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 between the particle and the sheet of graphene which is between 20% and 50% of that between the same particle and an ideal metal plate. Hence the observed force is much larger than the results found for the Casimir force between a metal half-space and a layer of graphene.