Electrostatic responses of anisotropic dielectric films

Abstract

We study the electrostatic responses (i.e. retardation effects due to the propagation of electromagnetic waves are ignored) of a linear homogeneous and anisotropic (LHA) dielectric film to an arbitrary external electrostatic potential, which may be generated by charges located either inside or outside it. A formalism is developed to calculate the polarization charges induced in the film.In our derivation, the idea is exploited that a physical boundary can be looked upon as a region of rapid variation in polarization rather than a simple geometric separation. With this no boundary conditions are needed in solving the relevant electrostatics problem. Our approach makes it clear that the responses consist of two contributions, one arising from the very presence of surfaces while the other existing even in an infinite medium. The approach can be applied not just to electrostatic but also many problems and is of great pedagogical value. In light of the results, we discuss graphene plasma waves under the influence of a LHA dielectric film such as a few-layer hexagonal boron nitride. It is found that the dispersion of these waves is strongly affected by the anisotropy at wavelengths comparable to the film thickness.

On probable lossless surface plasma waves: a reply to criticisms

“…Our results, to be published elsewhere, perfectly agree with the exact microscopic theory, which lends strong support to the basic theory I developed in Refs. 1,[3][4][5]12 .…”

A Theory of Dynamical Responses for Metal Films: Surface Roughness Effects

“…Such an imposition is not justified in light of the above analysis; see also Refs. [66,69,73] and references therein.…”

“…To date, as we are concerned, existing studies using this method have been exclusively on infinite or semi-infinite metals and none on films. As an innovation, our derivation treats the surfaces of a film as physical though negligibly thin regions rather than geometric separations [66][67][68][69]. In this way we are able to avoid the imposition of additional boundary conditions permeating existing work [57][58][59].…”

Coulomb’s and Ohm’s laws in an anisotropic medium

“…Schindlmayr [8] has presented a simple analytic scheme for calculating the binding energy of excitons in semiconductors that takes full account of the existing anisotropy in the effective mass, as a complement to the qualitative treatment in most textbooks. Recently, Deng [9] has studied the electrostatic responses of anisotropic dielectric films.…”