Power-laws in one-dimensional transport: Luttinger liquid
 or disorder?

Michael Fogler
 University of California at San Diego

When the conductance of a 1D wire shows a power-law dependence on temperature T and voltage V, it is often attributed to Luttinger liquid or related interaction effects. For this explanation to hold the power-law exponents in T and V must be equal. This condition is systematically violated in long wires (typically, longer than a few micron), where the thermal exponent is much larger than the voltage one. To shed light on the physics involved we study a theoretical model of a long 1D wire with a finite density of strong random impurities that convert it into a chain of weakly-coupled quantum dots. Electron transport in such a system is shown to exhibit a rich dependence on V and T due to the interplay of sequential and co-tunneling. Remarkably, we indeed find a broad parameter range where the conductance exhibits an algebraic dependence on T and V with unequal exponents, in agreement with the experiments. At much lower temperatures the conductance eventually crosses over to the stretched exponential laws typical of the variable-range hopping.  Reference: M. M. Fogler, S. V. Malinin, T. Nattermann, "Coulomb blockade and transport in a chain of one-dimensional quantum dots," Phys. Rev. Lett. 97 (2006).