Variable-range cotunneling and non-Ohmic transport in a chain of one-dimensional quantum dots

A 1D wire with a finite density of strong random impurities is modeled as a chain of weakly coupled quantum dots. The resistance of such a system is shown to exhibit a rich dependence on bias voltage $V$ and temperature $T$ due to the interplay of Coulomb blockade, Luttinger-liquid, and disorder effects. At low $T$ and $V$ electrons propagate through the wire by means of thermal activation and a multiple cotunneling. In this regime the resistance is limited by the ``breaks'': randomly occurring clusters of dots with a special length distribution pattern that inhibits the transport no matter how the activation and tunneling are combined. As $T$ or $V$ increases, the breaks become shorter and less resistive. The resistance can exhibit a (stretched) exponential and a quasi power-law dependence on $T$ and $V$ depending on the position at the $T$-$V$ diagram. Unlike the case of a single impurity the effect of $T$ and $eV$ is not symmetric. The Ohmic resistance of a macroscopic wire is always dictated by breaks not single impurities. Our results imply that the power-laws reported in several recent transport measurements of one-dimensional systems may reflect not only intrinsic Luttinger parameters but also impurity distribution statistics.