Variational calculation of the lowest exciton states in phosphorene and transition metal dichalcogenides

Several transition metal dichalcogenides (TMDs) can be exfoliated to produce nearly two-dimensional (2D) semiconductor layers supporting robust excitons with non-hydrogenic Rydberg series of states. Black phosphorus (BP) can also be layered to create a nearly 2D material with interesting properties including its pronounced in-plane anisotropy that influences, in particular, exciton states making them different from those in other 2D semiconductors. We apply the Rayleigh-Ritz variational method to evaluate the energies and approximate the wavefunctions of the ground and lowest excited states of the exciton in a 2D semiconductor with anisotropic effective masses of electrons and holes. The electron-hole interaction is described by the Rytova-Keldysh potential, which is considered beyond the standard zero-thickness approximation. The exciton binding energies calculated for BP and TMD (molybdenum disulphide and tungsten disulphide) monolayers are compared with previously published data.