Low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with graphene

Abstract

The analytic expressions for the free energy and entropy of the Casimir-Polder interaction between a polarizable and magnetizable atom and a graphene sheet are found in the limiting case of low temperature. In so doing, the response of graphene to electromagnetic fluctuations is described in the framework of the Dirac model by means of the polarization tensor in (2+1)-dimensional space-time. It is shown that the dominant contribution to the low-temperature behavior is given by an explicit dependence of the polarization tensor on temperature as a parameter. We demonstrate that the Lifshitz theory of atom-graphene interaction satisfies the Nernst heat theorem, i.e., is thermodynamically consistent. On this basis possible reasons of thermodynamic inconsistency arising for the Casimir-Polder and Casimir interactions in the case of Drude metals are discussed. The conclusion is made that although large thermal effect arising in the Casimir interaction between Drude metals at short separations should be considered as an artifact, the giant thermal effect predicted for graphene systems is an important physical phenomenon which awaits for its experimental observation.

22 pages; 2 typos in the list of references are corrected

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• Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution
• Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics
• Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response
• Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics
• The Nernst heat theorem for an atom interacting with graphene: Dirac model with nonzero energy gap and chemical potential
• Casimir effect for magnetic media: Spatially nonlocal response to the off-shell quantum fluctuation
• The Casimir effect in graphene systems: Experiment and theory
• On the convergence of the polarization tensor in space-time of three dimensions
• The Casimir-Polder interaction of an atom and real graphene sheet: Verification of the Nernst heat theorem
• Nernst heat theorem for the Casimir-Polder interaction between a magnetizable atom and ferromagnetic dielectric plate
• Testing Gravity and Predictions Beyond the Standard Model at Short Distances: The Casimir Effect
• Reflectance of graphene-coated dielectric plates in the framework of Dirac model: Joint action of energy gap and chemical potential