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

G. L. Klimchitskaya, V. M. Mostepanenko, and Bo E. Sernelius

PHYSICAL REVIEW B 89, 125407 (2014)

DOI: 10.1103/PhysRevB.89.125407

We have compared two theoretical approaches to the description of the Casimir interaction in layered systems including graphene. It is shown that at zero temperature, the approach using the polarization tensor in (2+1) dimensions 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. Only the longitudinal version has been available up til now. 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. To summarize: In this work we have shown that the formalisms derived from QED and condensed matter theory converge. We have furthermore provided the field with some missing pieces viz. the transverse dielectric function of graphene at zero temperature and the finite temperature versions of both the transverse and longitudinal dielectric functions.

Fig. Two examples of diatomic Li2 adsorbed at a (110) cellulose surface. The first example is with atoms a and c both at a distance za = zc from the surface. The second example is with Li atoms a and b situated one outside the other near a cellulose surface.


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