Multifractal and Ergodic Properties of Conductance Fluctuations under Strong Disorder

TL;DR

This study explores how conductance fluctuations in disordered mesoscopic systems transition from non-ergodic to ergodic behavior with increasing disorder, revealing persistent multifractality and the dominance of distributional effects in strong disorder regimes.

Contribution

It demonstrates the transition of conductance fluctuations from non-ergodic to ergodic regimes and analyzes the persistence of multifractality across these regimes using multifractal analysis.

Findings

Conductance fluctuations transition from non-ergodic to ergodic with increasing disorder.

Multifractality persists in both regimes but becomes insensitive to shuffling in the ergodic regime.

Results are robust against changes in lead geometry.

Abstract

Understanding the stochastic properties of conductance fluctuations in disordered mesoscopic systems is fundamental to quantum transport. In this work, we investigate the multifractal and ergodic properties of the fictitious time series of conductance in two-dimensional tight-binding models under varying Anderson disorder. Using standard multifractal analysis, we show that conductance fluctuations exhibit a transition from non-ergodic to ergodic behavior as the disorder strength increases, as evidenced by the decay of the conductance correlation function. Remarkably, multifractality persists in both regimes; however, it becomes insensitive to shuffling in the strong-disorder (ergodic) regime, suggesting that distributional effects dominate temporal organization. On the contrary, in the weakly disordered (non-ergodic) regime, long-range correlations play a significant role. These findings are robust against changes in lead geometry (asymmetric vs. symmetric). Our results provide new insights into the interplay between ergodicity, multifractality, and rare events in disordered quantum transport.