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. A set of algebraic equations has been established to calculate the polarisation 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 polarisation 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. 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.
Highlights
We study the electrostatic responses of a linear homogeneous and anisotropic (LHA) dielectric film to an arbitrary external electrostatic potential
As is well known in electrostatics [1], an exterior probe charge cannot induce volume polarisation charges in a linear homogeneous and isotropic (LHI) dielectric, as the divergence of the displacement field D and that of the electric field E—which is proportional to D in a LHI—vanish in the body
In the traditional textbook approach of evaluating the amount of polarisation charges on the surface of—for instance—a semi-infinite medium (SIM), the electrostatic fields residing on the opposite sides of the surface are treated separately on a piece-wise homogeneity basis and joined by a set of boundary conditions requiring the continuity of the normal component of D and that of the electrostatic potential Φ at the surface [2]
Summary
As is well known in electrostatics [1], an exterior probe charge cannot induce volume polarisation charges in a linear homogeneous and isotropic (LHI) dielectric, as the divergence of the displacement field D and that of the electric field E—which is proportional to D in a LHI—vanish in the body. In the traditional textbook approach of evaluating the amount of polarisation charges on the surface of—for instance—a semi-infinite medium (SIM), the electrostatic fields residing on the opposite sides of the surface are treated separately on a piece-wise homogeneity basis and joined by a set of boundary conditions requiring the continuity of the normal component of D and that of the electrostatic potential Φ at the surface [2]. Plasma waves are electron density waves that can propagate either in the volume or on the surface of a conductor [13,14,15,16] They can exist within two-dimensional worlds such as semiconductor heterostructures [6] and graphene [17, 18]. We find that the plasma wave dispersion is strongly affected by the anisotropy at wavelengths comparable to the film thickness
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