Topological Surface States on Three-Dimensional Photonic Structures with Weyl Points

Topological surface states are a class of novel electronic states that are of potential interest in quantum computing or spintronic applications. Unlike conventional two-dimensional electron states, these surface states are expected to be immune to localization and to overcome barriers caused by material imperfection. Previous experiments have demonstrated that topological surface states do not backscatter between equal and opposite momentum states, owing to their chiral spin texture. However, so far there is no evidence that these states in fact transmit through naturally occurring surface defects. Here we use a scanning tunnelling microscope to measure the transmission and reflection probabilities of topological surface states of antimony through naturally occurring crystalline steps separating atomic terraces. In contrast to non-topological surface states of common metals (copper, silver and gold), which are either reflected or absorbed by atomic steps, we show that topological surface states of antimony penetrate such barriers with high probability. This demonstration of the extended nature of antimony's topological surface states suggests that such states may be useful for high current transmission even in the presence of atomic-scale irregularities-an electronic feature sought to efficiently interconnect nanoscale devices.

Iron-based superconductors offer an ideal platform for studying topological superconductivity and Majorana fermions. In this paper, we carry out a comprehensive study of the band topology and topological surface states of a number of iron-based superconductors using a combination of density functional theory (DFT) and dynamical mean field theory. We find that the strong electronic correlation of Fe 3d electrons plays a crucial role in determining the band topology and topological surface states of iron-based superconductors. Electronic correlation not only strongly renormalizes the bandwidth of Fe 3d electrons, but also shifts the band positions of both Fe 3d and As/Se p electrons. As a result, electronic correlation moves the DFT-calculated topological surface states of many iron-based superconductors much closer to the Fermi level, which is crucial for realizing topological superconducting surface states and observing Majorana zero modes as well as achieving practical applications, such as quantum computation. More importantly, electronic correlation can change the band topology and make some iron-based superconductors topologically nontrivial with topological surface states whereas they have trivial band topology and no topological surface states in DFT calculations. Our paper demonstrates that it is important to take into account electronic correlation effects in order to accurately determine the band topology and topological surface states of iron-based superconductors and other strongly correlated materials.

We review recent progress in the electronic structure study of intrinsic magnetic topological insulators (MnBi2Te4) · (Bi2Te3)n ([Formula: see text]) family. Specifically, we focus on the ubiquitously (nearly) gapless behavior of the topological Dirac surface state observed by photoemission spectroscopy, even though a large Dirac gap is expected because of surface ferromagnetic order. The dichotomy between experiment and theory concerning this gap behavior is perhaps the most critical and puzzling question in this frontier. We discuss various proposals accounting for the lack of magnetic effect on the topological Dirac surface state, which are mainly categorized into two pictures, magnetic reconfiguration and topological surface state redistribution. Band engineering towards opening a magnetic gap of topological surface states provides great opportunities to realize quantized topological transport and axion electrodynamics at higher temperatures.

Topological insulators (TIs) represent a novel quantum state of matter, characterized by edge or surface-states, showing up on the topological character of the bulk wave functions. Allowing electrons to move along their surface, but not through their inside, they emerged as an intriguing material platform for the exploration of exotic physical phenomena, somehow resembling the graphene Dirac-cone physics, as well as for exciting applications in optoelectronics, spintronics, nanoscience, low-power electronics, and quantum computing. Investigation of topological surface states (TSS) is conventionally hindered by the fact that in most of experimental conditions the TSS properties are mixed up with those of bulk-states. Here, we activate, probe, and exploit the collective electronic excitation of TSS in the Dirac cone. By engineering Bi2Te(3-x)Sex stoichiometry, and by gating the surface of nanoscale field-effect-transistors, exploiting thin flakes of Bi2Te2.2Se0.8 or Bi2Se3, we provide the first demonstration of room-temperature terahertz (THz) detection mediated by overdamped plasma-wave oscillations on the "activated" TSS of a Bi2Te2.2Se0.8 flake. The reported detection performances allow a realistic exploitation of TSS for large-area, fast imaging, promising superb impacts on THz photonics.

1D topological systems for next-generation electronics

Topological insulators host spin-polarized surface states born out of the energetic inversion of bulk bands driven by the spin-orbit interaction. Here we discover previously unidentified consequences of band-inversion on the surface electronic structure of the topological insulator Bi2Se3. By performing simultaneous spin, time, and angle-resolved photoemission spectroscopy, we map the spin-polarized unoccupied electronic structure and identify a surface resonance which is distinct from the topological surface state, yet shares a similar spin-orbital texture with opposite orientation. Its momentum dependence and spin texture imply an intimate connection with the topological surface state. Calculations show these two distinct states can emerge from trivial Rashba-like states that change topology through the spin-orbit-induced band inversion. This work thus provides a compelling view of the coevolution of surface states through a topological phase transition, enabled by the unique capability of directly measuring the spin-polarized unoccupied band structure.

