Semianalytical study of excitons and quasiparticle band gap in two-dimensional insulators

A theoretical study of the exciton binding energy in the two-dimensional hexagonal boron nitride monolayer is presented within the tight-binding approximation (TBA). A self-consistent equation for the interband electron-hole propagators is derived and in the long wavelength limit reduced to the standard hydrogen atom like Schrodinger equation. It is shown that inclusion of dynamically screened Coulomb interaction in ladder term is of crucial importance for proper description of exciton binding energy. This leads to the self-consistent eigenvalue problem with dynamical screening. The dependence of the exciton energy on the orbital quantum number is studied. It is predicted that for the fixed principal quantum number the states with higher orbital momentum have lower energy than the states with lower orbital momentum. Using the developed formulas and the experimental optical gap the quasiparticle gap is estimated. In the limit of high polarizability, a semiclassical procedure was used to obtain the exciton binding energy. The TBA parametrization is supported by ab initio calculations.