The Nernst heat theorem for an atom interacting with graphene: Dirac model with nonzero energy gap and chemical potential

Abstract

We derive the low-temperature behavior of the Casimir-Polder free energy for a polarizable atom interacting with graphene sheet which possesses the nonzero energy gap $\Delta$ and chemical potential $\mu$. The response of graphene to the electromagnetic field is described by means of the polarization tensor in the framework of Dirac model on the basis of first principles of thermal quantum field theory in the Matsubara formulation. It is shown that the thermal correction to the Casimir-Polder energy consists of three contributions. The first of them is determined by the Matsubara summation using the polarization tensor defined at zero temperature, whereas the second and third contributions are caused by an explicit temperature dependence of the polarization tensor and originate from the zero-frequency Matsubara term and the sum of all Matsubara terms with nonzero frequencies, respectively. The asymptotic behavior for each of the three contributions at low temperature is found analytically for any value of the energy gap and chemical potential. According to our results, the Nernst heat theorem for the Casimir-Polder free energy and entropy is satisfied for both $\Delta >2\mu$ and $\Delta <2\mu$. We also reveal an entropic anomaly arising in the case $\Delta =2\mu$. The obtained results are discussed in connection with the long-standing fundamental problem in Casimir physics regarding the proper description of the dielectric response of matter to the electromagnetic field.

37 pages, 1 Table; several typos are corrected

References in corpus (29)

• The electronic properties of graphene
• Optical properties of graphene
• Measurement of the Temperature Dependence of the Casimir-Polder Force
• On the universal AC optical background in graphene
• Dynamical polarization, screening, and plasmons in gapped graphene
• Control of the Casimir force by the modification of dielectric properties with light
• Detecting Chameleons through Casimir Force Measurements
• Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate
• Conductivity of dielectric and thermal atom-wall interaction
• Experiment and theory in the Casimir effect
• Surface Casimir densities and induced cosmological constant in higher dimensional braneworlds
• Theory of the Casimir interaction for graphene-coated substrates using the polarization tensor and comparison with experiment
• Casimir-Polder force between an atom and a dielectric plate: thermodynamics and experiment
• Precision measurements of the gradient of the Casimir force between ultra clean metallic surfaces at larger separations
• On the Casimir entropy for a ball in front of a plane
• Force sensor for chameleon and Casimir force experiments with parallel-plate configuration
• Tuning quantum fluctuations with an external magnetic field: Casimir-Polder interaction between an atom and a graphene sheet
• Emending thermal dispersion interactions of Li, Na, K and Rb alkali metal-atoms with graphene in the Dirac model
• Low-temperature behavior of the Casimir free energy and entropy of metallic films
• Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential
• Impact of graphene coating on the atom-plate interaction
• Constraints on non-Newtonian gravity and axionlike particles from measuring the Casimir force in nanometer separation range
• Thermal effect in the Casimir force for graphene and graphene-coated substrates: Impact of nonzero mass gap and chemical potential
• Casimir entropy for magnetodielectrics
• Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy
• Nernst heat theorem for the thermal Casimir interaction between two graphene sheets
• Constraining axion coupling constants from measuring the Casimir interaction between polarized test bodies
• 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

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• Quantum field theoretical framework for the electromagnetic response of graphene and dispersion relations with implications to the Casimir effect
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• The low-temperature expansion of the Casimir-Polder free energy of an atom with graphene
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• On the convergence of the polarization tensor in space-time of three dimensions
• Testing Gravity and Predictions Beyond the Standard Model at Short Distances: The Casimir Effect
• Nonequilibrium Casimir-Polder Force between Nanoparticles and Graphene-Coated Silica Plate: Combined Effect of the Chemical Potential and Mass Gap
• Casimir-Polder Force on Atoms or Nanoparticles from the Gapped and Doped Graphene: Asymptotic Behavior at Large Separations
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