Three-dimensional topological insulators support a metallic non-trivial surface state with unique spin texture, where spin and momentum are locked perpendicular to each other. In this work, we investigate the orbital selective spin-texture associated with the topological surface states in Sb2Te3, using the first principles calculations. Sb2Te3 is a strong topological insulator with a p-p type bulk band inversion at the Γ-point and supports a single topological metallic surface state with upper (lower) Dirac-cone has left (right) handed spin-texture. Here, we show that the topological surface state has an additional locking between the spin and orbitals, leading to an orbital selective spin-texture. The out-of-plane orbitals (pz orbitals) have an isotropic orbital texture for both the Dirac cones with an associated left and right handed spin-texture for the upper and lower Dirac cones, respectively. In contrast, the in-planar orbital texture (px and py projections) is tangential for the upper Dirac-cone and is radial for the lower Dirac-cone surface state. The dominant in-planar orbital texture in both the Dirac cones lead to a right handed orbital-selective spin-texture.

We present a square-lattice photonic crystal that supports chiral topological photonic surface states at the interface to free space. Such unidirectional, back-scattering-immune surface states, as opposed to topological states at the interface between band-gap materials, allow to simplify the design of out-coupling from surface modes to functionalized radiated fields, removing the usual impedance matching conditions. The photonic crystal consists of gyromagnetic rods, which under the time-reversal-symmetry breaking induced by an external magnetic field together with a carefully tuned bulk band structure allow for the emergence of chiral topologically protected surface states. We demonstrate the topological nature of the surface states through unit cell and supercell band structure calculations showing the existence of a topological mode below the light-line where the sum of the Chern numbers in the bands below is non-zero. Additionally we perform direct scattering and a subsequent spatial, frequency dependent, Fourier Transform analysis that independently demonstrates the topological surface mode’s chiral dispersion relation, unidirectional propagation, and immunity to back-scattering.

Topological semimetals have aroused great research interest due to their intrinsic topological physics and potential applications in devices. A key feature for all topological materials is the so-called bulk-boundary correspondence, which means that if there is non-trivial band topology in the bulk, then we can expect unique topologically protected conducting states in the surface, i.e. the topological surface state (TSS). Previously, the studies of the surface states of topological materials mainly focused on the pristine surfaces, while the topological nodal line semimetal surface states with adsorbates are rarely systematically studied. In this paper, the topological properties of the topological semimetal AlB<sub>2</sub> are studied by first-principles calculations, and the TSS position is calculated by constructing the Al- and B-terminated slab models. Observing the topological surface state, it is found that the drumhead-like TSS connects two Dirac nodes with no energy gaps on the node line, and the TSS of the Al end-terminated slab has a smaller energy dispersion than that of the B-terminated slab. The adsorption characteristics of AlB<sub>2</sub> (010) surface are studied, and it is found that the Gibbs free energy (<inline-formula><tex-math id="M2">\begin{document}$ {\Delta }{G}_{{{\mathrm{H}}}^{*}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240404_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240404_M2.png"/></alternatives></inline-formula>) for hydrogen adsorption on the surface of Al is only –0.031 eV, demonstrating excellent hydrogen evolution reaction (HER) performance. The changes of TSS after H, OH and H<sub>2</sub>O are adsorbed on the surface of AlB<sub>2</sub> in aqueous solution environment are observed. The TSS change is the most significant when H is adsorbed, followed by OH adsorption. And the influence of H<sub>2</sub>O on TSS due to its electrical neutrality and weak surface adsorption is very weak. Before and after adsorption, because the topology protection TSS still exists, only the energy changes, which confirms its robustness in the environment. The results of this work provide a systematic understanding of the effects of different adsorbents on the TSS of AlB<sub>2</sub>, paving the way for future theoretical and experimental research in related fields, and alsopresent theoretical support for putting the topological materials into practical applications .

Bi2−xTe2.4Se0.6 single crystals show gapless topological surface states, and doping (x) with vanadium allows to shift the chemical potential in the bulk bandgap. Accordingly, the resistivity, carrier density, and mobility are constant below 10 K, and the magnetoresistance shows weak antilocalization as expected for low-temperature transport properties dominated by gapless surface states of so-called three-dimensional topological insulators. However, the magnetoresistance also shows a hysteresis depending on the sweep rate and the magnetic field direction. Here, we provide evidence that such magnetoresistance hysteresis is enhanced if both three-dimensional bulk states and quasi-two-dimensional topological states contribute to the transport (x = 0 and 0.03), and it is mostly suppressed if the topological states govern transport (x = 0.015). It is proposed that the hysteresis in the magnetoresistance results from different spin-dependent scattering rates of the topological surface and bulk states. Generally, this observation is of relevance to the studies of topologically insulating materials in which both topological surface and bulk states exist.

