Magnetoconductance Autocorrelation Function for Few--Channel Chaotic Microstructures

TL;DR

This paper analyzes the autocorrelation function of conductance in few-channel chaotic microstructures using random matrix theory and supersymmetry, revealing non-analytic behavior at zero magnetic field difference.

Contribution

It provides analytical calculations for small channel numbers and compares results with semiclassical theory, highlighting non-analytic features for few-channel systems.

Findings

Autocorrelation function exhibits non-analytic behavior at t=0 for small M.

Analytical asymptotic expansion derived for small t using supersymmetry.

Numerical simulations support analytical results for small M.

Abstract

Using the Landauer formula and a random matrix model, we investigate the autocorrelation function of the conductance versus magnetic field strength for ballistic electron transport through few-channel microstructures with the shape of a classically chaotic billiard coupled to ideal leads. This function depends on the total number M of channels and the parameter t which measures the difference in magnetic field strengths. Using the supersymmetry technique, we calculate for any value of M the leading terms of the asymptotic expansion for small t. We pay particular attention to the evaluation of the boundary terms. For small values of M, we supplement this analytical study by a numerical simulation. We compare our results with the squared Lorentzian suggested by semiclassical theory and valid for large M. For small M, we present evidence for non--analytic behavior of the autocorrelation function at t = 0.