Electromagnetic description of three-dimensional time-reversal invariant ponderable topological insulators

Abstract

A general technique to analyze the classical interaction between ideal topological insulators, and electromagnetic sources and fields, has been previously elaborated. Nevertheless it is not immediately applicable in the laboratory as it fails to describe real ponderable media. In this work we provide a description of real topologically insulating materials taking into account their dielectric and magnetic properties. For inhomogeneous permittivity and permeability, the problem of finding the Green's function must be solved in an ad hoc manner. Nevertheless, the physically feasible cases of piecewise constant $\epsilon ,\mu$ and $\theta$ make the problem tractable, where $\theta$ encodes the topological magnetoelectric polarizability properties of the medium. To this end we employ the Green's function method to find the fields resulting form the interaction between these materials and electromagnetic sources. Furthermore we exploit the fact that in the cases here studied, the full Green's function can be successfully found if the Green's function of the corresponding ponderable media with $\theta =0$ is known. Our results, satisfactorily reproduce previously existing ones and also generalize some others. The method here elaborated can be exploited to determine the electromagnetic fields for more general configurations aiming to measure the interaction between real 3D topological insulators and electromagnetic fields.

Accepted for publication in PRD

References in corpus (6)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Tunable Casimir repulsion with three dimensional topological insulators
• Fractional topological insulators in three dimensions
• Electric-Magnetic Duality and Topological Insulators
• Effect of finite temperature and uniaxial anisotropy on the Casimir effect with three-dimensional topological insulators
• Optical Properties Chern-Simons (3+1)D $\theta$-systems

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• Magnetoelectric effect of a conducting sphere near a planar topological insulator
• Electromagnetic Radiation in chiral matter: the Cherenkov case
• Dynamics of a Rydberg hydrogen atom near a topologically insulating surface
• Gravitational waves propagation in nondynamical Chern-Simons gravity
• Optical intersubband properties of a core-shell semiconductor-topological insulator quantum dot described by $\theta$-Electrodynamics
• Exact solution of the Schrödinger equation for an hydrogen atom at the interface between the vacuum and a topologically insulating surface
• Electromagnetic coupling and transport in a topological insulator-graphene hetero-structure
• Scalar Casimir effect for a conducting cylinder in a Lorentz violating background