The Low-Temperature Expansion of the Casimir-Polder Free Energy of an Atom with Graphene - Nail Khusnutdinov (Universe, 2021)
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 <semantics>μ</semantics> and mass gap parameter m. The key role plays the dependence of graphene conductivities on the <semantics>μ</semantics> and m. For simplicity, we made the manifest calculations for zero values of the Fermi velocity. For <semantics>μ>m</semantics>, the thermal correction <semantics>∼T2</semantics>, and for <semantics>μ<m</semantics>, we confirm the recent result of Klimchitskaya and Mostepanenko, that the thermal correction <semantics>∼T5</semantics>. In the case of exact equality <semantics>μ=m</semantics>, the correction <semantics>∼T</semantics>. This point is unstable, and the system falls to the regime with <semantics>μ>m</semantics> or <semantics>μ<m</semantics>. The analytical calculations are illustrated by numerical evaluations for the Hydrogen atom/graphene system.