Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos

TL;DR

This paper explores electron transport in nano-wires with surface disorder under magnetic fields, revealing giant localization lengths and dynamical tunneling effects due to regular-chaotic phase space interactions.

Contribution

It provides analytical and numerical analysis of mode-specific localization lengths and their relation to dynamical tunneling in disordered nano-wires with magnetic fields.

Findings

Exponential divergence of localization lengths in the quantum-classical crossover.

Mode-specific localization lengths are well-defined and analytically estimable.

Transmission probabilities exhibit intricate structures explained by dynamical tunneling.

Abstract

We investigate electron quantum transport through nano-wires with one-sided surface roughness in the presence of a perpendicular magnetic field. Exponentially diverging localization lengths are found in the quantum-to-classical crossover regime, controlled by tunneling between regular and chaotic regions of the underlying mixed classical phase space. We show that each regular mode possesses a well-defined mode-specific localization length. We present analytic estimates of these mode localization lengths which agree well with the numerical data. The coupling between regular and chaotic regions can be determined by varying the length of the wire leading to intricate structures in the transmission probabilities. We explain these structures quantitatively by dynamical tunneling in the presence of directed chaos.