Semiclassical transport in nearly symmetric quantum dots II: symmetry-breaking due to asymmetric leads

TL;DR

This paper investigates how asymmetric leads affect symmetry-induced quantum interference effects in nearly symmetric quantum dots, revealing suppression patterns and confirming results through a random-matrix theory model.

Contribution

It provides a semiclassical analysis of symmetry-breaking effects on quantum transport and introduces a random-matrix model to validate the theoretical predictions.

Findings

Symmetry-induced contributions are suppressed by asymmetric leads.

Contributions to conductance fluctuations are suppressed quadratically compared to weak localization.

The random-matrix model confirms the theoretical suppression patterns.

Abstract

In this work - the second of a pair of articles - we consider transport through spatially symmetric quantum dots with leads whose widths or positions do not obey the spatial symmetry. We use the semiclassical theory of transport to find the symmetry-induced contributions to weak localization corrections and universal conductance fluctuations for dots with left-right, up-down, inversion and four-fold symmetries. We show that all these contributions are suppressed by asymmetric leads, however they remain finite whenever leads intersect with their images under the symmetry operation. For an up-down symmetric dot, this means that the contributions can be finite even if one of the leads is completely asymmetric. We find that the suppression of the contributions to universal conductance fluctuations is the square of the suppression of contributions to weak localization. Finally, we develop a random-matrix theory model which enables us to numerically confirm these results.