Conductance Correlations Near Integer Quantum Hall Transitions

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.

4 pages, 4 figures, minor corrections, to appear in Phys. Rev. Lett

References in corpus (1)

• Conductances, Conductance Fluctuations, and Level Statistics on the Surface of Multilayer Quantum Hall States

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