Discrete spectrum of edge states in a two-dimensional topological insulator

The interaction model of two electrons in the edge states of a two-dimensional topological insulator is investigated. Both solutions of the Schr"odinger equation and solutions of the Bethe-Salpeter equation at different values of the Fermi energy are considered. It is shown that for the Bethe-Salpeter equation, which takes into account the existence of the Fermi surface, there is a discrete spectrum in the system of two electrons. This phenomenon does not appear in the case of the Schr"odinger equation. We found the bound-state energy for nonzero total momentum of electrons.