Linear dynamic polarizability and absorption spectrum of an exciton in a quantum ring in a magnetic field

TL;DR

This paper derives an exact analytical model for an exciton in a quantum ring under a magnetic flux, revealing unique optical features including dark states and flux-dependent energy spectra.

Contribution

It provides a novel exact solution for the exciton energy spectrum and optical properties in a quantum ring with magnetic flux, highlighting unusual features like dark states.

Findings

Exact energy spectrum derived for the exciton system.

Identification of flux-dependent dark excitonic states.

Unusual features in the optical absorption spectrum.

Abstract

The problem of an electron-hole system interacting through a contact potential and moving in a one-dimensional quantum ring threaded by an Aharonov-Bohm flux is considered, both with respect to the system's energetics as well as its optical properties. An exact analytical expression for the energy spectrum is derived using a straightforward method based on boundary conditions for wavefunctions and their derivatives along the ring. The optical properties of this exciton system, namely the linear dynamic polarizability and absorption spectrum are investigated demonstrating certain unusual features. It is shown, for example, that for special values of the magnetic flux there are energies in the spectrum that correspond to the dark excitonic states.