Penetration of hot electrons through a cold disordered wire

TL;DR

This paper investigates how high-energy electrons penetrate a strongly disordered, cold wire, revealing a transmission distribution with rare high-transmission events and a reduced decay rate compared to elastic tunneling.

Contribution

It introduces a new distribution function for electron transmission in disordered wires, accounting for inelastic hopping and rare high-transmission configurations.

Findings

Typical transmission remains exponentially small in wire length.

Average transmission is dominated by rare disorder configurations.

The decay decrement is reduced compared to elastic tunneling.

Abstract

We study a penetration of an electron with high energy E<<T through strongly disordered wire of length L<<a (a being the localization length). Such an electron can loose, but not gain the energy, when hopping from one localized state to another. We have found a distribution function for the transmission coefficient t. The typical t remains exponentially small in L/a, but with the decrement, reduced compared to the case of direct elastic tunnelling. The distribution function has a relatively strong tail in the domain of anomalously high t; the average <t>~(a/L)^2 is controlled by rare configurations of disorder, corresponding to this tail.