Interaction correction to the conductance of a ballistic conductor

TL;DR

This paper studies how electron-electron interactions modify conductance in ballistic, chaotic conductors, specifically analyzing the Altshuler-Aronov correction in a double quantum dot, revealing exponential suppression under certain conditions.

Contribution

It extends the understanding of interaction corrections to conductance from disordered to ballistic chaotic systems, focusing on the role of Ehrenfest time.

Findings

Exponential suppression of the correction when Ehrenfest time exceeds dwell time or inverse temperature.

Analysis of the Altshuler-Aronov correction in a double quantum dot as a model system.

Identification of conditions under which the correction becomes negligible.

Abstract

In disordered metals, electron-electron interactions are the origin of a small correction to the conductivity, the "Altshuler-Aronov correction". Here we investigate the Altshuler-Aronov correction of a conductor in which the electron motion is ballistic and chaotic. We consider the case of a double quantum dot, which is the simplest example of a ballistic conductor in which the Altshuler-Aronov correction is nonzero. The fact that the electron motion is ballistic leads to an exponential suppression of the correction if the Ehrenfest time is larger than the mean dwell time or the inverse temperature.