Orbital magnetism in ensembles of parabolic potentials

Abstract

We study the magnetic susceptibility of an ensemble of noninteracting 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 commensurate classical frequencies, being negligible elsewhere. We derive approximate analytical formulas for the susceptibility and compare the results with numerical calculations. © 1998 The American Physical Society.