Electrical and thermal transport in the quasi-atomic limit of coupled Luttinger liquids

TL;DR

This paper develops a model for quasi-one-dimensional materials composed of coupled Luttinger liquids, analyzing their electrical and thermal transport properties, revealing deviations from Fermi liquid behavior due to strong interactions.

Contribution

It introduces a new theoretical framework for understanding transport in coupled Luttinger liquids in the quasi-atomic limit, with explicit integral expressions and power law dependencies.

Findings

Transport coefficients follow specific power laws with temperature.

Violation of Wiedemann-Franz law observed, with Lorenz number exceeding Fermi liquid value.

Interaction strength influences the degree of deviation from classical behavior.

Abstract

We introduce a new model for quasi one-dimensional materials, motivated by intriguing but not yet well-understood experiments that have shown two-dimensional polymer films to be promising materials for thermoelectric devices. We consider a two-dimensional material consisting of many one-dimensional systems, each treated as a Luttinger liquid, with weak (incoherent) coupling between them. This approximation of strong interactions within each one-dimensional chain and weak coupling between them is the "quasi-atomic limit." We find integral expressions for the (interchain) transport coefficients, including the electrical and thermal conductivities and the thermopower, and we extract their power law dependencies on temperature. Luttinger liquid physics is manifested in a violation of the Wiedemann-Franz law; the Lorenz number is larger than the Fermi liquid value by a factor between $\gamma^2$ and $\gamma^4$, where $\gamma\geq 1$ is a measure of the electron-electron interaction strength in the system.