Heat conduction and Wiedemann-Franz Law in disordered Luttinger Liquids

Abstract

We consider heat transport in a Luttinger liquid (LL) with weak disorder and study the Lorenz number for this system. We start at a high-$T$ regime, and calculate both the electrical and thermal conductivities using a memory function approach. The resulting Lorenz number $L$ is independent of $T$ but depends explicitly on the LL exponents. Lowering $T$, however, allows for a renormalization of the LL exponents from their bare values by disorder, causing a violation of the Wiedemann-Franz law. Finally, we extend the discussion to quantum wire systems and study the wire size dependence of the Lorenz number.

4 pages, 1 eps figure; Changes made to address Referees' comments

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• Thermal transport measurements of individual multiwalled nanotubes
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• Heat transport by lattice and spin excitations in the spin chain compounds SrCuO_2 and Sr_2CuO_3
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