On the Problem of Bound States of Electron and Hole in Transition Metal Dichalcogenides

The interacting electron and hole in transition metal dichalcogenides are considered. To investigate the interaction the Bethe-Salpeter equation was obtained in the leading order in the interaction potential. It is shown that the behavior of the potential at short distances significantly affects the binding energy of the electron and the hole. We demonstrate that the expansion of the Bethe-Salpeter equation in the small coupling constant does not contain singular operators. Therefore, the binding energy of the electron and the hole does not contain the regularization parameter. Using the perturbation theory in the coupling constant we analytically calculated the energies of the ground and first excited states of the exiton. For arbitrary values of the coupling constant, the energies of the bound states of the electron and the hole are obtained numerically. The critical values of the coupling constant for the Coulomb potential and for the exponentially decreasing potential are also found numerically.