Orbital Magnetic Susceptibility of Disordered Mesoscopic Systems

TL;DR

This paper investigates the orbital magnetic susceptibility of disordered two-dimensional mesoscopic systems at low temperatures, revealing strong temperature and statistical ensemble effects, and discusses theoretical, numerical, and interaction aspects.

Contribution

It provides the first analysis of susceptibility behavior below the mean level spacing, highlighting ensemble dependence and the role of gauge invariance in theoretical modeling.

Findings

Strong temperature dependence of susceptibility below mean level spacing

Ensemble dependence of average and typical susceptibilities

Numerical simulations support theoretical predictions at higher temperatures

Abstract

In this paper we study the orbital weak-field susceptibility of two-dimensional diffusive mesoscopic systems. For the previously unstudied regime of temperatures lower than the mean level spacing we find unexpected strong temperature as well as statistical ensemble dependence of the average and typical susceptibilities. An explanation for these features is given in terms of the long tail of the zero-temperature susceptibility distribution, including the parametric form of the temperature dependence. For temperatures higher than the mean level spacing we calculate the difference between the true canonical ensemble and the effective grand-canonical ensemble. We also perform numerical simulations, which seem to generally confirm previous theoretical predictions for this regime of temperatures, although some difficulties arise. The important role of gauge-invariance, especially how it renders Random Matrix Theory inapplicable to the study of orbital susceptibility, is discussed. We conclude by considering interaction effects, giving a new interpretation to previous results as well as demonstrating the influence of in-plane magnetic field on the interaction-induced orbital response.