Van der Waals and Casimir interactions between two graphene sheets

TL;DR

This paper calculates the thermal free energy and pressure of dispersion interactions between two graphene sheets using the Lifshitz formula and polarization tensor, revealing differences based on the mass gap parameter.

Contribution

It introduces a method to compute van der Waals and Casimir interactions between graphene sheets using the polarization tensor within the Lifshitz framework, including effects of a nonzero mass gap.

Findings

Results agree with Coulomb coupling calculations for pristine graphene.

Nonzero mass gap leads to qualitatively different behavior.

The approach tests various models of graphene's response function.

Abstract

The thermal free energy and pressure of dispersion interaction between two graphene sheets described by the Dirac model are calculated using the Lifshitz formula with reflection coefficients expressed via the polarization tensor. The obtained results for a pristine graphene are found to be in agreement with computations using Coulomb coupling between density fluctuations. For a graphene with nonzero mass gap parameter a qualitatively different behavior for the free energy and pressure is obtained. The Lifshitz formula with reflection coefficients expressed via the polarization tensor is used as a test for different computational approaches proposed in the literature for modeling the response function and conductivity of graphene at both zero and nonzero temperature.