The Casimir-Polder interaction of an atom and real graphene sheet: Verification of the Nernst heat theorem

TL;DR

This paper investigates the low-temperature Casimir-Polder interaction between an atom and a real graphene sheet, confirming the Nernst heat theorem and analyzing the effects of free charge carriers.

Contribution

It demonstrates that the Casimir-Polder entropy for graphene with nonzero energy gap and chemical potential vanishes at low temperatures, satisfying thermodynamic consistency.

Findings

Entropy approaches zero as temperature decreases

The Nernst heat theorem is verified for graphene interactions

Analysis of free charge carriers' impact on Lifshitz theory

Abstract

We find the low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with real graphene sheet possessing nonzero energy gap and chemical potential. Employing the formalism of the polarization tensor, it is shown that the Casimir-Polder entropy goes to zero by the power law with vanishing temperature, i.e., the Nernst heat theorem is satisfied. This result is discussed in connection with the problems connected with account of free charge carriers in the Lifshitz theory.