Two-dimensional excitons in monolayer transition metal dichalcogenides from radial equation and variational calculations

Exciton energy spectra of monolayer transition metal dichalcogenides (TMDs) in various dielectric environments are studied with an effective mass model using the Keldysh potential for the screened electron-hole interaction. Two-dimensional (2D) excitons are calculated by solving a radial equation (RE) with a shooting method, using boundary conditions that are derived by applying the asymptotic properties of the Keldysh potential. For any given main quantum number n, the exciton Bohr orbit shrinks as vertical bar m vertical bar becomes larger (m is the orbital quantum number) resulting in increased strength of the electron-hole interaction and a decrease of the exciton energy. Further, both the exciton energy and its effective radius decrease linearly with vertical bar m vertical bar. The screened hydrogen model (SHM) (Olsen et al 2016 Phys. Rev. Lett. 116 056401) is examined by comparing its exciton energy spectra with our RE solutions. While the SHM is found to describe the nonhydrogenic exciton Rydberg series (i.e. the energy's dependence on n) reasonably well, it fails to account for the linear dependence of the exciton energy on the orbital quantum number. The exciton effective radius expression of the SHM can characterize the exciton radius's dependence on n, but it cannot properly describe the exciton radius's dependence on m, which is the cause of the SHM's poor description of the exciton energy's m-dependence. Analytical variational wave-functions are constructed with the 2D hydrogenic wave-functions for a number of strongly bound exciton states, and very close exciton energies and wave-functions are obtained with the variational method and the RE solution (exciton energies are within a 6% of deviation). The variational wave-functions are further applied to study the Stark effects in 2D TMDs, with an analytical expression derived for evaluating the redshift the ground state energy.