Enhancement of Persistent Current in Metal Rings by Correlated Disorder

TL;DR

This paper analytically investigates how correlated disorder in a one-dimensional metal ring enhances the persistent current, contrasting with uncorrelated disorder which reduces it, with detailed results for various electron fillings.

Contribution

It provides an exact second-order perturbation analysis of flux-dependent energy levels in a correlated disordered ring, revealing conditions under which persistent current is enhanced.

Findings

Correlated disorder enhances persistent current compared to uncorrelated disorder.

Half-filled band shows a flux-dependent enhancement of persistent current.

At low filling, the effect depends on electron number parity, reducing current for odd and increasing for even N_e.

Abstract

We study analytically the effect of a correlated random potential on the persistent current in a one-dimensional ring threaded by a magnetic flux $\phi$, using an Anderson tight-binding model. In our model, the system of $N=2M$ atomic sites of the ring is assumed to be partitioned into $M$ pairs of identical nearest-neighbour sites (dimers). The site energies for different dimers are taken to be uncorrelated gaussian variables. For this system we obtain the exact flux-dependent energy levels to second order in the random site energies, using an earlier exact transfer matrix perturbation theory. These results are used to study the mean persistent current generated by $N_e\leq N$ spinless electrons occupying the $N_e$ lowest levels of the flux-dependent energy band at zero temperature. Detailed analyses are carried out in the limit $1\ll N_e\ll N$ and for a half-filled band ($N_e=N/2$), for magnetic fluxes $-1/2 <\phi/\phi_0<1/2$. While the uncorrelated disorder leads to a reduction of the persistent current, the disorder correlation acts to enhance it. In particular, in the half-filled band case the correlated disorder leads to a global flux-dependent enhancement of persistent current which has the same form for even and odd $N_e$. At low filling of the energy band the effect of the disorder on the persistent current is found to depend on the parity of $N_e$: the correlated disorder yields a reduction of the current for odd $N_e$ and an enhancement of the current for even $N_e$.