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

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The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap $\mathrm{\ensuremath{\Delta}}$ and chemical potential $\ensuremath{\mu}$ are derived at arbitrarily low… Click to show full abstract

The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap $\mathrm{\ensuremath{\Delta}}$ and chemical potential $\ensuremath{\mu}$ 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 $\mathrm{\ensuremath{\Delta}}g2\ensuremath{\mu}$, $\mathrm{\ensuremath{\Delta}}=2\ensuremath{\mu}$, and $\mathrm{\ensuremath{\Delta}}l2\ensuremath{\mu}$ 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 $\mathrm{\ensuremath{\Delta}}g2\ensuremath{\mu}$ and $\mathrm{\ensuremath{\Delta}}l2\ensuremath{\mu}$ the Casimir entropy satisfies the third law of thermodynamics (the Nernst heat theorem), whereas for $\mathrm{\ensuremath{\Delta}}=2\ensuremath{\mu}$ 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.

Keywords: mathrm ensuremath; ensuremath; ensuremath delta; delta ensuremath; thermodynamics

Journal Title: Physical Review D
Year Published: 2020

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