Recovery of the persistent current induced by the electron-electron interaction in mesoscopic metallic rings

TL;DR

This paper investigates how electron-electron interactions affect persistent currents in mesoscopic metallic rings, showing that interactions can enhance current in the presence of weak disorder, with results supported by perturbation theory.

Contribution

It introduces a Hamiltonian model including disorder and Hubbard interaction, demonstrating the recovery of persistent current strength through electron-electron interactions.

Findings

Interactions increase persistent current in weakly disordered rings.

Averaging over ring lengths diminishes the primary Fourier component of the current.

Perturbation theory accurately describes correlations for moderate interaction strength.

Abstract

Persistent currents in mesoscopic metallic rings induced by static magnetic fields are investigated by means of a Hamiltonian which incorporates diagonal disorder and the electron-electron interaction through a Hubbard term ($U$). Correlations are included up to second order perturbation theory which is shown to work accurately for $U$ of the order of the hopping integral. If disorder is not very strong, interactions increase the current up to near its value for a clean metal. Averaging over ring lengths eliminates the first Fourier component of the current and reduces its value, which remains low after interactions are included.