Chiral Spin Mode on the Surface of a Topological Insulator

Surface plasmons in anisotropic 3D gapped topological insulators

Topological insulators (TIs) are materials having conductive surfaces but insulating bulk, which are ideal platforms for plasmonic applications. The most commonly known TIs, such as Bi₂Se₃and Bi₂Te₃, are in fact highly anisotropic. The dielectric constants are largely different parallel and perpendicular to the surface. Here, we have extended the electromagnetic calculations of the surface plasmons in TIs to the anisotropic case. Magnetic field perpendicular to the surface is allowed, which opens a gap among the surface states. We model anisotropic TIs as bulk dielectric materials with different in-plane and out-of-plane permittivities; the surface states caused by the band inversion lead to a two-dimensional conductivity which supports surface plasmons. We have found two rather than one surface modes. Due to such anisotropy, quasi transverse electric (TE) polarized mode may occur near the interband transition threshold. Far below the transition frequency, another mode with both TE and transverse magnetic polarized components dominates, the dispersion relation of which is seriously modified by the Hall conductivity. By taking Bi₂Te₃as an example, we have derived the conductivity tensor with the consideration of the hexagonal warping effect, and solved the above mentioned two surface plasmon modes. In the end, finite element method has been used to calculate the electric field distributions. Our extension of the electromagnetic calculations of surface plasmons including a specific kind of anisotropy might be useful in other surface conductive materials with similar symmetry as well.

A Chirality-Based Quantum Leap

There is increasing interest in the study of chiral degrees of freedom occurring in matter and in electromagnetic fields. Opportunities in quantum sciences will likely exploit two main areas that are the focus of this Review: (1) recent observations of the chiral-induced spin selectivity (CISS) effect in chiral molecules and engineered nanomaterials and (2) rapidly evolving nanophotonic strategies designed to amplify chiral light-matter interactions. On the one hand, the CISS effect underpins the observation that charge transport through nanoscopic chiral structures favors a particular electronic spin orientation, resulting in large room-temperature spin polarizations. Observations of the CISS effect suggest opportunities for spin control and for the design and fabrication of room-temperature quantum devices from the bottom up, with atomic-scale precision and molecular modularity. On the other hand, chiral-optical effects that depend on both spin- and orbital-angular momentum of photons could offer key advantages in all-optical and quantum information technologies. In particular, amplification of these chiral light-matter interactions using rationally designed plasmonic and dielectric nanomaterials provide approaches to manipulate light intensity, polarization, and phase in confined nanoscale geometries. Any technology that relies on optimal charge transport, or optical control and readout, including quantum devices for logic, sensing, and storage, may benefit from chiral quantum properties. These properties can be theoretically and experimentally investigated from a quantum information perspective, which has not yet been fully developed. There are uncharted implications for the quantum sciences once chiral couplings can be engineered to control the storage, transduction, and manipulation of quantum information. This forward-looking Review provides a survey of the experimental and theoretical fundamentals of chiral-influenced quantum effects and presents a vision for their possible future roles in enabling room-temperature quantum technologies.

Real-space nanoimaging of THz polaritons in the topological insulator Bi2Se3

Plasmon polaritons in topological insulators attract attention from a fundamental perspective and for potential THz photonic applications. Although polaritons have been observed by THz far-field spectroscopy on topological insulator microstructures, real-space imaging of propagating THz polaritons has been elusive so far. Here, we show spectroscopic THz near-field images of thin Bi₂Se₃ layers (prototypical topological insulators) revealing polaritons with up to 12 times increased momenta as compared to photons of the same energy and decay times of about 0.48 ps, yet short propagation lengths. From the images we determine and analyze the polariton dispersion, showing that the polaritons can be explained by the coupling of THz radiation to various combinations of Dirac and massive carriers at the Bi₂Se₃ surfaces, massive bulk carriers and optical phonons. Our work provides critical insights into the nature of THz polaritons in topological insulators and establishes instrumentation and methodology for imaging of THz polaritons.

Resolving Dirac electrons with broadband high-resolution NMR

Detecting the metallic Dirac electronic states on the surface of Topological Insulators (TIs) is critical for the study of important surface quantum properties (SQPs), such as Majorana zero modes, where simultaneous probing of the bulk and edge electron states is required. However, there is a particular shortage of experimental methods, showing at atomic resolution how Dirac electrons extend and interact with the bulk interior of nanoscaled TI systems. Herein, by applying advanced broadband solid-state ¹²⁵Te nuclear magnetic resonance (NMR) methods on Bi₂Te₃ nanoplatelets, we succeeded in uncovering the hitherto invisible NMR signals with magnetic shielding that is influenced by the Dirac electrons, and we subsequently showed how the Dirac electrons spread inside the nanoplatelets. In this way, the spin and orbital magnetic susceptibilities induced by the bulk and edge electron states were simultaneously measured at atomic scale resolution, providing a pertinent experimental approach in the study of SQPs.

