Casimir and Casimir-Polder Forces in Graphene Systems: Quantum Field Theoretical Description and Thermodynamics

Abstract

We review recent results on the low-temperature behaviors of the Casimir-Polder and Casimir free energy an entropy for a polarizable atom interacting with a graphene sheet and for two graphene sheets, respectively. These results are discussed in the wide context of problems arising in the Lifshitz theory of van der Waals and Casimir forces when it is applied to metallic and dielectric bodies. After a brief treatment of different approaches to theoretical description of the electromagnetic response of graphene, we concentrate on the derivation of response function in the framework of thermal quantum field theory in the Matsubara formulation using the polarization tensor in (2+1)-dimensional space-time. The asymptotic expressions for the Casimir-Polder and Casimir free energy and entropy at low temperature, obtained with the polarization tensor, are presented for a pristine graphene as well as for graphene sheets possessing some nonzero energy gap $\Delta$ and chemical potential $\mu$ under different relationships between the values of $\Delta$ and $\mu$. Along with reviewing the results obtained in the literature, we present some new findings concerning the case of zero gap and nonzero chemical potential. The conclusion is made that the Lifshitz theory of the Casimir and Casimir-Polder forces in graphene systems using the quantum field theoretical description of a pristine graphene, as well as real graphene sheets with $\Delta >2\mu$ or $\Delta <2\mu$, is consistent with the requirements of thermodynamics. The case of graphene with $\Delta =2\mu \ne 0$ leads to an entropic anomaly, but is argued to be physically unrealistic. The way to a resolution of thermodynamic problems in the Lifshitz theory based on the results obtained for graphene is discussed.

34 pages, 2 figures; Special issue "Development of Modern Methods of QFT and Their Applications"

References in corpus (50)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Optical far-infrared properties of graphene monolayer and multilayers
• The optical conductivity of graphene in the visible region of the spectrum
• Measurement of the Temperature Dependence of the Casimir-Polder Force
• Casimir forces between arbitrary compact objects
• Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect
• Dynamical polarization, screening, and plasmons in gapped graphene
• Control of the Casimir force by the modification of dielectric properties with light
• Casimir forces in a T operator approach
• The Schwinger mechanism and graphene
• Casimir Forces between Compact Objects: I. The Scalar Case
• Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate
• Lifshitz-type formulas for graphene and single-wall carbon nanotubes: van der Waals and Casimir interations
• Conductivity of dielectric and thermal atom-wall interaction
• Experiment and theory in the Casimir effect
• Retarded interactions in Graphene systems
• Van der Waals interaction between a microparticle and a single-wall carbon nanotube
• 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
• Casimir-Polder force between an atom and a dielectric plate: thermodynamics and experiment
• Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation
• Plasma vs Drude modelling of the Casimir force: beyond the proximity force approximation
• 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
• On the Casimir entropy for a ball in front of a plane
• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
• Spontaneous decay dynamics in atomically doped carbon nanotubes
• Tuning quantum fluctuations with an external magnetic field: Casimir-Polder interaction between an atom and a graphene sheet
• Going beyond PFA: a precise formula for the sphere-plate Casimir force
• 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
• Apparatus for measuring the thermal Casimir force at large distances
• 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
• Comparison of hydrodynamic model of graphene with recent experiment on measuring the Casimir interaction
• Quantum electrodynamic approach to the conductivity of gapped graphene
• Casimir entropy for magnetodielectrics
• Isolelectronic apparatus to probe the thermal Casimir force
• Casimir-Polder interaction of fullerene molecules with surfaces
• Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy
• Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics
• Nernst heat theorem for the thermal Casimir interaction between two graphene sheets
• Optical properties of dielectric plates coated with gapped graphene
• Nonperturbative theory of atom-surface interaction: Corrections at short separations

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• Casimir effect for magnetic media: Spatially nonlocal response to the off-shell quantum fluctuation
• Experimentum crucis for electromagnetic response of metals to evanescent waves and the Casimir puzzle
• The Casimir effect in graphene systems: Experiment and theory
• The low-temperature expansion of the Casimir-Polder free energy of an atom with graphene
• Using graphene conductors to enhance the functionality of atom-chips
• Impact of Mass-Gap on the Dispersion Interaction of Nanoparticles with Graphene out of Thermal Equilibrium
• Sign inversion in the lateral van der Waals force
• On the convergence of the polarization tensor in space-time of three dimensions
• Casimir effect for fermion condensate in conical rings
• 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 interaction with Chern-Simons boundary layers
• Casimir-Polder Force on Atoms or Nanoparticles from the Gapped and Doped Graphene: Asymptotic Behavior at Large Separations
• Large-Separation Behavior of the Casimir-Polder Force from Real Graphene Sheet Deposited on a Dielectric Substrate
• Comment on "Electric conductivity of graphene: Kubo model versus a nonlocal quantum field theory model (arXiv:2403.02279v3)"