Abstract
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–Büttiker formalism for rectangular and disk-shaped (Corbino) devices in ballistic graphene is also provided.
Highlights
Soon after the advent of graphene, it became clear that this two-dimensional form of carbon shows exceptional thermal conductivity, reaching the room temperature value of∼5000 W/m/K [1], being over 10 times higher than that of copper or silver [2]
The dominant contribution to the thermal conductivity originates from lattice vibrations, these corresponding to out-of-plane deformations [3,4] allowing graphene to outperform more rigid carbon nanotubes, the electronic contribution to the thermal conductivity was found to be surprisingly high [5] in relation to the electrical conductivity (σ) close to the charge-neutrality point [6]
The peak in the Lorentz number appearing at the charge neutrality point for relatively high temperatures can be understood within a hydrodynamic transport theory for graphene [14,15,16], which can be regarded as adaptation of a universal theory of interacting, themalizing physical systems to this specific material
Summary
Soon after the advent of graphene, it became clear that this two-dimensional form of carbon shows exceptional thermal conductivity, reaching the room temperature value of. High values of the Lorentz number (L/L0 > 10) were observed much earlier for semiconductors [11], where the upper limit is determined by the energy gap (∆) to temperature ratio, Lmax ≈ (∆/2eT ) , but for zero-gap systems strong deviations from the WF law are rather unexpected. The peak in the Lorentz number appearing at the charge neutrality point for relatively high temperatures (close to the nitrogen boiling point) can be understood within a hydrodynamic transport theory for graphene [14,15,16], which can be regarded as adaptation of a universal theory of interacting, themalizing physical systems to this specific material.
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