The detection of topological states is restricted to limited experimental tools. Here, the authors apply broadband solid-state ¹²⁵Te nuclear magnetic resonance on Bi₂Te₃ nanoplatelets uncovering signals distinguishing edge Dirac electrons and bulk electrons.

Tuning inelastic light scattering via symmetry control in the two-dimensional magnet CrI3

The coupling between spin and charge degrees of freedom in a crystal gives rise to magneto-optical effects with applications in the sensitive detection of local magnetic order, optical modulation and data storage. In two-dimensional magnets these effects manifest themselves in the large magneto-optical Kerr effect^1,2, spontaneous helical light emission^3,4 from ferromagnetic (FM) monolayers and electric-field induced Kerr rotation^5-7 and giant second-order non-reciprocal optical effects⁸ in antiferromagnetic (AFM) bilayers. Here we demonstrate the tuning of inelastically scattered light through symmetry control in atomically thin chromium triiodide (CrI₃). In monolayers, we found an extraordinarily large magneto-optical Raman effect from an A_1g phonon mode due to the emergence of FM order. The linearly polarized, inelastically scattered light rotates by ~40°, more than two orders of magnitude larger than the rotation from the magneto-optical Kerr effect under the same experimental conditions. In CrI₃ bilayers, the same phonon mode becomes Davydov-split into two modes of opposite parity, which exhibit divergent selection rules that depend on inversion symmetry and the underlying magnetic order. We demonstrate the magneto-electrical control over these selection rules by activating or suppressing Raman activity for the odd-parity phonon mode and the magneto-optical rotation of scattered light from the even-parity phonon mode. Our work underlines the unique opportunities provided by two-dimensional magnets to control the combined time-reversal and inversion symmetries to manipulate Raman optical selection rules and for exploring emergent magneto-optical effects and spin-phonon coupled physics.

Observation of chiral surface excitons in a topological insulator Bi2Se3

The protected electron states at the boundaries or on the surfaces of topological insulators (TIs) have been the subject of intense theoretical and experimental investigations. Such states are enforced by very strong spin-orbit interaction in solids composed of heavy elements. Here, we study the composite particles-chiral excitons-formed by the Coulomb attraction between electrons and holes residing on the surface of an archetypical 3D TI, [Formula: see text] Photoluminescence (PL) emission arising due to recombination of excitons in conventional semiconductors is usually unpolarized because of scattering by phonons and other degrees of freedom during exciton thermalization. On the contrary, we observe almost perfectly polarization-preserving PL emission from chiral excitons. We demonstrate that the chiral excitons can be optically oriented with circularly polarized light in a broad range of excitation energies, even when the latter deviate from the (apparent) optical band gap by hundreds of millielectronvolts, and that the orientation remains preserved even at room temperature. Based on the dependences of the PL spectra on the energy and polarization of incident photons, we propose that chiral excitons are made from massive holes and massless (Dirac) electrons, both with chiral spin textures enforced by strong spin-orbit coupling. A theoretical model based on this proposal describes quantitatively the experimental observations. The optical orientation of composite particles, the chiral excitons, emerges as a general result of strong spin-orbit coupling in a 2D electron system. Our findings can potentially expand applications of TIs in photonics and optoelectronics.

Spin-helix Larmor mode

A two-dimensional electron gas (2DEG) with equal-strength Rashba and Dresselhaus spin-orbit coupling sustains persistent helical spin-wave states, which have remarkably long lifetimes. In the presence of an in-plane magnetic field, there exist single-particle excitations that have the character of propagating helical spin waves. For magnon-like collective excitations, the spin-helix texture reemerges as a robust feature, giving rise to a decoupling of spin-orbit and electronic many-body effects. We prove that the resulting spin-flip wave dispersion is the same as in a magnetized 2DEG without spin-orbit coupling, apart from a shift by the spin-helix wave vector. The precessional mode about the persistent spin-helix state is shown to have an energy given by the bare Zeeman splitting, in analogy with Larmor’s theorem. We also discuss ways to observe the spin-helix Larmor mode experimentally.