Critical Conductance of a Mesoscopic System: Interplay of the Spectral and Eigenfunction Correlations at the Metal-Insulator Transition

TL;DR

This paper investigates how the critical conductance in a mesoscopic system scales with size at the metal-insulator transition, linking spectral and eigenfunction correlations to conductance corrections.

Contribution

It establishes a relationship between conductance corrections and spectral/eigenfunction correlations, providing a new theoretical framework for understanding the Anderson transition.

Findings

Conductance correction scales as L^{-y} and relates to spectral correlations.

The correction can be expressed via quantum return probability.

The critical exponent y equals the eigenfunction correlation exponent η.

Abstract

We study the system-size dependence of the averaged critical conductance $g(L)$ at the Anderson transition. We have: (i) related the correction $\delta g(L)=g(\infty)-g(L)\propto L^{-y}$ to the spectral correlations; (ii) expressed $\delta g(L)$ in terms of the quantum return probability; (iii) argued that $y=\eta$ -- the critical exponent of eigenfunction correlations. Experimental implications are discussed.