A microscopic kinetic-theory explanation of why the Wiedemann-Franz law fails in Dirac-fluid systems. Solving the Boltzmann transport equation in the relaxation-time approximation for the massless electron-hole plasma of graphene and, in parallel, for the ultra-relativistic quark-gluon plasma, the Lorenz ratio in the hydrodynamic low-net-carrier-density regime is shown to be proportional to the enthalpy per net charge carrier, forcing it away from the universal Lorenz number. At high carrier density graphene crosses over to Fermi-liquid metallic behavior that restores the law, and the computed graphene result matches experiment in the Dirac-fluid regime.
A comparative kinetic-theory study of why the Wiedemann-Franz law - the expectation that the Lorenz ratio (thermal conductivity divided by the product of electrical conductivity and temperature) equa…