Suppression of weak localization and enhancement of noise by tunneling in semiclassical chaotic transport

Abstract

We add simple tunneling 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 tunneling rates and arbitrary (positive) Ehrenfest time ${\ensuremath{\tau}}_{E}$. For all Ehrenfest times, we show that the shot noise is enhanced by the tunneling, while the weak localization is suppressed. In the opaque barrier limit (small tunneling rates with large lead widths, such that the Drude conductance remains finite), the weak localization goes to zero linearly with the tunneling rate, while the Fano factor of the shot noise remains finite but becomes independent of the Ehrenfest time. The crossover from random matrix theory behavior $({\ensuremath{\tau}}_{E}=0)$ to classical behavior $({\ensuremath{\tau}}_{E}=\ensuremath{\infty})$ goes exponentially with the ratio of the Ehrenfest time to the paired-path survival time. The paired-path 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.