The Low-Temperature Expansion of the Casimir-Polder Free Energy of an Atom with Graphene

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 similar to T-2, and for mum or mu

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The study investigated the low-temperature expansion of the Casimir-Polder free energy for an atom and graphene using the Poisson representation. The analysis extended to different relations between chemical potential mu and mass gap parameter m, with a focus on the dependence of graphene conductivities on mu and m. Results revealed the thermal correction for mu>m resembling T-2, and differing behavior for mu<m or mu