Non-Ohmic Variable-Range Hopping Transport in One-Dimensional Conductors

We investigate theoretically the effect of a finite electric field on the resistivity of a disordered one-dimensional system in the variable-range hopping regime. We find that at low fields the transport is inhibited by rare fluctuations in the random distribution of localized states that create high-resistance breaks in the hopping network. As the field increases, the breaks become less resistive. In strong fields the breaks are overrun and the electron distribution function is driven far from equilibrium. The logarithm of the resistance initially shows a simple exponential drop with the field, followed by a logarithmic dependence, and finally, by an inverse square-root law.

Figure 1

(a) Ohmic and (b) non-Ohmic breaks. The dots represent hopping sites. The horizontal thin lines are the links of the optimal path carrying the current across the breaks. The width of each break is $a{u}_I/2$.

Figure 2

Plots of $E(x)$ (thin line), $E_{<}(x)$ (thick line) and the optimal path (dotted line). Ticks and dots represent lattice sites and their energy levels, respectively; $x_I=9b$ is assumed.