Screening of persistent currents in mesoscopic metal rings

TL;DR

This study investigates how Coulomb interactions influence persistent currents in disordered mesoscopic metal rings using a simplified self-consistent Hartree approach, revealing reduced particle number fluctuations but unchanged energy level fluctuations.

Contribution

It introduces a numerical analysis of Coulomb effects on persistent currents in mesoscopic rings using a simplified Hartree model, highlighting specific fluctuation behaviors.

Findings

Variance of total particle number is strongly reduced by Coulomb interactions.

Variance of energy level counts near Fermi energy remains unaffected.

Results agree with predictions of the random-phase approximation.

Abstract

The effect of the Coulomb-interaction on persistent currents in disordered mesoscopic metal rings threaded by a magnetic flux $\phi$ is studied numerically. We use the simplest form of ``self-consistent'' Hartree theory, where the spatial variations of the self-consistent Hartree potential are ignored. In this approximation the self-consistent Hartree energies are simply obtained by diagonalizing the non-interacting system via the Lanczos method and then calculating the (disorder-dependent) particle number on the ring self-consistently. In the diffusive regime we find that the variance of the total particle number is strongly reduced, in agreement with the prediction of the random-phase approximation. On the other hand, the variance of the number of energy levels in a small interval below the Fermi energy is not affected by the Coulomb interaction.