Persistent Currents in Finite‐Width Mesoscopic Rings. The Role of the Interchannel Coupling and of the Electron‐Electron Interaction

Abstract

AbstractThe persistent currents of few interacting electrons with spin in mesoscopic rings are calculated in the ballistic regime. The energy bands of the finite‐width multi‐channel ring are calculated with the transfer‐matrix method including the interchannel coupling induced by the impurity scattering, and the electron—electron interaction. It is shown that in the case of a narrow‐width ring the electron—electron interaction and the confining potential build a rotating Wigner crystal of the few electrons, where the relative angular motions are harmonic oscillations if the impurity potential is weak. As long as this picture remains valid, the persistent current is not influenced by the electron—electron interaction. It is shown that the width of the mesoscopic ring is the critical parameter for the influence of the electron—electron interaction on the persistent current. With increasing width of the mesoscopic ring, the electron—electron interaction decreases the amplitude of the persistent current at low temperatures and increases it at higher temperatures. Further, for a finite width of the mesoscopic ring the interchannel coupling becomes important, which results in the occurrence of higher harmonics in the persistent current.