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

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(ε), where ε is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity in the linear (L), i.e. σ(T) ∼exp [-(T<Subscript>L</Subscript>/T)<Superscript>γL</Superscript>], and current in the non-linear (NL), i.e. <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$j({\mathcal E}) \sim \exp[-({\mathcal E}_{NL} / \mathcal{E})^{\gamma_{NL}}]$</EquationSource> </InlineEquation>, response regimes (<InlineEquation ID="Equ2"> <EquationSource Format="TEX">${\mathcal E}$</EquationSource> </InlineEquation> 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, i.e. with respect to the disorder-dependence of T<Subscript>L</Subscript> and <InlineEquation ID="Equ3"> <EquationSource Format="TEX">${\mathcal E}_{NL}$</EquationSource> </InlineEquation> and the values of γ<Subscript>L</Subscript> and γ<Subscript>NL</Subscript>. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006