Mesoscopic conductance fluctuations in dirty quantum dots with single channel leads

TL;DR

This paper investigates the distribution of conductance fluctuations in quantum dots with single channel leads, revealing non-Gaussian behavior and strong dependence on time-reversal symmetry, especially near the Anderson transition.

Contribution

It provides a detailed analysis of conductance fluctuation distributions in mesoscopic quantum dots with single channel leads, highlighting their non-Gaussian nature and symmetry dependence, using diagrammatic and non-perturbative methods.

Findings

Distribution is non-Gaussian with strong symmetry dependence.

Lognormal tails appear for weak disorder, becoming more pronounced near the Anderson transition.

Results align with non-perturbative techniques in the absence of time-reversal symmetry.

Abstract

We consider a distribution of conductance fluctuations in quantum dots with single channel leads and continuous level spectra and we demonstrate that it has a distinctly non-Gaussian shape and strong dependence on time-reversal symmetry, in contrast to an almost Gaussian distribution of conductances in a disordered metallic sample connected to a reservoir by broad multi-channel leads. In the absence of time-reversal symmetry, our results obtained within the diagrammatic approach coincide with those derived within non-perturbative techniques. In addition, we show that the distribution has lognormal tails for weak disorder, similar to the case of broad leads, and that it becomes almost lognormal as the amount of disorder is increased towards the Anderson transition.