The Lorenz ratios (L = κ/σT) of the Dirac-fermion systems were numerically calculated using the Boltzmann transport theory, where κ, σ and T are the thermal conductivity, electrical conductivity and absolute temperature, respectively. The bipolar-diffusion effect, which enhances the electronic thermal conductivity κe in intrinsic semiconductors, was introduced to account for the reported giant L of a Dirac-fermion system, graphene at its neutrality condition. It was found that the calculations qualitatively reproduce the experimentally observed gate-voltage dependence of σ , S and κe by considering the energy dependence of the relaxation time; and the electron- and hole-puddles. The calculated value of L amounts to (2?4)L0, where L0= 2.45 × 10-8 W・Ω・K-2 is Sommerfeld value of Wiedemann-Franz law, while the reported ?? of graphene reaches about 20L0 at most. The rather large L (=3.7L0) was also observed for another Dirac-fermion system, α-(BEDT-TTF)2I3 (BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene) by measuring simultaneously the change in the σ and κ associated with its charge-ordering transition at about 135 K for a single crystal. Another explanation of the giant L on the basis of quantum hydrodynamics is also introduced briefly, while both the bipolar-diffusion and quantum-hydrodynamic mechanisms are not exclusive to each other.
Keywords:Wiedemann–Franz law, Lorenz ratio, Dirac fermion, graphene, organic conductor, α-(BEDT-TTF)2I3
Publication Date: 2017-07-25