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arXiv:cond-mat/0602374 · Physical Review B

Wiedemann-Franz law in the SU(N) Wolff model

Balázs Dóra

Published Oct 4, 2006• 5 citations
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Abstract

We study the electrical and thermal transport through the SU$(N)$ Wolff model with the use of bosonization. The Wilson ratio reaches unity as $N$ grows to infinity. The electric conductance is dominated by the charge channel, and decreases monotonically with increasing interaction. The thermal conductivity enhances in the presence of a local Hubbard $U$. The Wiedemann-Franz law is violated; the Lorentz number depends strongly on the interaction parameter, which can be regarded as a manifestation of spin-charge separation.

DOI
10.1103/physrevb.74.161101

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We show that in weakly disordered Luttinger liquids close to a commensurate filling the ratio of thermal conductivity $\ensuremath{\kappa}$ and electrical conductivity $\ensuremath{\sigma}$ can deviate strongly from the Wiedemann-Franz law valid for Fermi liquids scattering from impurities. In the regime where the umklapp scattering rate ${\ensuremath{\Gamma}}_{U}$ is much larger than the impurity scattering rate ${\ensuremath{\Gamma}}_{\mathrm{imp}}$, the Lorenz number $L=\ensuremath{\kappa}/(\ensuremath{\sigma}T)$ rapidly changes from very large values $L\ensuremath{\sim}{\ensuremath{\Gamma}}_{U}/{\ensuremath{\Gamma}}_{\mathrm{imp}}\ensuremath{\gg}1$ at the commensurate point to very small values $L\ensuremath{\sim}{\ensuremath{\Gamma}}_{\mathrm{imp}}/{\ensuremath{\Gamma}}_{U}\ensuremath{\ll}1$ for a slightly doped system. This surprising behavior is a consequence of approximate symmetries existing even in the presence of strong umklapp scattering.
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We propose that the recently observed violation of the Wiedemann-Franz law in the normal state of underdoped cuprates is caused by spin-charge separation and dynamical chiral symmetry breaking in a (2+1)(2+1)(2+1)-dimensional system consisting of massless Dirac fermions, charged bosons, and a gauge field. While the d-wave spinon gap vanishes at the Fermi points, the nodal fermions acquire a finite mass due to strong gauge fluctuations. This mass provides a gap below which no free fermions can be excited. This implies that there is not a residual linear term for the thermal conductivity, in good agreement with experiments. Other physical implications of the chiral symmetry breaking are also discussed.