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

Mostepanenko, V. M.

doi:10.1103/physreva.98.032506

Cited by 21 publications

(19 citation statements)

References 67 publications

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“…In doing so, the predictions of the Lifshitz theory using the exact graphene response functions are in good agreement with an experiment on measuring the Casimir force between an Au-coated sphere and a graphene-coated plate [131,132]. What is more, the Casimir and Casimir-Polder entropies calculated for both the pristine graphene sheets and for graphene possessing the nonzero energy gap and chemical potential satisfy the Nernst heat theorem [133][134][135][136][137]. This means that there is no Casimir puzzle for graphene.…”

Section: The Nonlocal Drude-like Response To Quantum Fluctuations Off the Mass Shell And The Casimir Puzzlesupporting

confidence: 69%

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

Mostepanenko

2021

Universe

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This paper provides a review of the complicated problems in Lifshitz theory describing the Casimir force between real material plates composed of metals and dielectrics, including different approaches to their resolution. For both metallic plates with perfect crystal lattices and any dielectric plates, we show that the Casimir entropy calculated in the framework of Lifshitz theory violates the Nernst heat theorem when the well-approved dielectric functions are used in computations. The respective theoretical Casimir forces are excluded by the measurement data of numerous precision experiments. In the literature, this situation has been called the Casimir puzzle and the Casimir conundrum for the cases of metallic and dielectric plates, respectively. This review presents a summary of both the main theoretical and experimental findings on this subject. Next, a discussion is provided of the main approaches proposed in the literature to bring the Lifshitz theory into agreement with the measurement data and with the laws of thermodynamics. Special attention is paid to the recently suggested spatially nonlocal Drude-like response functions, which consider the relaxation properties of conduction electrons, as does the standard Drude model, but lead to the theoretical results being in agreement with both thermodynamics and the measurement data through the alternative response to quantum fluctuations of the mass shell. Further advances and trends in this field of research are discussed.

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Section: The Nonlocal Drude-like Response To Quantum Fluctuations Off the Mass Shell And The Casimir Puzzlesupporting

confidence: 69%

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

Mostepanenko

2021

Universe

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“…The asymptotic behavior of the free energy for an atom interacting with a sheet of ideal graphene possessing ∆ = µ = 0 at low T was investigated using the formalism of the polarization tensor [147]. The Casimir-Polder free energy was expressed according to (5) and the reflection coefficients presented in (33).…”

Section: Low-temperature Behavior Of the Casimir-polder Free Energy A...mentioning

confidence: 99%

“…The main idea of the perturbation approach used in [147] is to present the polarization tensor as a sum of two contributions (27), where for a pristine graphene with ∆ = µ = 0 the quantities Π…”

Section: Low-temperature Behavior Of the Casimir-polder Free Energy A...mentioning

confidence: 99%

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

Mostepanenko

2020

Universe

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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 Δ and chemical potential μ under different relationships between the values of Δ and μ. Along with reviewing the results obtained in the literature, we present some new findings concerning the case μ≠0, Δ=0. 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 Δ>2μ or Δ<2μ, is consistent with the requirements of thermodynamics. The case of graphene with Δ=2μ≠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.

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“…According to the recently derived representation for the reflection coefficient based on the Dirac model, the reflection coefficient of graphene for the TE mode is not zero [14,34]. Thus, the plasma model may be more suitable to the expression of the permittivity of multilayer graphene.…”

Section: Casimir Energy Between a Multilayer Graphene Sheet And mentioning

confidence: 99%

Casimir Force Acting on a Multilayer Graphene Sheet with Strong Diamagnetism

Inui

2019

e-J. Surf. Sci. Nanotechnol.

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We calculate the Casimir force acting on randomly stacked graphene layers and investigate the impact of diamagnetism on the Casimir force. The randomly stacked graphene layers are predicted to have a much smaller permeability than regularly stacked graphene layers such as graphite. We show that the Casimir force between randomly stacked graphene layers and a conducting plate is enhanced as the permeability of the randomly stacked graphene layers decreases from 1 to 0, especially for large separations. Conversely, the magnitude of the Casimir force between the randomly stacked graphene layers and a magnetic-dielectric plate such as yttrium-iron-garnet decreases as the permeability of the randomly stacked graphene layers decreases, and the force can be repulsive if the permittivity of the magnetic-dielectric plate contains a permeability much smaller than its permeability.

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

Cited by 21 publications

References 67 publications

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

Casimir Puzzle and Casimir Conundrum: Discovery and Search for Resolution

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

Casimir Force Acting on a Multilayer Graphene Sheet with Strong Diamagnetism

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