Transport in chaotic quantum dots: effects of spatial symmetries which interchange the leads

TL;DR

This paper studies how spatial symmetries that interchange leads in chaotic quantum dots influence electronic transport, revealing that such symmetries cause the transmission eigenvalue density to be N-independent and eliminate weak localization effects.

Contribution

It demonstrates, using random matrix theory and numerical simulations, that lead-interchanging symmetries in chaotic quantum dots fundamentally alter conductance and shot noise behavior.

Findings

Transmission eigenvalue density is N-independent in symmetric systems

Weak localization correction to conductance vanishes with lead-interchanging symmetry

Shot noise suppression factor F is independent of N in these systems

Abstract

We investigate the effect of spatial symmetries on phase coherent electronic transport through chaotic quantum dots. For systems which have a spatial symmetry that interchanges the source and drain leads, we find in the framework of random matrix theory that the density of the transmission eigenvalues is indepedent of the number of channels N in the leads. As a consequence, the weak localization correction to the conductance vanishes in these systems, and the shot noise suppression factor F is independent of N. We confirm this prediction by means of numerical calculations for stadium billiards with various lead geometries. These calculations also uncover transport signatures of partially preserved symmetries.