Transport in Luttinger Liquids with Strong Impurities

TL;DR

This paper investigates the transport properties of Luttinger liquids with strong impurities, revealing multiple crossover regimes in conductivity behavior driven by temperature and electric field variations.

Contribution

It introduces an instanton approach to calculate tunnel current, identifying crossover regimes and constructing a comprehensive global phase diagram for impurity effects.

Findings

Conductivity exhibits variable range hopping at low T and E.

Power law behavior emerges at intermediate T and E.

Multiple crossover lines define the global transport regime diagram.

Abstract

The tunnel current of a Luttinger liquid with a finite density of strong impurities is calculated using an instanton approach. For very low temperatures $T$ or electric fields $E$ the (nonlinear) conductivity is of variable range hopping (VRH) type as for weak pinning. For higher temperatures or fields the conductivity shows power law behavior corresponding to a crossover from multi- to single-impurity tunneling. For even higher $T$ and not too strong pinning there is a second crossover to weak pinning. The determination of the position of the various crossover lines both for strong and weak pinning allows the construction of the global regime diagram.