Effect Of Coulomb Interactions on The Amplitude Of Persistent Currents In One Dimensional Disordered Mesoscopic Metallic Rings

TL;DR

This study investigates how Coulomb interactions and disorder influence persistent currents in one-dimensional metallic rings, revealing that interactions can both suppress and enhance current depending on filling, with a metal-insulator transition at half-filling.

Contribution

It provides a detailed numerical analysis of electron interactions and disorder effects on persistent currents in small disordered rings using the Lanczos algorithm.

Findings

Interactions suppress persistent current at half-filling due to localization.

Disorder combined with interactions can enhance persistent current away from half-filling.

A metal-insulator transition occurs at half-filling as Coulomb repulsion increases.

Abstract

Persistent current is a small but perpetual electric current that flows in metallic rings in the absence of any applied source. We compute the persistent currents of one-dimensional disordered metallic rings of interacting electrons in the presence of impurity on lattices up to 8-sites at half-filling and also away from half-filling using the Lanczos algorithm. For the case of half-filling, we observe that both interaction and disorder suppress the amplitude of the persistent currents by localizing the electrons. However, in the presence of disorder and away from half-filling, the Coulomb interaction is observed to enhance the persistent current. Furthermore, in the half-filled case, there is a transition from metal to insulator as U is increased significantly. In addition, shifting away from half-filling, the system is observed to remain in the metallic state irrespective of the value of the Coulomb repulsion (U). The observations are quite in agreement with the results from other techniques.