A covariant Boltzmann equation with one relaxation time yields L/L0 = (3/pi^2)(h/(k_BT))^2 for both graphene and QGP, so the Wiedemann-Franz law fails as the net carrier density approaches zero.
Electronic hydrodynamics in graphene
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In this paper I report a pedagogical derivation of the unconventional electronic hydrodynamics in graphene on the basis of the kinetic theory. While formally valid in the weak coupling limit, this approach allows one to derive the unconventional hydrodynamics in the system which is neither Galilean- nor Lorentz-invariant, such that hydrodynamic equations can not be inferred from symmetry arguments. I generalize earlier work to include external magnetic fields and give explicit expressions for dissipative coefficients, the shear viscosity and electrical conductivity. I also compare the resulting theory with relativistic hydrodynamics.
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On the Wiedemann-Franz law violation in Graphene and quark-gluon plasma systems
A covariant Boltzmann equation with one relaxation time yields L/L0 = (3/pi^2)(h/(k_BT))^2 for both graphene and QGP, so the Wiedemann-Franz law fails as the net carrier density approaches zero.