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

TL;DR

This paper investigates the electron-hole bound states in transition-metal dichalcogenides by deriving the Bethe-Salpeter equation, analyzing binding energies under various potentials, and developing methods for different interaction strengths.

Contribution

It introduces a Bethe-Salpeter framework for Dirac particles in transition-metal dichalcogenides and analyzes how potential behavior influences binding energies.

Findings

Binding energies depend strongly on the potential at small distances.

A perturbative method is developed for small interaction constants.

Numerical solutions are provided for large interaction constants.

Abstract

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.