Magneto-Image Effects in the van der Waals Interaction of an Atom and a Bounded, Dynamic, Nonlocal Plasma-like Medium

We present a theory of van der Waals (vdW) atom-surface attraction in which the second order vdW energy is explicitly exhibited as a correlation/self-energy of atomic electrons generated by a dynamic, nonlocal image potential due to polarization of the electrons of the bounded metal-semiconductor surface system in the electrostatic limit. This formulation is applied to a metal/semiconductor plasma in a magnetic field perpendicular to its bounding surface. The dependence of atom-surface vdW energy on magnetic field strength provides an adjustable parameterization of the underlying zero-point photon energy (represented in terms of the nonretarded longitudinal plasmon-photons of the Coulomb interaction), opening the possibility of analyzing the concomitant fundamental quantum phenomenology in detail with material parameters that can be examined experimentally. The determination of the image potential, including its nonlocal and dynamic magnetic field effects, involves the construction of a “surface dielectric function”, which is carried out using a Green’s function joining procedure for nonlocal dynamic electrostatics. In this aspect of our second order vdW energy calculation, we take account of the role of the magnetic field by means of a hydrodynamic model of magnetoplasma nonlocality in dynamic longitudinal dielectric response. Both local and nonlocal magnetic field effects in vdW energy are analyzed within the framework of a multipole expansion, and are also discussed, respectively, in expansions in powers of ω c (ωc is the cyclotron frequency). Furthermore, we determine the role of Landau quantization magnetic field effects in the skewing of the surface electron charge distribution from its uniform positive background, exhibiting de-Haas-van Alphen oscillatory (and “staircase”) behavior.