Spectral correlations in disordered mesoscopic metals and their relevance for persistent currents

TL;DR

This paper investigates spectral correlations in disordered mesoscopic metals using the Lanczos method, revealing flux-dependent variance behavior and implications for persistent currents.

Contribution

It applies the Lanczos method to analyze spectral variance in disordered rings, highlighting limitations of existing models at higher energies.

Findings

Flux-dependent variance matches known Feynman diagram at small E

Extrapolation fails at energies where density of states varies significantly

Discusses implications for persistent current phenomena

Abstract

We use the Lanczos method to calculate the variance of the number of energy levels in an energy window of width E below the Fermi energy for non-interacting disordered electrons on a thin three-dimensional ring threaded by an Aharonov-Bohm flux . We find that for small E the flux-dependent part of the variance is well described by a well-known Feynman diagram involving two Cooperons. However, 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.