Effect of nonlocal electrical conductivity on near-field radiative heat transfer between graphene sheets

Abstract

Graphene's near-field radiative heat transfer is determined from its electrical conductivity, which is commonly modeled using the local (wavevector independent) Kubo and Drude formulas. In this letter, we analyze the non-locality of the graphene electrical conductivity using the Lindhard model combined with the Mermin relaxation time approximation. We also study how the variation of the electrical conductivity with the wavevector affects near-field radiative conductance between two graphene sheets separated by a vacuum gap. It is shown that the variation of the electrical conductivity with the wavevector, 𝑘 𝜌 , is appreciable for 𝑘 𝜌 s greater than 100𝑘 0 , where 𝑘 0 is the magnitude of the wavevector in the free space. The Kubo model is obtained by assuming 𝑘 𝜌 → 0, and thus is not valid for 𝑘 𝜌 > 100𝑘 0 . The Kubo electrical conductivity provides an accurate estimation of the spectral radiative conductance between two graphene sheets except for around the surface-plasmon-polariton frequency of graphene and at separation gaps smaller than 20 nm where there is a non-negligible contribution from electromagnetic modes with 𝑘 𝜌 > 100𝑘 0 to the radiative conductance. The Drude formula proves to be inaccurate for modeling the electrical conductivity and radiative conductance of graphene except for at temperatures much below the Fermi temperature and frequencies much smaller than 2𝜇 𝑐 ℏ , where 𝜇 𝑐 and ℏ are the chemical potential and reduced Planck's constant, respectively. It is also shown that the electronic scattering

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