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

TL;DR

This paper calculates the Casimir-Polder interaction between a rubidium atom and a disordered graphene sheet using real-space methods, revealing how defect-induced optical properties influence atom-surface forces.

Contribution

It introduces an accurate real-space calculation of the Casimir-Polder interaction with defected graphene beyond the Dirac cone approximation, considering full spectral optical response.

Findings

Optical response varies with doping level, showing distinct behaviors near the Dirac point and at high doping.

Casimir-Polder energy exhibits non-monotonic dependence on doping, with minimal variation near neutrality.

At high doping, the interaction aligns with predictions from the Drude model.

Abstract

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 calculations. As a model of defected graphene, we consider a tight-binding model of \Pi-electrons on a honeycomb lattice with a small concentration of point defects. 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 with in excess of ten million atoms. At low temperatures, the optical response of defected graphene is found to display two qualitatively distinct behavior with a clear transition around non-zero Fermi energy, \mu~\mu*. 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 \omega > 2\mu. These characteristics translate into a non-monotonic 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.