Four-Particle Anyon Exciton: Boson Approximation

TL;DR

This paper develops a theoretical model for four-particle anyon excitons, analyzing their symmetry, energy levels, and angular momentum, revealing complex splitting behavior as exciton momentum increases.

Contribution

It introduces a comprehensive theory of four-particle anyon excitons with detailed symmetry classification and energy expressions, advancing understanding of their quantum properties.

Findings

Energy levels expressed by hypergeometric functions

Ground state angular momentum depends on confinement plane distance

Exciton density splits into bundles with increasing momentum

Abstract

A theory of anyon excitons consisting of a valence hole and three quasielectrons with electric charges $(-e/3)$ is presented. A full symmetry classification of the $k=0$ states is given, where $k$ is the exciton momentum. The energy levels of these states are expressed by quadratures of confluent hypergeometric functions. It is shown that the angular momentum $L$ of the exciton ground state depends on the distance between electron and hole confinement planes and takes the values $L=3n$, where $n$ is an integer. With increasing $k$ the electron density shows a spectacular splitting on bundles. At first a single anyon splits off of the two-anyon core, and finally all anyons become separated.