SPECTRAL CORRELATIONS IN DISORDERED MESOSCOPIC METALS AND THEIR RELEVANCE FOR PERSISTENT CURRENTS

Abstract

We use the Lanczos method to calculate the variance σ2(E, ϕ) of the number of energy levels in an energy window of width E below the Fermi energy for noninteracting disordered electrons on a thin three-dimensional ring threaded by an Aharonov–Bohm flux ϕ. We confirm numerically that for small E the flux-dependent part of σ2(E, ϕ) is well described by the Altshuler–Shklovskii-diagram involving two Cooperons. However, in the absence of electron–electron interactions this result cannot be extrapolated to energies E where the energy-dependence of the average density of states becomes significant. We discuss consequences for persistent currents and argue that for the calculation of the difference between the canonical- and grand canonical current it is crucial to take the electron–electron interaction into account.