To the problem of electron-hole bound state in transition-metal dichalcogenides

The interacting electron and hole in transition-metal dichalcogenides is considered. For investigation of the interaction between electron and hole we obtain the Bethe-Salpeter equation for two interacting Dirac particles. The dependence of a few lowest binding energies of electron and hole on the interaction constant for different potentials is found. We demonstrate that the behavior of the potential at small distances significantly affects on the values of the binding energies. For small interaction constant we have developed the perturbative method of the binding energy calculation. For the largre interaction constant the binding energies are found numerically. The critical values of the interaction constant for the Coulomb potential and exponential potential are found.