LAUSR

Abstract Recent experiments have shown that the electron-hole interaction in monolayer materials, such as MoS2, MoSe2, WS2, WSe2, is no longer Coulombic but screened by the effect of reduced dimensionality, effectively described by the Keldysh potential. In this paper, we develop an algebraic method for calculating energies of a screened exciton in a two-dimensional space with a constant magnetic field. First, we use the Levi-Civita transformation to rewrite the problem into an anharmonic oscillator which can be solved by the algebraic technique based on annihilation and creation operators. Second, we modify the Feranchuk-Komarov operator method to use on the Schrodinger equation. As a result, we are able to obtain high-accuracy numerical solutions with the precision of twelve decimal places for the ground and highly excited states. In our simulation, such high precision persists even for much stronger magnetic field intensities and much longer Keldysh screening length than the present experimental values. Therefore, our numerical data can sufficiently cover most practical analyses. Furthermore, we compare them with the recent experimental data and analyze the screening effect with a conclusion that it strongly enhances the magnetic field effect. Notably, comparing the experimental 1s − 2s and 2s − 3s energy differences with the theoretical calculations, we can predict the screening length and the exciton reduced mass in the monolayers.