Suppression of weak-localization (and enhancement of noise) by tunnelling in semiclassical chaotic transport

TL;DR

This paper extends semiclassical theory of quantum chaotic transport by incorporating tunnelling effects, revealing how tunnelling suppresses weak-localization and enhances shot-noise across various tunnelling rates and Ehrenfest times.

Contribution

It introduces a method to analyze tunnelling effects in quantum chaotic transport, deriving explicit formulas for conductance corrections and shot-noise, and explaining the physical origin of weak-localization suppression.

Findings

Weak-localization is suppressed by tunnelling.

Shot-noise is enhanced by tunnelling.

Weak-localization vanishes linearly with tunnelling rate in the opaque barrier limit.

Abstract

We add simple tunnelling effects and ray-splitting into the recent trajectory-based semiclassical theory of quantum chaotic transport. We use this to derive the weak-localization correction to conductance and the shot-noise for a quantum chaotic cavity (billiard) coupled to $n$ leads via tunnel-barriers. We derive results for arbitrary tunnelling rates and arbitrary (positive) Ehrenfest time, $\tau_{\rm E}$. For all Ehrenfest times, we show that the shot-noise is enhanced by the tunnelling, while the weak-localization is suppressed. In the opaque barrier limit (small tunnelling rates with large lead widths, such that Drude conductance remains finite), the weak-localization goes to zero linearly with the tunnelling rate, while the Fano factor of the shot-noise remains finite but becomes independent of the Ehrenfest time. The crossover from RMT behaviour ($\tau_{\rm E}=0$) to classical behaviour ($\tau_{\rm E}=\infty$) goes exponentially with the ratio of the Ehrenfest time to the paired-paths survival time. The paired-paths survival time varies between the dwell time (in the transparent barrier limit) and half the dwell time (in the opaque barrier limit). Finally our method enables us to see the physical origin of the suppression of weak-localization; it is due to the fact that tunnel-barriers ``smear'' the coherent-backscattering peak over reflection and transmission modes.