Numerical calculation of the Casimir-Polder interaction between a graphene sheet with vacancies and an atom

In this work the Casimir-Polder interaction energy between a rubidium atom and a disordered graphene sheet is investigated beyond the Dirac cone approximation by means of accurate real-space tight-binding calculations. As a model of defected graphene, we consider a tight-binding model of π electrons on a honeycomb lattice with a small concentration of vacancies. The optical response of the graphene sheet is evaluated with full spectral resolution by means of exact Chebyshev polynomial expansions of the Kubo formula in large lattices in excess of 10 million atoms. At low temperatures, the optical response of defected graphene is found to display two qualitatively distinct behaviors with a clear transition around finite (nonzero) Fermi energy. In the vicinity of the Dirac point, the imaginary part of optical conductivity is negative for low frequencies while the real part is strongly suppressed. On the other hand, for high doping, it has the same features found in the Drude model within the Dirac cone approximation, namely, a Drude peak at small frequencies and a change of sign in the imaginary part above the interband threshold. These characteristics translate into a nonmonotonic behavior of the Casimir-Polder interaction energy with very small variation with doping in the vicinity of the neutrality point while having the same form of the interaction calculated with Drude's model at high electronic density.