Quantum rings for beginners: Energy spectra and persistent currents

TL;DR

This paper reviews theoretical models of quantum rings with few electrons, highlighting their energy spectra and persistent current behaviors influenced by electron interactions and spin states.

Contribution

It compares discrete Hubbard and continuum models, describing energy spectra as rotation-vibration of a Wigner molecule and analyzing flux periodicity in persistent currents.

Findings

Energy spectra resemble rotation-vibration of localized electrons

Persistent current oscillates with magnetic flux, showing periodicity changes

Flux periodicity depends on electron polarization and interaction strength

Abstract

Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body states can be described by a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of the magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the periodicity of the oscillations is always the flux quantum Phi_0. For nonpolarized electrons the periodicity depends on the strength of the effective Heisenberg coupling and changes from Phi_0 first to Phi_0/2 and eventually to Phi_0/N when the ring gets narrower.