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

Graphene's near-field radiative heat transfer is determined from its electrical conductivity, which is commonly modeled using the local (wave-vector independent) Kubo and Drude formulas. In this paper, we analyze the nonlocality 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 wave vector 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 wave vector, k(rho), is appreciable for k(rho)s greater than 100k(0), where k(0) is the magnitude of the wave vector in the free space. The Kubo model is obtained by assuming k(rho) -> 0, and thus is not valid for k(rho) > 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(rho) > 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 2 mu(c)/(h) over bar , where mu(c) and (h) over bar are the chemical potential and reduced Planck's constant, respectively. It is also shown that the electronic scattering processes should be considered in the Lindhard model properly, such that the local electron number is conserved. A simple substitution of omega by omega + i gamma (omega, i, and gamma being the angular frequency, imaginary unit, and scattering rate, respectively) in the collisionless Lindhard model does not satisfy the conservation of the local electron number and results in significant errors in computing the electrical conductivity and radiative conductance of graphene.

Automated summary

In this paper, the nonlocality of graphene electrical conductivity and its effect on near-field radiative conductance are analyzed using the Lindhard model combined with the Mermin relaxation time approximation. It is shown that the commonly used local Kubo and Drude formulas are not accurate in estimating the electrical conductivity and radiative conductance of graphene in certain conditions.