Conductance Correlations Near Integer Quantum Hall Transitions

TL;DR

This paper investigates conductance correlations near integer quantum Hall transitions, revealing how critical phenomena influence conductance fluctuation behavior in disordered mesoscopic systems.

Contribution

It presents the first analysis of conductance correlations at quantum Hall transitions, highlighting the role of critical phenomena in these correlations.

Findings

Conductance correlation function behavior is affected by critical properties.

The study links static and dynamic critical phenomena to conductance fluctuations.

First exploration of conductance correlations near quantum Hall critical points.

Abstract

In a disordered mesoscopic system, the typical spacing between the peaks and the valleys of the conductance as a function of Fermi energy $E_F$ is called the conductance energy correlation range $E_c$. Under the ergodic hypothesis, the latter is determined by the half-width of the ensemble averaged conductance correlation function: $F= < \delta g(E_F) \delta g(E_F + \Delta E) >$. In ordinary diffusive metals, $E_c\sim D/L^2$, where $D$ is the diffusion constant and $L$ is the linear dimension of the phase-coherent sample. However, near a quantum phase transition driven by the location of the Fermi energy $E_F$, the above picture breaks down. As an example of the latter, we study, for the first time, the conductance correlations near the integer quantum Hall transitions of which $E_F$ is a critical coupling constant. We point out that the behavior of $F$ is determined by the interplay between the static and the dynamic properties of the critical phenomena.