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

Abstract

Electron-electron interactions are responsible for a correction to the conductance of a diffusive metal, the “Altshuler-Aronov correction” δGAA. 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 τE 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, δGAA 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 δGAA may change as a function of temperature for temperatures in the vicinity of ℏ/τE.