Violation of the Wiedemann-Franz law in clean graphene layers

Abstract

The Wiedemann-Franz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electron-electron (e-e) interactions are strong. In ultra-clean conductors, however, large deviations from the standard form of the law are expected, due to the fact that e-e interactions affect the two conductivities in radically different ways. Thus, the standard Wiedemann-Franz ratio between the thermal and the electric conductivity is reduced by a factor $1+\tau /{\tau }_{\mathrm{th}}^{\mathrm{ee}}$, where $1/\tau$ is the momentum relaxation rate, and $1/{\tau }_{\mathrm{th}}^{\mathrm{ee}}$ is the relaxation time of the thermal current due to e-e collisions. Here we study the density and temperature dependence of $1/{\tau }_{\mathrm{th}}^{\mathrm{ee}}$ in the important case of doped, clean single layers of graphene, which exhibit record-high thermal conductivities. We show that at low temperature $1/{\tau }_{\mathrm{th}}^{\mathrm{ee}}$ is $8/5$ of the quasiparticle decay rate. We also show that the many-body renormalization of the thermal Drude weight coincides with that of the Fermi velocity.

6 pages, 5 appendices (13 pages)

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• Non-equilibrium dynamics of photo-excited electrons in graphene: collinear scattering, Auger processes, and the impact of screening
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