Wiedemann-Franz law in graphene

TL;DR

This paper reexamines the failure of the Wiedemann-Franz law in graphene, proposing that disorder-induced gap opening and bipolar diffusion, rather than non-Fermi liquid behavior, could explain experimental observations.

Contribution

It offers a Fermi liquid-based explanation for the Wiedemann-Franz law violation in graphene, challenging the non-Fermi liquid interpretation and emphasizing disorder effects.

Findings

Gap opening at the Dirac point may explain observations.

Finite-temperature bipolar diffusion influences transport.

Disorder and phonons play significant roles in graphene's thermal and electrical transport.

Abstract

We analyze a well-known experimental work [J. Crossno et al., Science 351, 1058 (2016)] which reported on the failure of the Wiedemann-Franz law in graphene at $T\sim 10$-$100\,\mathrm{K}$, attributing this failure to the non-Fermi liquid nature of the Dirac fluid associated with undoped intrinsic graphene. In spite of serious theoretical efforts, the reported observations remain unexplained. Our detailed quantitative analysis based on Fermi liquid considerations, which apply to extrinsic doped graphene, establishes that one possible explanation for the reported observations is the opening of a gap at the Dirac point, induced perhaps by the boron nitride substrate. We suggest that more experiments are necessary to resolve the issue, and we believe that the experiment may not actually have anything to do with Dirac fluid hydrodynamics, but relates to finite-temperature low-density bipolar diffusive transport by electrons and holes in the presence of short- and long-range disorder, and phonons.