Semiclassical theory of the interaction correction to the conductance of antidot arrays

TL;DR

This paper develops a semiclassical theory for the interaction correction to conductance in ballistic antidot arrays, highlighting the role of Ehrenfest time in quantum interference effects and their suppression.

Contribution

It introduces a semiclassical framework incorporating Ehrenfest time to analyze interaction corrections in ballistic conductors, extending previous diffusive models.

Findings

Ehrenfest time causes exponential suppression of conductance correction when large.

Interaction correction can change sign near / au_E temperature scale.

Explicit dependence on Ehrenfest time is derived for quasi-1D and 2D antidot arrays.

Abstract

Electron-electron interactions are responsible for a correction to the conductance of a diffusive metal, the "Altshuler-Aronov correction" $\delta G_{AA}$. Here we study the counterpart of this correction for a ballistic conductor, in which the electron motion is governed by chaotic classical dynamics. In the ballistic conductance, the Ehrenfest time $\tau_{E}$ enters as an additional time scale that determines the magnitude of quantum interference effects. The Ehrenfest time effectively poses a short-time threshold for the trajectories contributing to the interaction correction. As a consequence, $\delta G_{AA}$ becomes exponentially suppressed if the Ehrenfest time is larger than the dwell time or the inverse temperature. We discuss the explicit dependence on Ehrenfest time in quasi-one and two-dimensional antidot arrays. For strong interactions, the sign of $\delta G_{AA}$ may change as a function of temperature for temperatures in the vicinity of $\hbar/\tau_{E}$.