Persistent currents in one- and two-dimensional mesoscopic rings: Influence of the Coulomb interaction, impurity scattering, and periodic potential.

Abstract

We address the discrepancies between measured values of the persistent current in mesoscopic devices in the diffusive regime, and theoretical expectations. We investigate analytically and numerically the influence of the (screened) Coulomb interaction between electrons, of the impurity scattering of electrons, and of the periodic lattice potential acting on each electron, on the persistent current in mesoscopic rings at zero temperature. Our analytical arguments apply to one and two dimensions while the numerical simulation is restricted to one- and two-channel rings. We pay particular attention to the symmetry properties of the many-body wave functions but find that these do not qualitatively influence our results. Without Coulomb interaction, the impurity potential strongly suppresses the current both in the absence and in the presence of a periodic potential. We show that the Coulomb interaction very effectively counteracts the impurity suppression of the persistent current. This is our central result. There is evidence that the Coulomb interaction restores the impurity-suppressed average persistent current to a value close to the one in the absence of impurity scattering. This is a strong effect even for an interaction strength which is quite small compared to realistic estimates of the screened Coulomb interaction. Moreover, we show that in the absence of one-body potentials, the persistent current is exactly [one-dimensional (1D)] or essentially (2D) the same without and with the Coulomb interaction. A periodic potential alone does not affect the persistent current; when combined with the Coulomb interaction, it tends to reduce the current.