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Thermal Casimir effect in the interaction of graphene with dielectrics and metals

We investigate the thermal Casimir interaction of a suspended graphene described by the Dirac model with a plate made of dielectric or metallic materials. The reflection coefficients on graphene expressed in terms of a temperature-dependent polarization tensor are used. We demonstrate that for a graphene with nonzero mass gap parameter the Casimir free energy remains nearly constant (and the thermal correction negligibly small) over some temperature interval. For the interaction of graphene with metallic plate, the free energy is nearly the same, irrespective of whether the metal is nonmagnetic or magnetic and whether it is described using the Drude- or plasma-model approaches. The free energy computed using the Dirac model was compared with that computed using the hydrodynamic model of graphene and big differences accessible for experimental observation have been found. For dielectric and nonmagnetic metallic plates described by the Drude model these differences vanish with increasing temperature (separation). However, for nonmagnetic metals described by the plasma model and for magnetic metals, a severe dependence on the chosen theoretical description of graphene remains even at high temperature. In all cases the analytic asymptotic expressions for the free energy at high temperature are obtained and found in a very good agreement with the results of numerical computations.