Electron-electron interaction and the persistent current in a quantum ring

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Abstract
We have studied the effect of electron-electron interaction on the magnetic moment (associated with the persistent current) of electrons in a quantum ring. We have introduced a model where the electron makes a circular motion in a parabolic confinement simulating a quantum ring which is subjected to a perpendicular magnetic field. The electron states in such a ring with and without the Coulomb interaction are then investigated. We have also explored the limits of narrow and wide rings. Our detailed calculations of the energy spectrum where the interelectron interactions are also included indicate that when the electrons occupy the states of only the lowest Landau band, the interaction merely shifts the spectrum to higher energy and its effect on magnetization is insignificant. The result can be understood as entirely due to conservation of the angular momentum. A qualitative estimate for a large system where electrons also occupy higher Landau bands indicates that the Coulomb interaction mixes some of the states resulting in a rapid increase in the magnetization.