Multifractal Magnetoconductance Fluctuations in Mesoscopic Systems

TL;DR

This study applies multifractal analysis to magnetoconductance data in mesoscopic systems, revealing increased multifractality in the quantum regime and linking it to magnetic field-induced correlations.

Contribution

It introduces a novel multifractal detrended fluctuation analysis of magnetoconductance, demonstrating stronger multifractality in quantum regimes and quantifying it via q-Gaussian distributions.

Findings

Multifractality is present in all studied mesoscopic systems.

Multifractality intensifies in the quantum conduction regime.

Distribution of conductance increments fits q-Gaussian functions.

Abstract

We perform a multifractal detrended fluctuation analysis of the magnetoconductance data of two standard types of mesoscopic systems: a disordered nanowire and a ballistic chaotic billiard, with two different lattice structures. We observe in all cases that multifractality is generally present and that it becomes stronger in the quantum regime of conduction, i.e., when the number of open scattering channels is small. We argue that this behavior originates from correlations induced by the magnetic field, which can be characterized through the distribution of conductance increments in the corresponding "stochastic time series," with the magnetic field playing the role of a fictitious time. More specifically, we show that the distributions of conductance increments are well fitted by $q$ Gaussians and that the value of the parameter $q$ is a useful quantitative measure of multifractality in magnetoconductance fluctuations.