Thermal Casimir-Polder interaction of different atoms with graphene

The thermal correction to the energy of the Casimir-Polder interaction of atoms with a suspended graphene membrane described by the Dirac model is investigated. We show that a major impact on the thermal correction is made by the size of the gap in the energy spectrum of graphene quasiparticles. Specifically, if the temperature is much lower than the gap parameter (alternatively, higher or on the order of the gap parameter), the thermal correction is shown to be relatively small (alternatively, large). We have calculated the free energy of the thermal Casimir-Polder interaction of atoms of He*, Na, Rb, and Cs with graphene described by both the hydrodynamic and the Dirac models. It is shown that, in exact computations using the Dirac model, one should use the polarization operator at nonzero temperatures. The computational results for the Casimir-Polder free energy obtained in the framework of the hydrodynamic model of graphene are several times larger than in the Dirac model within the separation region below 2 mu m. We conclude that the theoretical predictions following from the two models can be reliably discriminated in experiments on quantum reflection of different atoms on graphene.