Transport in disordered systems often occurs via variable range hopping (VRH) in the dilute carrier density limit, where electrons hop between randomly distributed localized levels. We study the nonequilibrium transport by a uniform DC electric field on a one-dimensional (1D) insulating tight-binding chain with the on-site disorder, using a disordered-lattice calculation and the coherent potential approximation. We develop a theory of electric-field-assisted VRH as a mechanism for nonlinear transport in a disordered chain. Our disordered-lattice calculations of the electron propagation distance and the electron mobility determine the range of VRH as $\mathrm{\Delta }<W\lesssim 2\mathrm{\Delta }$ in the gap $\mathrm{\Delta }$. We further propose a nonlinear scaling of the conductivity by an electric field by extending Mott's VRH. The nonlinear conductivity of an electronic lattice model follows the scaling law $\sigma \left(E\right)\propto exp[-{(E_0/E)}^{\nu }]$, with the exponent $\nu =\frac{1}{3}$ in 1D for VRH. We also discuss the experimental relevance of temperature-dependent nonlinear current-voltage relation.

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• Anderson localization
• Electrical conductivity
• Hopping transport
• Transport phenomena
• Weak localization
• Disordered systems
• Nonequilibrium Green's function