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.