Wiedemann-Franz law for massless Dirac fermions with implications for graphene

TL;DR

This paper extends the understanding of the Wiedemann-Franz law to massless Dirac fermions in graphene, predicting enhanced thermal conductivity at low temperatures and comparing theoretical results with numerical simulations.

Contribution

It adapts the Wiedemann-Franz law derivation for Dirac fermions and predicts enhanced thermal conductivity in graphene at sub-kelvin temperatures, contrasting with previous hydrodynamic explanations.

Findings

Enhanced thermal conductivity predicted at sub-kelvin temperatures.

Comparison of theoretical predictions with numerical Landauer-Büttiker results.

Implication that interactions are negligible at very low temperatures.

Abstract

In the 2016 experiment by Crossno et al. [Science 351, 1058 (2016)], 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, what 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-B\"uttiker formalism for rectangular and disk-shaped (Corbino) devices in ballistic graphene is also provided.