Conductance correlations near integer quantum Hall transitions

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 similar to (h) over bar 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. [S0031-9007(98)07253-6].