Electron-electron interactions in one- and three-dimensional mesoscopic disordered rings: a perturbative approach

TL;DR

This paper studies how small electron-electron interactions affect persistent currents in disordered mesoscopic rings across 1D and 3D, revealing interaction-dependent paramagnetic or diamagnetic contributions and their impact on current magnitude.

Contribution

It provides a first-order perturbative analysis of electron-electron interactions in disordered rings, highlighting the different effects of contact and nearest neighbor interactions in various dimensions.

Findings

Hubbard interaction increases typical current and causes paramagnetism.

Nearest neighbor interaction decreases current and causes diamagnetism in 1D.

Results are supported by numerical simulations and analytical justification.

Abstract

We have computed persistent currents in a disordered mesoscopic ring in the presence of small electron-electron interactions, treated in first order perturbation theory. We have investigated both a contact (Hubbard) and a nearest neighbour interaction in 1D and 3D. Our results show that a repulsive Hubbard interaction produces a paramagnetic contribution to the average current (whatever the dimension) and increases the value of the typical current. On the other hand, a nearest neighbour repulsive interaction results in a diamagnetic contribution in 1D and paramagnetic one in 3D, and tends to decrease the value of the typical current in any dimension. Our study is based on numerical simulations on the Anderson model and is justified analytically in the presence of very weak disorder. We have also investigated the influence of the amount of disorder and of the statistical (canonical or grand-canonical) ensemble.