  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.
