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

• URL: http://arxiv.org/abs/2006.15557v2
• Date: Fri, 10 Jul 2020 15:16:38 GMT
• Title: Quantum field theoretical description of the Casimir effect between two real graphene sheets and thermodynamics
• Authors: G. L. Klimchitskaya and V. M. Mostepanenko
• Abstract summary: Graphene is described in the framework of thermal quantum field theory in the Matsubara formulation. Different expressions are found under the conditions $Delta>2mu$, $Delta=2mu$, and $Delta2mu$. For both $Delta>2mu$ and $Delta2mu$ the Casimir entropy satisfies the third law of thermodynamics.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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