Interaction-induced corrections to conductance and thermopower in quantum wires

TL;DR

This paper investigates how weak interactions among spinless electrons in one-dimensional quantum wires lead to corrections in conductance and thermopower, emphasizing the importance of three-particle collisions and exchange effects beyond the Luttinger-liquid approximation.

Contribution

It introduces a scattering approach to analyze interaction effects on transport in quantum wires, highlighting the role of exchange terms in three-particle scattering processes.

Findings

Interaction-induced corrections depend on three-particle collisions.

Transitions at the band bottom are exponentially suppressed at low temperatures.

Exchange terms significantly influence scattering amplitudes.

Abstract

We study transport properties of weakly interacting spinless electrons in one-dimensional single channel quantum wires. The effects of interaction manifest as three-particle collisions due to the severe constraints imposed by the conservation laws on the two-body processes. We focus on short wires where the effects of equilibration on the distribution function can be neglected and collision integral can be treated in perturbation theory. We find that interaction-induced corrections to conductance and thermopower rely on the scattering processes that change number of right- and left-moving electrons. The latter requires transition at the bottom of the band which is exponentially suppressed at low temperatures. Our theory is based on the scattering approach that is beyond the Luttinger-liquid limit. We emphasize the crucial role of the exchange terms in the three-particle scattering amplitude that was not discussed in the previous studies.