Thermal transport in a Luttinger liquid

TL;DR

This paper investigates thermal transport properties in a one-dimensional interacting electron system modeled as a Luttinger liquid, revealing how impurities and interactions modify conductance and thermopower.

Contribution

It provides a detailed analysis of thermal conductance and thermopower in Luttinger liquids, including impurity effects and deviations from the Wiedemann-Franz law.

Findings

Lorenz number depends on interaction parameter g and diverges for g<1/2 at low T.

Thermopower remains linear in temperature despite interactions.

Impurity effects significantly alter thermal transport properties.

Abstract

We study thermal transport in a one-dimensional (1d) interacting electron gas, employing the Luttinger liquid model. Both thermal conductance and thermopower are analyzed for a pure 1d gas and with impurities. The universal ratio of electrical to thermal conductance in a Fermi-liquid - the Wiedeman-Franz law - is modified, whereas the thermopower is still linear in temperature. For a single impurity the Lorenz number is given by $L(T \rightarrow 0) = 3L_0/(2g+g^2)$ - with $L_0$ the Fermi liquid value - and the conductance $1/2 < g < 1$. For $g<1/2$ the Lorenz number {\it diverges} as $T \rightarrow 0$. Possible relevance to thermal transport in conducting polymer systems is discussed.