Distribution of the resistance of nanowires with strong impurities

TL;DR

This paper provides a theoretical analysis of how strong impurities affect the electrical resistance distribution in finite quantum wires, revealing a Gumbel distribution with finite-size effects and temperature-dependent behaviors.

Contribution

It introduces a detailed statistical description of resistance fluctuations due to strong impurities, including finite-size corrections and temperature effects, which were not previously characterized.

Findings

Resistance distribution follows a Gumbel distribution with finite-size corrections.

Finite-size corrections decay as 1/ln L with wire length.

At higher temperatures, the resistance behavior and corrections change significantly.

Abstract

Motivated by recent experiments on nanowires and carbon nanotubes, we study theoretically the effect of strong, point-like impurities on the linear electrical resistance R of finite length quantum wires. Charge transport is limited by Coulomb blockade and cotunneling. ln R is slowly self-averaging and non Gaussian. Its distribution is Gumbel with finite-size corrections which we compute. At low temperature, the distribution is similar to the variable range hopping (VRH) behaviour found long ago in doped semiconductors. We show that a result by Raikh and Ruzin does not apply. The finite-size corrections decay with the length L like 1/ln L. At higher temperatures, this regime is replaced by new laws and the shape of the finite-size corrections changes strongly: if the electrons interact weakly, the corrections vanish already for wires with a few tens impurities.