Plasmon-Polariton from a Helical State in a Dirac Magnet

Abstract

Optical field interacting with a topologically protected one-dimensional helical state is shown to support a one-dimensional plasmon-polariton that is characterized by a non-linear dispersion. In a two-dimensional Dirac magnet these electro-optical excitations are confined to domain walls, thus, offering a possibility to manipulate quantum optical states by altering magnetic domain configurations. An exact spectral equation for such topological plasmon-polariton is derived. PACS numbers:One of the key problems of the modern plasmonics is the search for the new material platforms supporting plasmonic excitations with sufficiently lower losses than in conventional plasmonic materials such as gold or silverBoltasseva2011. It was recently realized that the materials exhibiting topologically non-trivial electronic spectrum as well as certain broken symmetries can host extremely low loss plasmonic excitations. Namely, long-lived plasmons and plasmons polaritons have been predicted for a variety of topological and Chern insulators [1][2][3][4][5]. Moreover, materials with intrinsically broken time reversal symmetry such as Weyl semimetals have been reported to support low-loss plasmonic excitations [6][7][8][9].Dirac magnet is another example of a system with broken time reversal invariance. It can be realized, e. g., in the form of a ferromagnet thin film in a close proximity to a surface of 3D topological insulator or topological semimetal. A perpendicular-to-the plane magnetization component in the ferromagnet induces a finite effective mass of Dirac electrons in the topological insulator. As the result such a magnetic proximity opens up a band gap in the Dirac electron spectrum, which destroys the two-dimensional Dirac surface state. A one-dimensional domain wall in the ferromagnet is, however, imaged in the Dirac electron system as a zero mass line that supports a helical electronic state. The properties of such a state are similar to those of a quantum Hall edge state. The difference is that the helical state at the domain wall originates in the anomalous Hall effect in the Dirac magnet.The physics proposed can be realized e. g. in Bi 2 Se 3 /EuS interface, where the magnetic proximity effect on topological states has been already experimentally demonstrated [10,11]. One can also expect similar phenomena in ZrSiS thin crystal [12] that is weakly coupled through an oxide layer to a ferromagnetic thin film.In this letter we investigate how these helical electronic states may give rise to one dimensional plasmonpolariton excitations in the presence of THz radiation. Excitation and detection of the plasmon-polaritons are illustrated in Fig. 1 in a setup that is similar to the one used recently in a series of experiments with scattering SNOM technique [13-15]. FM TI SPP S-SNOM FIG. 1: Schematic image of the near-field optical imaging of the ferromagnetic wall via the excitation of the edge plasmonpolariton in Dirac magnet.For a sake of qualitative analysis we choose the simplest model of Dirac magnet that gives rise to...

Broadband enhancement of second-harmonic generation at the domain walls of magnetic topological insulators

“…In the study by Iorsh et al [27], we have shown that these currents support a strongly localized low-loss helical plasmon-polaritons with almost linear dispersion. Here, we consider a SHG supported by this EPP mode, namely, we consider the situation shown schematically in Figure 1.…”

“…It can be seen that as ν approaches zero, the phase mismatch is small across all of the gap regions. As shown in the study by Iorsh et al [27], the structure excited by a point-like scatterer such as a tip of scattering SNOM would support a long-living quasione-dimensional plasmon-polariton with the dispersion defined by (8).…”

“…The current operator is found as J ∂V/∂A(t). The linear conductivity of this system has been evaluated in the study by Iorsh et al [27] and is written as: Figure 1: Scheme of the second-harmonic generation (SHG) by the chiral current in magnetic TI. A point dipole excited an edge plasmon-polariton (EPP) localized at the domain wall.…”

“…While these plasmons cannot be excited by a plane wave since their dispersion lies well below the light cone, they can be excited by a evanescent field of the point-like scatterers. The dressing of the chiral plasmon by the electromagnetic field leads to formation of plasmon-polariton defined by the equation [27]:…”

“…We now consider the situation similar to one considered in the study by Iorsh et al [27]: a helical EPP is excited by a point-like scatterer and propagates along the domain wall. At the sufficient distance from the scatterer, the profile electric field is dominantly defined by the field of the EPP.…”