The archetypical 3D topological insulators Bi2Se3, Bi2Te3, and Sb2Te3 commonly exhibit high bulk conductivities, hindering the characterization of the surface state charge transport. The optimally doped topological insulators Bi2Te2Se and Bi2−xSbxTe2S, however, allow for such characterizations to be made. Here we report an experimental comparison of the conductance for the topological surface and bulk states in Bi2Te2Se and Bi1.1Sb0.9Te2S, based on temperature-dependent high-pressure measurements. We find that the surface state conductance at low temperature remains constant in the face of orders of magnitude increase in the bulk state conductance, revealing in a straightforward way that the topological surface states and bulk states are decoupled at low temperatures, consistent with theoretical models, and confirming topological insulators to be an excellent venue for studying charge transport in 2D Dirac electron systems.

InBi(001) is formed epitaxially on InAs(111)-A by depositing Bi onto an In-rich surface. Angle-resolved photoemission measurements reveal topological electronic surface states, close to the M¯ high symmetry point. This demonstrates a heteroepitaxial system entirely in the III–V family with topological electronic properties. InBi shows coexistence of Bi and In surface terminations, in contradiction with other III–V materials. For the Bi termination, the study gives a consistent physical picture of the topological surface electronic structure of InBi(001) terminated by a Bi bilayer rather than a surface formed by splitting to a Bi monolayer termination. Theoretical calculations based on relativistic density functional theory and the one-step model of photoemission clarify the relationship between the InBi(001) surface termination and the topological surface states, supporting a predominant role of the Bi bilayer termination. Furthermore, a tight-binding model based on this Bi bilayer termination with only Bi–Bi hopping terms, and no Bi–In interaction, gives a deeper insight into the spin texture. Published by the American Physical Society 2024

Three-dimensional topological insulators feature Dirac-like surface states which are topologically protected against the influence of weak quenched disorder. Here we investigate the effect of surface disorder beyond the weak-disorder limit using large-scale numerical simulations. We find two qualitatively distinct regimes: Moderate disorder destroys the Dirac cone and induces diffusive metallic behavior at the surface. Even more remarkably, for strong surface disorder a Dirac cone reappears, as new weakly disordered ``surface'' states emerge in the sample beneath the disordered surface layer, which can be understood in terms of an interface between a topological and an Anderson insulator. Together, this demonstrates the drastic effect of disorder on topological surface states, which cannot be captured within effective two-dimensional models for the surface states alone.

Topological semimetals have garnered significant interest due to their intrinsic topological physics and potential applications in devices. A crucial feature shared by all topological materials is the bulk-boundary correspondence, indicating the presence of unique topologically protected conducting states at the edges when non-trivial band topology exists in the bulk. Previous studies on surface states of topological materials predominantly focused on pristine surfaces, leaving the exploration of surface states in topological semimetals with adsorbates relatively uncharted. This work, based on ab initio calculations, examines variations in the topological surface states of MgB2, a well-known conventional superconductor and topological nodal line semimetal. We employ a thick slab model with Mg/B atoms as surface terminations to simulate its topological surface states. Subsequently, we investigate the adsorption of hydrogen (H), hydroxide (OH), and water (H2O) on the surface slabs to observe changes in the surface states. The pristine slab model gives the drumhead-like surface states inside the surface projected nodal lines, while the topological surface states change differently after adsorbing H, OH, and H2O, which can be understood systematically by combining the surface adsorption Gibbs free energy ΔG, surface terminations, and surface charge density distributions. Especially, our findings suggest that the Bader charge transfer value of surface atoms providing topological states is a key indicator for evaluating the variation in topological surface states after adsorption. This study provides a systematic understanding of the topological surface states of MgB2 with different adsorbates, paving the way for future theoretical and experimental investigations in related fields and shedding light on the potential device applications of topological materials.

Signatures of nodal line/point superconductivity have been observed in half-Heusler compounds, such as LnPtBi (Ln = Y, Lu). Topologically non-trivial band structures, as well as topological surface states, has also been confirmed by angular-resolved photoemission spectroscopy in these compounds. In this work, we present a systematical classification of possible gap functions of bulk states and surface states in half-Heusler compounds and the corresponding topological properties based on the representations of crystalline symmetry group. Different from all the previous studies based on four band Luttinger model, our study starts with the six-band Kane model, which involves both four p-orbital type of {\Gamma}8 bands and two s-orbital type of {\Gamma}6 bands. Although the {\Gamma}6 bands are away from the Fermi energy, our results reveal the importance of topological surface states, which originate from the band inversion between {\Gamma}6 and {\Gamma}8 bands, in determining surface properties of these compounds in the superconducting regime by combining topological bulk state picture and non-trivial surface state picture.