Conductance fluctuations in chaotic systems with tunnel barriers

TL;DR

This paper investigates how conductance fluctuations in quantum chaotic systems with tunnel barriers depend on Ehrenfest time and transparency, revealing conditions where quantum coherence effects can increase in the semiclassical limit.

Contribution

It introduces a semiclassical theory showing a nonmonotonous, sinusoidal dependence of conductance variance on transparency and Ehrenfest time, challenging previous assumptions about quantum coherence decay.

Findings

Conductance fluctuations show a linear Ehrenfest time dependence.

Fluctuations can increase above universal values for low transparency.

Numerical simulations confirm the semiclassical predictions.

Abstract

Quantum effects are expected to disappear in the short-wavelength, semiclassical limit. As a matter of fact, recent investigations of transport through quantum chaotic systems have demonstrated the exponential suppression of the weak localization corrections to the conductance and of the Fano factor for shot-noise when the Ehrenfest time exceeds the electronic dwell time. On the other hand, conductance fluctuations, an effect of quantum coherence, retain their universal value in the limit of the ratio of Ehrenfest time over dwell time to infinity, when the system is ideally coupled to external leads. Motivated by this intriguing result we investigate conductance fluctuations through quantum chaotic cavities coupled to external leads via (tunnel) barriers of arbitrary transparency. Using the trajectory-based semiclassical theory of transport, we find a linear Ehrenfest time-dependence of the conductance variance showing a nonmonotonous, sinusoidal behavior as a function of the transperancy. Most notably, we find an increase of the conductance fluctuations with the Ehrenfest time, above their universal value, for the transparency less than 0.5. These results, confirmed by numerical simulations, show that, contrarily to the common wisdom, effects of quantum coherence may increase in the semiclassical limit, under special circumstances.