Correntes persistentes: uma aboradagem supersimétrica

Abstract

Starting from a simple model for the persistent current on a clean one-dimensional ring in the presence of an homogeneous magnetic field, we show the properties of that current in the ideal case, without disorder, for both a plane and a M¨obius-like geometry. We also show how to treat disorder and calculate the averaged current for an ensemble of isolated mesoscopic, quasi one-dimensional metal rings with a weak disorder. We model the disorder by means of Random Matrix Theory, which combined with supersymmetry techniques, has made possible to obtain the averaged persistent current. We show the equivalence between the IWZ model, which is discrete, and the continuous model, by calculating the current exactly for the zero mode and perturbatively for higher order modes.We also calculate the averaged persistent current for a ring with an embedded quantum dot with disorder. We conclude that the very presence of the quantum dot increases significantly the current amplitude but does not alter the symmetry and periodicity of the current with the external flux.