Signatures of Chaos in the Statistical Distribution of Conductance Peaks in Quantum Dots

TL;DR

This paper derives analytical expressions for conductance peak distributions in irregular quantum dots using random matrix theory, accounting for various symmetries and channel correlations, and validates results with a chaotic billiard model.

Contribution

It provides the first comprehensive analytical framework for conductance peak distributions in chaotic quantum dots considering multiple channels and symmetry conditions.

Findings

Analytical distributions match numerical chaotic billiard results.

Distributions depend on number of channels and their correlations.

Results applicable to systems with conserved or broken time-reversal symmetry.

Abstract

Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained using random matrix theory and are valid in general for any number of non-equivalent and correlated channels, assuming that the underlying classical dynamic of the electrons in the dot is chaotic or that the dot is weakly disordered. The results are expressed in terms of the channel correlation matrix which for chaotic systems is given in closed form for both point-like contacts and extended leads. We study the dependence of the distributions on the number of channels and their correlations. The theoretical distributions are in good agreement with those computed in a dynamical model of a chaotic billiard.