Enhancement of persistent current in metal rings by correlated disorder

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 φ, 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 nearest-neighbour sites (dimers). While the individual atomic site energies are assumed to be identically distributed gaussian variables with autocorrelation parameter ε 2 0 , the dimer site energies are chosen to be correlated with a gaussian strength α 2 < ε 2 0 . 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 ≤ N spinless electrons occupying the N e lowest levels of the flux-dependent energy band at zero temperature. Detailed analyzes are carried out in the case of low filling of the energy band (1 ≪ N e ≪ N ) and for a half-filled band (N e = N/2), for magnetic fluxes −1/2 < φ/φ 0 < 1/2.In the half-filled band case, the uncorrelated part of the disorder reduces the persistent current while the correlated part enhances it, in such a way that for α 2 < ε 2 0 /2 the current decreases with the disorder, while for α 2 > ε 2 0 /2 it increases with it. Also, while showing a specific dependence on the flux, the disorder effect has the same dependence on the parity of N e as the pure system free electron current. In contrast, at low filling of the energy-band, the disorder induced effect in the persistent current depends critically on the parity: due to a peculiar dependence on the flux, it yields a reduction of the current for odd N e and an enhancement of it for even N e . The observability of the effects of weak correlated disorder on persistent current in the half-filled band case is restricted to ring sizes in the nanoscale range, for which no measurements presently exist.

Large system asymptotics of persistent currents in mesoscopic quantum rings

“…Interest in persistent current phenomena remains strong both experimentally [4,5,6,7,8,9,10,11] and theoretically [12,13,14,15,16,17,18,19,20,21,22,23,24,25]. The main reason for this is the fact that there still is a discrepancy between experiment and theory.…”

Analytic study of persistent current in a two-channel disordered mesoscopic ring

“…In particular, Sedrakyan and Ossipov [17] have recently studied delocalized states in a disordered two-chain ladder model with a interchain correlation which is analogous to (19). For completeness sake we mention that the effect of short-range disorder correlation on persistent current has been studied recently by us in one dimension, using a simple generalization of the Anderson model [18] in which one defines a subset of pairs of nearest-neighbour sites whose energies are correlated while the energies of all other pairs are uncorrelated.…”

“…This generalizes our earlier treatment [8] of the effect of disorder on persistent current in a one-dimensional ring. The latter [8] has also been applied recently for studying the effect of short-range correlated disorder on persistent current in one dimension [18].…”

“…using ( 30), (30a) and (33). Since according to (24) eigenvalues of the disordered two-channel ring correspond to values of the partial traces which are independent of the disorder, it follows from (36) that the first order effect in the eigenvalues in the correlated site energies model (18)(19) is…”

Realization of a Nonlocal Persistent Current Qubit with the Help of Majorana Bound States

“…As a result, the persistent current is always an odd function of the magnetic flux J p ðÀÈÞ ¼ ÀJ p ðÈÞ, and the slope of the persistent current dJ p =dÈ for a small flux can be either negative or positive, which defines the persistent current being diamagnetic and paramagnetic, respectively. 29) Also, when various physical mechanisms are taken into account, such as quantum impurities, 30) electron correlation, 31) spinorbit effect, 32) disorders, 33) or new materials, 34,35) the persistent current shows intricate and interesting properties. Moreover, in addition to the isolated quantum ring, the current properties in the coupled-ring structure have attracted much interest.…”