. Despite intense research efforts, a systematic understanding of the layer-dependent electronic and optical properties of GaSe remains to be established, and there appear significant discrepancies between different experiments. We have performed GW plus Bethe-Salpeter equation (BSE) calculations for few-layer and bulk GaSe, aiming at understanding the effects of interlayer coupling and dielectric screening on excited state properties of GaSe, and how the electronic and optical properties evolve from strongly two-dimensional (2D) like to intermediate thick layers, and to three-dimensional (3D) bulk character. Using a new definition of the exciton binding energy, we are able to calculate the binding energies of all excitonic states. Our results reveal an interesting correlation between the binding energy of an exciton and the spread of its wave function in the real and momentum spaces. We find that the existence of (nearly) parallel valence and conduction bands facilitates the formation of excitonic states that spread out in the momentum space. Thus, these excitons tend to be more localized in real space and have large exciton binding energies. The interlayer coupling substantially suppresses the Mexican-hat-like dispersion of the top valence band seen in monolayer system, explaining the greatly enhanced photoluminescence (PL) as layer thickness increases. Our results also help resolve apparent discrepancies between different experiments. After including the quasiparticle and excitonic effects as well the optical activities of excitons, our results compare well with available experimental results.