Two-dimensional electron gas in a periodic potential and external magnetic field: states of pairs and three-particle systems

TL;DR

This paper classifies and analyzes the symmetry properties of two- and three-particle states in a 2D electron gas under a periodic potential and magnetic field, revealing degeneracy patterns and representation complexities.

Contribution

It introduces a group-theoretical framework for classifying multi-particle states in 2D electron systems with magnetic fields, including degeneracy and symmetry considerations.

Findings

Pair states have N-fold degeneracy for a period N.

Three-particle states have N^2-fold degeneracy.

Even N cases involve four inequivalent representations.

Abstract

The group-theoretical classification of states of identical particle pairs is presented. Then obtained states are coupled with those of an antiparticle to construct states of a three-particle system. Investigations are performed using products of irreducible projective representations of the 2D translation group. For a given BvK period N degeneracy of pair states is N, whereas three-particle states are N^2-fold degenerated. It has to be underlined that the case of even N is more complicated since pair states are labelled by four inequivalent irreducible projective representations. The problem of symmetry properties with respect to particles transposition is briefly discussed.