Origin of large thermal effect in the Casimir interaction between two graphene sheets

TL;DR

This paper derives simple analytic expressions for the Casimir interaction between two graphene sheets, revealing that explicit thermal effects dominate at short separations and providing insights into the thermal behavior of graphene-based Casimir forces.

Contribution

The paper introduces a new analytic approach to evaluate the thermal effects in the Casimir interaction between graphene sheets, accounting for both explicit and implicit temperature dependencies.

Findings

Explicit thermal effects dominate at short separations.

Implicit thermal effects become larger at greater separations.

The formalism can be applied to other phenomena beyond the Casimir effect.

Abstract

Using the recently derived representation for the polarization tensor in (2+1)-dimensional space-time allowing an analytic continuation to the entire plane of complex frequencies, we obtain simple analytic expressions for the reflection coefficients of graphene at nonzero Matsubara frequencies. In the framework of the Lifshitz theory, these coefficients are shown to lead to nearly exact results for the Casimir free energy and pressure between two graphene sheets. The constituent parts of large thermal effect, arising in the Casimir interaction at short separations due to an explicit parametric dependence of the polarization tensor on the temperature and an implicit dependence through a summation over the Matsubara frequencies, are calculated. It is demonstrated that an explicit thermal effect exceeds an implicit one at shorter separations, both effects are similar in magnitudes at moderate separations, and that an implicit effect becomes a larger one with further increase of separation. Possible applications of the developed formalism, other than the Casimir effect, are discussed.