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

Abstract

A comparison study 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.

Charge-Induced Fluctuation Forces in Graphitic Nanostructures

“…This is important for understanding the 1=z asymptotic distance dependence as compared to the 1=z 3 dependence of the thermal Casimir force. Similarly, the quantum mechanical regime of 1= ffiffi ffi z p is of much longer range as compared to the metal-graphene quantum mechanical asymptotics [11,12,14]. It is also important to note that the geometrical capacitance takes into account the geometry of the system in a rather straightforward manner.…”

“…The Casimir graphene-metallic substrate interaction has been calculated by the Lifshitz approach [11,12], and it is also summarized in the Appendix. In Fig.…”

“…The Casimir force f c between a metallic substrate and graphene separated by a distance z is presented here using the Lifshitz formalism [11,12,39],…”

“…For example, the Casimir-van der Waals force involving graphene systems has nontrivial scaling behavior, which can be tuned via temperature, chemical potential, and doping modifications [11][12][13][14][15]. Understanding the electromagnetic fluctuations in the context of building a fundamental knowledge and making technological designs for such materials can hardly be overestimated.…”

Optical properties of dielectric plates coated with gapped graphene

“…The results of Refs. [14,15] were applied to investigate the Casimir force in graphene systems in the framework of the Lifshitz theory [18][19][20][21][22][23] (previous calculations on this subject have been made using the density-density correlation functions, model dielectric permittivities of graphene and other methods [24][25][26][27][28][29]). …”