Thermal Casimir and Casimir-Polder interactions in $N$ parallel 2D Dirac materials

TL;DR

This paper investigates the thermal Casimir and Casimir-Polder interactions in stacks of graphene layers, highlighting the importance of temperature, spatial dispersion, and the Dirac spectrum in these quantum fluctuation phenomena.

Contribution

It provides explicit formulas for the Casimir energies in graphene stacks considering thermal effects and optical response, extending understanding beyond ideal conductors.

Findings

Thermal effects significantly influence Casimir interactions in graphene stacks.

Spatial dispersion and temperature dependence enhance interactions at small separations.

Analytical expressions for low and high temperature limits are derived and compared with ideal models.

Abstract

The Casimir and Casimir-Polder interactions are investigated in a stack of equally spaced graphene layers. The optical response of the individual graphene is taken into account using gauge invariant components of the polarization tensor extended to the whole complex frequency plane. The planar symmetry for the electromagnetic boundary conditions is further used to obtain explicit forms for the Casimir energy stored in the stack and the Casimir-Polder energy between an atom above the stack. Our calculations show that these fluctuation induced interactions experience strong thermal effects due to the graphene Dirac-like energy spectrum. The spatial dispersion and temperature dependence in the optical response are also found to be important for enhancing the interactions especially at smaller separations. Analytical expressions for low and high temperature limits and their comparison with corresponding expressions for an infinitely conducting planar stack are further used to expand our understanding of Casimir and Casimir-Polder energies in Dirac materials. Our results may be useful to experimentalists as new ways to probe thermal effects at the nanoscale in such universal interactions.