Conductance Fluctuations of Disordered Mesoscopic Devices with Many Weakly-Coupled Probes

TL;DR

This paper studies conductance fluctuations in disordered mesoscopic devices with many weakly-coupled probes, revealing deviations from traditional models and providing detailed analysis of ensemble-averaged conductance and autocorrelation functions.

Contribution

It introduces a theoretical framework for analyzing conductance with many weak contacts and derives a modified autocorrelation function showing significant deviations from Lorentzian behavior.

Findings

Ensemble-averaged conductance follows the Hauser-Feshbach formula.

Conductance autocorrelation deviates from Lorentzian form.

Autocorrelation function exhibits a negative tail.

Abstract

The conductance coefficients of disordered mesoscopic devices with $n$ probes are investigated within the noninteracting electron approximation at zero temperature. The probes are eliminated from the theoretical description at the expense of introducing nonlocal boundary conditions at the position of the contacts. Conductors with a large number of weak contacts are analyzed in detail. The ensemble-averaged conductance coefficients are in this case given by the so-called Hauser-Feshbach formula $g_{ab} \sim p_a p_b$ where $p_a$ is the probability for emission of an electron into lead $a$. The conductance energy autocorrelation function is shown to deviate significantly from the conventional Lorentzian form and to have a negative tail.