Absence of induced magnetic monopoles in Maxwellian magnetoelectrics

Abstract

The electromagnetic response of topological insulators is governed by axion electrodynamics, which features a topological magnetoelectric term in the Maxwell equations. As a consequence magnetic fields become the source of electric fields and vice-versa, a phenomenon that is general for any material exhibiting a linear magnetoelectric effect. Axion electrodynamics has been associated with the possibility to create magnetic monopoles, in particular by a electrical charge that is screened above the surface of a magnetoelectric material. Here we present the exact solution for the electromagnetic fields in this geometry and show that while vortex-like magnetic screening fields are generated by the electrical charge their divergence is identically zero at every point in space which implies a strict absence of magnetic monopoles. Although magnetic image charges can be made explicit in the problem, no bound state with electric charges yielding a dyon arises. A dyon-like angular momentum follows from our analysis, but is quantized in a universal way, because of its dependence on the dielectric constant. This is consistent with a general argument that precludes magnetic monopoles to be generated in Maxwell magnetoelectrics.

Exact solution of the Schrödinger equation for a hydrogen atom at the interface between the vacuum and a topologically insulating surface

“…We have solved analytically the Schrödinger equation for an hydrogen atom located at the interface between two θ-media. Interestingly enough, our setup can be viewed also as the solution of the motion of the electron in the magnetic field of a Pearl vortex [20,33].…”

“…θED postulates ∇ • B = 0 in such a way that real magnetic monopoles are not allowed in the theory, as emphasized once more in Ref. [20]. The physical origin of this magnetic field relies in the Hall currents at the interface which are induced by the TME effect.…”

“…It is worth mentioning that the formulation of θED pursued in this work can be considered as a particularly simple version of the so-called Janus field theories, which have been actively explored in the context of the AdS/CFT correspondence [31,32]. Also, when locating the nucleus just at the interface z = 0, the TEM effect in θED produces the magnetic field of a Pearl vortex [20,33]. In this way, our work yields the energy eigenvalues and eigenfunctions of an electron moving in the presence of such a vortex.…”

Axion Mie Theory of Electron Energy Loss Spectroscopy in Topological Insulators

“…In the past several years a number of predictions of electromagnetic phenomena related to TIs have been made based on the above equations of axion electrodynamics [9][10][11][12][13][14][15][16]. Experimentally, such phenomena are often difficult to probe, since some effects manifest themselves only through corrections ∼ O(α 2 ).…”

“…( 2) [12]. Indeed, the TI surface introduces a discontinuity in Θ mixing electric and magnetic boundary conditions even in the static case [10,14,16]. As a concequence, while there is only a transverse magnetic (TM) and no transverse electric (TE) component of the electric field in the usual theory for SPPs on planar surfaces, such a component does not vanish in the TI case.…”