Orbital Magnetism in Ensembles of Parabolic Potentials

TL;DR

This paper investigates the magnetic susceptibility of non-interacting electrons in parabolic potentials under magnetic fields, revealing unique paramagnetic responses at specific field values and providing analytical and numerical insights.

Contribution

It introduces analytical formulas for susceptibility in parabolic potentials and compares them with numerical results, highlighting differences from billiard systems.

Findings

Susceptibility shows large paramagnetic peaks at specific field values.

Average susceptibility is negligible at most field values.

Derived approximate formulas match numerical calculations.

Abstract

We study the magnetic susceptibility of an ensemble of non-interacting electrons confined by parabolic potentials and subjected to a perpendicular magnetic field at finite temperatures. We show that the behavior of the average susceptibility is qualitatively different from that of billiards. When averaged over the Fermi energy the susceptibility exhibits a large paramagnetic response only at certain special field values, corresponding to comensurate classical frequencies, being negligible elsewhere. We derive approximate analytical formulae for the susceptibility and compare the results with numerical calculations.