Out-of-plane excitons in two-dimensional crystals

Two-dimensional materials are ideal platforms to explore new physical phenomena and reveal unique optical properties. Excitonic and quasiparticle effects are strongly enhanced by the reduced screening. The response to a perturbing electromagnetic field is dominated by in-plane light polarization. The quantum confinement of the atomic sheets in normal direction also allows out-of-plane pair excitations, which are ruled by selection rules and local-field effects. We apply the GW approximation and the Bethe-Salpeter equation to investigate optical transitions for light polarization both parallel and normal to the atomic planes. Prototypical systems range from semimetals to large-gap insulators such as graphene, graphene oxide, boron nitride, and molybdenum disulfide. For the considered materials, the out-of-plane absorption edge and the first van Hove singularities are blueshifted in dependence of the effective sheet thickness, while the intensity of the optical conductivity is reduced by orders of magnitude.