Semiclassical transport in nearly symmetric quantum dots I: symmetry-breaking in the dot

TL;DR

This paper uses semiclassical theory to analyze how spatial symmetries in quantum dots influence transport properties, revealing how symmetry-breaking affects interference effects and conductance fluctuations.

Contribution

It provides a detailed semiclassical analysis of symmetry effects in quantum dot transport, including the impact of various symmetry-breaking mechanisms and the universal behavior of the symmetry-asymmetry crossover.

Findings

Symmetry-induced interference effects are destroyed by boundary deformations larger than an electron wavelength.

Partial boundary deformations smaller than a lead-width only partially reduce interference effects.

The symmetry-asymmetry crossover follows a universal dependence on a specific asymmetry parameter.

Abstract

We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry or four-fold symmetry. In this work - the first of a pair of articles - we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot's internal dynamics. The second article addresses symmetry-breaking by displacement of the leads. Using semiclassics, we identify the origin of the symmetry-induced interference effects that contribute to weak-localization corrections and universal conductance fluctuations. For perfect spatial symmetry, we recover results previously found using the random-matrix theory conjecture. We then go on to show how the results are affected by asymmetries in the dot, magnetic fields and decoherence. In particular, the symmetry-asymmetry crossover is found to be described by a universal dependence on an asymmetry parameter $\gamma_{asym}$. However, the form of this parameter is very different depending on how the dot is deformed away from spatial symmetry. Symmetry-induced interference effects are completely destroyed when the dot's boundary is globally deformed by less than an electron wavelength. In contrast, these effects are only reduced by a finite amount when a part of the dot's boundary smaller than a lead-width is deformed an arbitrarily large distance.