Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics

Abstract

The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap $\Delta$ and chemical potential $\mu$ are derived at arbitrarily low temperature. Graphene is described in the framework of thermal quantum field theory in the Matsubara formulation by means of the polarization tensor in (2+1)-dimensional space-time. Different asymptotic expressions are found under the conditions $\Delta >2\mu$, $\Delta =2\mu$, and $\Delta <2\mu$ taking into account both the implicit temperature dependence due to a summation over the Matsubara frequencies and the explicit one caused by a dependence of the polarization tensor on temperature as a parameter. It is shown that for both $\Delta >2\mu$ and $\Delta <2\mu$ the Casimir entropy satisfies the third law of thermodynamics (the Nernst heat theorem), whereas for $\Delta =2\mu$ this fundamental requirement is violated. The physical meaning of the discovered anomaly is considered in the context of thermodynamic properties of the Casimir effect between metallic and dielectric bodies.

37 pages; several typos are corrected

References in corpus (27)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Optical properties of graphene
• On the universal AC optical background in graphene
• Dynamical polarization, screening, and plasmons in gapped graphene
• The Schwinger mechanism and graphene
• Casimir Forces between Compact Objects: I. The Scalar Case
• Retarded interactions in Graphene systems
• Van der Waals and Casimir interactions between two graphene sheets
• Theory of the Casimir interaction for graphene-coated substrates using the polarization tensor and comparison with experiment
• Dirac fermions in strong electric field and quantum transport in graphene
• Observability of thermal effects in the Casimir interaction from graphene-coated substrates
• Precision measurements of the gradient of the Casimir force between ultra clean metallic surfaces at larger separations
• Origin of large thermal effect in the Casimir interaction between two graphene sheets
• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
• 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
• Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential
• Low-temperature behavior of the Casimir free energy and entropy of metallic films
• Impact of graphene coating on the atom-plate interaction
• Interaction of a graphene sheet with a ferromagnetic metal plate
• How to observe the giant thermal effect in the Casimir force for graphene systems
• 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
• The Casimir-Polder interaction of an atom and real graphene sheet: Verification of the Nernst heat theorem

Cited by in corpus (10)

• Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution
• An alternative response to the off-shell quantum fluctuations: A step forward in resolution of the Casimir puzzle
• Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics
• Next generation design and prospects for CANNEX
• Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response
• Casimir effect for magnetic media: Spatially nonlocal response to the off-shell quantum fluctuation
• Quantum field theoretical framework for the electromagnetic response of graphene and dispersion relations with implications to the Casimir effect
• Experimentum crucis for electromagnetic response of metals to evanescent waves and the Casimir puzzle
• The low-temperature expansion of the Casimir-Polder free energy of an atom with graphene
• On the convergence of the polarization tensor in space-time of three dimensions