Low-temperature nonequilibrium transport in a Luttinger liquid

TL;DR

This paper investigates the nonlinear conductance of a Luttinger liquid at low temperatures, revealing a crossover from a power-law to a universal quadratic temperature dependence in the presence of an external voltage.

Contribution

It provides a nonperturbative calculation of conductance for a Luttinger liquid near the special interaction parameter g=1/2, including a leading-log summation approach.

Findings

Conductance exhibits a crossover from T^{2/g-2} to T^2 law with increasing voltage.

Nonperturbative analysis valid for g close to 1/2.

Universal T^2 behavior emerges at high voltages.

Abstract

The temperature-dependent nonlinear conductance for transport of a Luttinger liquid through a barrier is calculated in the nonperturbative regime for $g=1/2-\epsilon$, where $g$ is the dimensionless interaction constant. To describe the low-energy behavior, we perform a leading-log summation of all diagrams contributing to the conductance which is valid for $|\epsilon| << 1$. With increasing external voltage, the asymptotic low-temperature behavior displays a turnover from the $T^{2/g-2}$ to a universal $T^2$ law.