Design and analysis of nanopatterned graphene-based structures for trapping applications

Trapping, levitating, and manipulating nanoscale objects with light forces shaped by patterned metamaterials continues to hold great interest for optical and condensed matter physics and engineering. Successful developments to date have concentrated on constraining movement only in one dimension, along the vertical axis to a material plane. Here we propose a realistic structure, consisting of alternating layers of graphene and dielectric, and periodically nanopatterned on the surface, that is capable of levitating and trapping nanoscale particles in two dimensions: one perpendicular and one parallel to the material plane. Repulsive forces arising from high- k modes of the metamaterial provide particle levitation along the vertical axis. At the point where this repulsive force balances the downward gravitational force, the particle is trapped at stable equilibrium. Periodic nanopatterning in the metamaterial surface furnishes the second, horizontal axis constraining particle motion. We show that the equilibrium position above the surface can be controlled by adjusting both the Fermi level and the number of graphene layers. Furthermore, to explicate the role of the high-k modes in generating the repulsive forces, we also propose a semianalytical method to calculate both the potential well and the forces generated by dipole radiation above the nanopatterned surface.