Non-monotonic disorder-induced enhanced tunneling

TL;DR

This paper analytically investigates quantum tunneling through disordered barriers, revealing a non-monotonic relationship between disorder strength and transmission, with maximum transmission at intermediate disorder levels.

Contribution

It provides a quantitative analysis of disorder-induced enhanced tunneling, extending prior phenomenological observations with detailed theoretical insights.

Findings

Transmission increases with weak disorder

Maximum transmission occurs at crossover from weak to strong disorder

Transmission decreases at strong disorder

Abstract

The quantum-mechanical transmission through a disordered tunnel barrier is investigated analytically in the following regime: (correlation range of the random potential) << (penetration length) << (barrier length). The mean and/or the width of the potential can either be constant, or vary slowly across the barrier. The typical transmission is found to be a non-monotonic function of the disorder strength, increasing at weak disorder, reaching a maximum in the crossover from weak to strong disorder, and decreasing at strong disorder. This work provides a quantitative analysis of the phenomenon of disorder-induced enhanced tunneling, put forward by Freilikher et al. [Phys. Rev. E {\bf 51}, 6301 (1995); B {\bf 53}, 7413 (1996)].