Variable-range hopping in quasi-one-dimensional electron crystals

TL;DR

This paper investigates how impurities affect electron transport in quasi-one-dimensional electron crystals, revealing a transition from Efros-Shklovskii to Mott variable-range hopping laws as impurity concentration varies.

Contribution

It introduces a detailed theoretical model describing impurity effects on electron transport and charge excitations in quasi-1D electron crystals, including a novel Coulomb gap and nonmonotonic conductivity dependence.

Findings

Conductivity follows Efros-Shklovskii law at high impurity concentrations.

A new linear-in-energy Coulomb gap is identified due to anisotropic screening.

At low impurity concentrations, the Mott law dominates the transport behavior.

Abstract

We study the effect of impurities on the ground state and the low-temperature dc transport in a 1D chain and quasi-1D systems of many parallel chains. We assume that strong interactions impose a short-range periodicicity of the electron positions. The long-range order of such an electron crystal (or equivalently, a $4 k_F$ charge-density wave) is destroyed by impurities. The 3D array of chains behaves differently at large and at small impurity concentrations $N$. At large $N$, impurities divide the chains into metallic rods. The low-temperature conductivity is due to the variable-range hopping of electrons between the rods. It obeys the Efros-Shklovskii (ES) law and increases exponentially as $N$ decreases. When $N$ is small, the metallic-rod picture of the ground state survives only in the form of rare clusters of atypically short rods. They are the source of low-energy charge excitations. In the bulk the charge excitations are gapped and the electron crystal is pinned collectively. A strongly anisotropic screening of the Coulomb potential produces an unconventional linear in energy Coulomb gap and a new law of the variable-range hopping $-\ln\sigma \sim (T_1 / T)^{2/5}$. $T_1$ remains constant over a finite range of impurity concentrations. At smaller $N$ the 2/5-law is replaced by the Mott law, where the conductivity gets suppressed as $N$ goes down. Thus, the overall dependence of $\sigma$ on $N$ is nonmonotonic. In 1D, the granular-rod picture and the ES apply at all $N$. The conductivity decreases exponentially with $N$. Our theory provides a qualitative explanation for the transport in organic charge-density wave compounds.