Effective-field-theory approach to persistent currents

TL;DR

This paper employs an effective-field-theory framework to analyze persistent currents in disordered metal rings, confirming Gaussian behavior at lowest order and showing higher-order effects are negligible, thus challenging existing explanations for experimental observations.

Contribution

It introduces a systematic nonlinear sigma model approach to calculate higher-order moments of persistent currents, demonstrating their minimal impact and questioning previous interaction-based explanations.

Findings

Gaussian distribution of persistent currents at lowest order

Higher-order contributions are negligible compared to Gaussian results

Experimental persistent currents cannot be explained solely by interacting diffusons and cooperons

Abstract

Using an effective-field-theory (nonlinear sigma model) description of interacting electrons in a disordered metal ring enclosing magnetic flux, we calculate the moments of the persistent current distribution, in terms of interacting Goldstone modes (diffusons and cooperons). At the lowest or Gaussian order we reproduce well-known results for the average current and its variance that were originally obtained using diagrammatic perturbation theory. At this level of approximation the current distribution can be shown to be strictly Gaussian. The nonlinear sigma model provides a systematic way of calculating higher-order contributions to the current moments. An explicit calculation for the average current of the first term beyond Gaussian order shows that it is small compared to the Gaussian result; an order-of-magnitude estimation indicates that the same is true for all higher-order contributions to the average current and its variance. We therefore conclude that the experimentally observed magnitude of persistent currents cannot be explained in terms of interacting diffusons and cooperons.