Boundary effects produced by a Chern-Simons (CS) extension to electrodynamics are analyzed exploiting the Green's function (GF) method. We consider the electromagnetic field coupled to a θ term in a way that has been proposed to provide the correct low-energy effective action for topological insulators (TI). We take the θ term to be piecewise constant in different regions of space separated by a common interface Σ, which will be called the θ boundary. Features arising due to the presence of the boundary, such as magnetoelectric effects, are already known in CS extended electrodynamics, and solutions for some experimental setups have been found, each with its specific configuration of sources. In this work we illustrate a method to construct the GF that allows us to solve the CS modified field equations for a given θ boundary with otherwise arbitrary configuration of sources. The method is illustrated by solving the case of a planar θ boundary but can also be applied for cylindrical and spherical geometries for which the θ boundary can be characterized by a surface where a given coordinate remains constant. The static fields of a pointlike charge interacting with a planar TI, as described by a planar discontinuity in θ, are calculated and successfully compared with previously reported results. We also compute the force between the charge and the θ boundary by two different methods, using the energy-momentum tensor approach and the interaction energy calculated via the GF. The infinitely straight current-carrying wire is also analyzed.
-We investigate the Casimir stress on a topological insulator (TI) between two metallic plates. The TI is assumed to be joined to one of the plates and its surface in front of the other is covered by a thin magnetic layer, which turns the TI into a full insulator. We also analyze the limit where one of the plates is sent to infinity yielding the Casimir stress between a conducting plate and a TI. To this end we employ a local approach in terms of the stress-energy tensor of the system, its vacuum expectation value being subsequently evaluated in terms of the appropriate Green's function. Finally, the construction of the renormalised vacuum stress-energy tensor in the region between the plates yields the Casimir stress. Numerical result are also presented.
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 ε, µ and θ make the problem tractable, where θ 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 θ = 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.
The CPT-even sector of the standard model extension amounts to extending Maxwell electrodynamics by a gauge invariant term of the form − 1 4 (kF ) αβµν F αβ F µν , where the Lorentz-violating (LV) background tensor (kF ) αβµν possesses the symmetries of the Riemann tensor. The electrodynamics in ponderable media is still described by Maxwell equations in matter with modified constitutive relations which depend on the coefficients for Lorentz violation. We study the effects of this theory on the Casimir force between two semi-infinite ponderable media. The Fresnel coefficients characterizing the vacuum-medium interface are derived, and with the help of these, we compute the Casimir energy density. At leading-order in the LV coefficients, the Casimir energy density is numerically evaluated and successfully compared with the standard result. We also found a variety of intriguing effects, such as a non-trivial Kerr effect and the Casimir effect between two phases of the electromagnetic vacuum. We consider a bubble of Lorentz-symmetric (Maxwell) vacuum embedded in the infinite Lorentz-violating vacuum, and we calculate the Casimir energy at leading order, which in this case is quadratic in the LV coefficients. The Casimir force can be positive, zero, or negative, depending on the relative strengths between the LV coefficients.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.