Variable-range hopping in 2D quasi-1D electronic systems

TL;DR

This paper develops a semi-phenomenological theory for variable-range hopping in 2D quasi-1D systems, revealing unique Coulomb gaps and VRH laws due to anisotropy and dielectric properties.

Contribution

It introduces a new theoretical framework for VRH in anisotropic 2D quasi-1D systems, deriving Coulomb gaps and unconventional VRH laws with specific exponents.

Findings

Unusual Coulomb gaps due to anisotropy and dielectric properties.

Derived exponential dependence of conductivity and current in different regimes.

Identified unique VRH laws with specific exponents for 2D quasi-1D systems.

Abstract

A semi-phenomenological theory of variable-range hopping (VRH) is developed for two-dimensional (2D) quasi-one-dimensional (quasi-1D) systems such as arrays of quantum wires in the Wigner crystal regime. The theory follows the phenomenology of Efros, Mott and Shklovskii allied with microscopic arguments. We first derive the Coulomb gap in the single-particle density of states, $g(\epsilon)$, where $\epsilon$ is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity in the linear (L), {\it i.e.} $\sigma(T) \sim \exp[-(T_L/T)^{\gamma_L}]$, and current in the non-linear (NL), {\it i.e.} $j({\mathcal E}) \sim \exp[-({\mathcal E}_{NL} / \mathcal{E})^{\gamma_{NL}}]$, response regimes (${\mathcal E}$ is the applied electric field). Due to the strong anisotropy of the system and its peculiar dielectric properties we show that unusual, with respect to known results, Coulomb gaps open followed by unusual VRH laws, {\it i.e.} with respect to the disorder-dependence of $T_L$ and ${\mathcal E}_{NL}$ and the values of $\gamma_L$ and $\gamma_{NL}$.