Transport properties of a quantum wire in the presence of impurities and long-range Coulomb forces

TL;DR

This paper studies how long-range Coulomb forces and impurities affect the transport properties of quantum wires, revealing dominant 4k_F scattering and the influence of two key length scales on the system's behavior.

Contribution

It introduces a detailed analysis of transport in Wigner crystal quantum wires with impurities, highlighting the roles of long-range interactions and disorder, and compares quantum and classical behaviors.

Findings

Transport dominated by 4k_F impurity scattering.

Identification of pinning length and Coulomb interaction length.

Frequency and temperature dependence of conductivity derived.

Abstract

One-dimensional electron systems interacting with long-range Coulomb forces (quantum wires) show a Wigner crystal structure. We investigate in this paper the transport properties of such a Wigner crystal in the presence of impurities. Contrary to what happens when only short-range interactions are included, the system is dominated by $4 k_F$ scattering on the impurities. There are two important length scales in such a problem: one is the pinning length above which the (quasi-)long-range order of the Wigner crystal is destroyed by disorder. The other length $\xi_{cr}$ is the length below which Coulomb interactions are not important and the system is behaving as a standard Luttinger liquid with short-range interactions. We obtain the frequency and temperature dependence of the conductivity. We show that such a system is very similar to a classical charge density wave pinned by impurities, but with important differences due to quantum fluctuations and long-range Coulomb interactions. Finally we discuss our results in comparison with experimental systems.