Persistent current of relativistic electrons on a Dirac ring in presence of impurities

TL;DR

This paper investigates how relativistic electrons on a one-dimensional ring exhibit persistent currents affected by impurities, revealing behaviors that differ from non-relativistic systems, especially with multiple scatterers.

Contribution

It provides a detailed analysis of persistent currents in relativistic electron rings with impurities, highlighting differences from non-relativistic cases and the effects of scatterer configurations.

Findings

Persistent current decreases with a single scatterer, similar to non-relativistic systems.

Finite persistent current persists even with strong scattering potentials.

Random scatterer configurations can enhance the average persistent current as scatterer number increases.

Abstract

We study the behavior of persistent current of relativistic electrons on a one dimensional ring in presence of attractive/repulsive scattering potentials. In particular, we investigate the persistent current in accordance with the strength as well as the number of the scattering potential. We find that in presence of single scatterer the persistent current becomes smaller in magnitude than the scattering free scenario. This behaviour is similar to the non-relativistic case. Even for a very strong scattering potential, finite amount of persistent current remains for a relativistic ring. In presence of multiple scatterer we observe that the persistent current is maximum when the scatterers are placed uniformly compared to the current averaged over random configurations. However if we increase the number of scatterers, we find that the random averaged current increases with the number of scatterers. The latter behaviour is in contrast to the non-relativistic case.