Heat conduction and Wiedemann-Franz law in disordered Luttinger liquids
Department of Physics, University of Guelph -
Guelph, Ontario, Canada N1G 2W1
2 LPTENS, CNRS UMR8549 - 24 rue Lhomond, 75231 Paris Cedex 05, France
Accepted: 19 August 2002
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.
PACS: 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) / 72.15.Eb – Electrical and thermal conduction in crystalline metals and alloys / 72.15.Nj – Collective modes (e.g., in one-dimensional conductors)
© EDP Sciences, 2002