The low-temperature expansion of the Casimir-Polder free energy of an atom with graphene

Abstract

We consider the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene by using the Poisson representation of the free energy. We extend our previous analysis on the different relations between chemical potential $\mu$ and mass gap parameter $m$. The key role plays the dependence of graphene conductivities on the $\mu$ and $m$. For simplicity, we made the manifest calculations for zero values of the Fermi velocity. For $\mu >m$ the thermal correction $\sim T^2$ and for $\mu <m$ we confirm the recent result of Klimchitskaya and Mostepanenko, that the thermal correction $\sim T^5$. In the case of exact equality $\mu =m$ the correction $\sim T$. This point is unstable and the system falls to the regime with $\mu >m$ or $\mu <m$. The analytical calculations are illustrated by numerical evaluations for the Hydrogen atom/graphene system.

12 pages

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Cited by in corpus (4)

• Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response
• Nonequilibrium Casimir-Polder Force between Nanoparticles and Graphene-Coated Silica Plate: Combined Effect of the Chemical Potential and Mass Gap
• 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