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Anisotropy enhancement of the Casimir-Polder force between a nanoparticle and graphene

We derive the analytical expressions for the thermal Casimir-Polder energy and force between a spheroidal nanoparticle above a semi-infinite material and a graphene covered interface. We analyze in detail the Casimir-Polder force between a gold nanoparticle and a single sheet of pristine graphene focusing on the impact of anisotropy. We show that the effect of anisotropy, i.e. the shape and orientation of the spheroidal nanoparticle, has a much larger influence on the force than the tunability of graphene. The effect of tuning and anisotropy both add up such that we observe a force which is between 20-50% of that in the ideal metal case which is much larger than the results found for the Casimir force between a metal halfspace and a layer of graphene.