Wiedemann-Franz Law for Massless Dirac Fermions with Implications for Graphene

In the 2016 experiment by Crossno et al. the electronic contribution to the thermal conductivity of graphene was found to violate the well-known Wiedemann-Franz (WF) law for metals. At liquid nitrogen temperatures, the thermal to electrical conductivity ratio of charge-neutral samples was more than 10 times higher than predicted by the WF law, which was attributed to interactions between particles leading to collective behavior described by hydrodynamics. Here, we show, by adapting the handbook derivation of the WF law to the case of massless Dirac fermions, that significantly enhanced thermal conductivity should appear also in few- or even sub-kelvin temperatures, where the role of interactions can be neglected. The comparison with numerical results obtained within the Landauer-Buttiker formalism for rectangular and disk-shaped (Corbino) devices in ballistic graphene is also provided.

Automated summary

The 2016 experiment by Crossno et al. found that the thermal conductivity of graphene violates the WF law at low temperatures, attributed to interactions between particles. Even at temperatures of few- or sub-kelvin, significantly enhanced thermal conductivity should appear, even when neglecting the role of interactions. Numerical results obtained within the Landauer-Buttiker formalism also support this finding.