Enhancement of persistent current in metal rings by correlated disorder

Abstract

We study analytically the effect of a correlated random potential on thepersistent current in a one-dimensional ring threaded by a magnetic fluxϕ, using an Anderson tight-binding model. In our model, the system ofN = 2M atomic sites of the ring is assumed to be partitioned intoM pairs of nearest-neighbour sites (dimers). While the individual atomic site energies areassumed to be identically distributed Gaussian variables with autocorrelation parameterε02, the dimer site energies are chosen to be correlated with a Gaussian strengthα2<ε02. For this system we obtain the exact flux-dependent energy levels to second order inthe random site energies, using an earlier exact transfer matrix perturbationtheory. These results are used to study the mean persistent current generated byNe≤N spinless electronsoccupying the Ne lowest levels of the flux-dependent energy band at zero temperature. Detailed analyses arecarried out in the case of low filling of the energy band () and for a half-filled band (Ne = N/2), for magnetic fluxes −1/2<ϕ/ϕ0<1/2. In the half-filled band case, the uncorrelated part of the disorder reduces thepersistent current while the correlated part enhances it, in such a way that forα2<ε02/2 the current decreases with the disorder, while forα2>ε02/2 it increases with it. Also, while showing a specific dependence onthe flux, the disorder effect has the same dependence on the parity ofNe as the pure system-free electron current. In contrast, at low filling of the energy band, thedisorder-induced effect in the persistent current depends critically on the parity: due toa peculiar dependence on the flux, it yields a reduction of the current for oddNe and an enhancementof it for even Ne. The observability of the effects of weak correlated disorder on persistent current in thehalf-filled band case is restricted to ring sizes in the nanoscale range, for which nomeasurements presently exist.