Gravitational Search Algorithm for Calculating Exciton Binding Energy in Monolayer Transition Metal Dichalcogenides

Large excitonic binding energies in monolayers of transition metal dichalcogenides such as molybdenum disulfide (MoS 2 ), molybdenum diselenide (MoSe 2 ), tungsten disulfide (WS 2 ) and tungsten diselenide (WSe 2 ), were calculated using a gravitational search algorithm. The optimized fitness function is based on a two dimensional (2D) effective mass model of excitons, parameterized by first principle calculations, including a suitable treatment of screening. In addition to the ground state, the binding energies of the first few excited states of the exciton were computed, hence the optical transition energies, as a function of principal quantum number n, were obtained for the exciton states. The method was also used to predict the corresponding 2D polarizabilities, and consequently, dielectric constants for the 2D semiconductors. Dependence of the effective dielectric constants on n was also investigated. Our results compare favorably with existing theoretical methods based on density function theory or GW approximation and the Bethe–Salpeter equation. Furthermore, our results are in reasonable agreement with recent experimental measurements.