Effect of two-dimensional non-local screening on characteristics of transition metal dichalcogenide monolayers

On the basis of the theory developed for the dielectric function of atomic thin layer insulating materials (Cudazzo et al 2011 Phys. Rev. B 84 085406), some characteristics of transition metal dichalcogenide monolayers are calculated in the framework of variational method. This method initially was designed to work for very weak or strong magnetic fields, but it is also in very good agreement with the numerical results obtained for intermediate magnetic fields. The expressions of the energy and effective radius of the ground impurity state, depending on the effective screening parameter of the problem, are obtained both without and with magnetic fields.