Two approaches for describing the Casimir interaction with graphene: density-density correlation function versus polarization tensor

Abstract

The comparison studies of theoretical approaches to the description of the Casimir interaction in layered systems including graphene is performed. It is shown that at zero temperature the approach using the polarization tensor leads to the same results as the approach using the longitudinal density-density correlation function of graphene. An explicit expression for the zero-temperature transverse density-density correlation function of graphene is provided. We further show that the computational results for the Casimir free energy of graphene-graphene and graphene-Au plate interactions at room temperature, obtained using the temperature-dependent polarization tensor, deviate significantly from those using the longitudinal density-density correlation function defined at zero temperature. We derive both the longitudinal and transverse density-density correlation functions of graphene at nonzero temperature. The Casimir free energy in layered structures including graphene, computed using the temperature-dependent correlation functions, is exactly equal to that found using the polarization tensor.

17 pages, 6 figures. Minor additions have been made in accordance with the Journal version; to appear in Phys. Rev. B

References in corpus (7)

• The electronic properties of graphene
• Dynamical polarization of graphene at finite doping
• Optical far-infrared properties of graphene monolayer and multilayers
• The optical conductivity of graphene in the visible region of the spectrum
• Retarded interactions in Graphene systems
• Van der Waals and Casimir interactions between two graphene sheets
• Classical limit of the Casimir interaction for thin films with applications to graphene

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