Quantum Levitation of Graphene Sheet by Repulsive Casimir Forces

We calculate the repulsive Casimir force between a single graphene sheet and a metamaterial slab whose magnetic permeability is expressed by using the Lorentz model, focusing on the possibility of realizing quantum levitation. It is shown that the graphene sheet can be levitated by the repulsive Casimir force because of the very small density of the graphene sheet. The levitation height depends on the magnetic properties of the metamaterial slab, and this height reaches the micrometer range when metamaterials with large permeabilities are used. The possibility of observing quantum levitation in vacuum is also considered.