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

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, ${\tau }_{\mathrm{E}}$. 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 (${\tau }_{\mathrm{E}}=0$) to classical behaviour (${\tau }_{\mathrm{E}}=\infty$) 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.

20 pages (version3: fixed error in sect. VC - results unchanged) - Contents: Tunnelling in semiclassics (3pages), Weak-localization (5pages), Shot-noise (5pages)

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• Semiclassical treatment of quantum chaotic transport with a tunnel barrier
• Dephasing in the semiclassical limit is system-dependent
• Superconductivity-induced macroscopic resonant tunneling
• Temperature and magnetic-field dependence of the quantum corrections to the conductance of a network of quantum dots
• Combinatorial problems in the semiclassical approach to quantum chaotic transport
• Crossover of thermal to shot noise in chaotic cavities
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Exponentially small quantum correction to conductance
• Quantum transport in chaotic cavities with tunnel barriers
• Electronic transport in three-terminal chaotic systems with a tunnel barrier