Enhanced Transmission Through Disordered Potential Barrier

TL;DR

This paper analytically investigates how weak disorder affects quantum tunneling through a potential barrier, revealing that disorder can increase both conductance and resistance on average.

Contribution

It develops a diagrammatic analytical approach and derives the transmission coefficient distribution for tunneling through disordered barriers, highlighting the counterintuitive effects of disorder.

Findings

Disorder increases average tunneling conductance.

Disorder also increases average tunneling resistance.

The distribution of transmission coefficients is derived and analyzed.

Abstract

Effect of weak disorder on tunneling through a potential barrier is studied analytically. A diagrammatic approach based on the specific behavior of subbarrier wave functions is developed. The problem is shown to be equivalent to that of tunneling through rectangular barriers with Gaussian distributed heights. The distribution function for the transmission coefficient $T$ is derived, and statistical moments $\left< T^n\right>$ are calculated. The surprising result is that in average disorder increases both tunneling conductance and resistance.