Conductance length autocorrelation in quasi one-dimensional disordered wires

TL;DR

This paper calculates the conductance length correlation function in quasi-one-dimensional disordered wires using a Fokker-Planck approach, revealing different behaviors in metallic and localized regimes.

Contribution

It provides a comprehensive calculation of the conductance length correlation function valid for all lengths and regimes, including the metallic and localized limits.

Findings

Correlation function is a squared Lorentzian in the metallic limit.

Exponential decay of correlation in the localized regime.

Correlation length scales with L in the metallic regime and saturates at the localization length.

Abstract

Employing techniques recently developed in the context of the Fokker--Planck approach to electron transport in disordered systems we calculate the conductance length correlation function $< \delta g(L) \delta g(L+\Delta L) >$ for quasi 1d wires. Our result is valid for arbitrary lengths L and $\Delta L$. In the metallic limit the correlation function is given by a squared Lorentzian. In the localized regime it decays exponentially in both L and $\Delta L$. The correlation length is proportional to L in the metallic regime and saturates at a value approximately given by the localization length $\xi$ as $L\gg\xi$.