Observation of a warped helical spin texture in Bi2Se3 from circular dichroism angle-resolved photoemission spectroscopy

Berry curvature signatures in chiroptical excitonic transitions

The topology of the electronic band structure of solids can be described by its Berry curvature distribution across the Brillouin zone. We theoretically introduce and experimentally demonstrate a general methodology based on the measurement of energy- and momentum-resolved optical transition rates, allowing to reveal signatures of Berry curvature texture in reciprocal space. By performing time- and angle-resolved photoemission spectroscopy of atomically thin WSe2 using polarization-modulated excitations, we demonstrate that excitons become an asset in extracting the quantum geometrical properties of solids. We also investigate the resilience of our measurement protocol against ultrafast scattering processes following direct chiroptical transitions.

Singular Hall Response from a Correlated Ferromagnetic Flat Nodal-Line Semimetal

Topological quantum phases are largely understood in weakly correlated systems, which have identified various quantum phenomena, such as the spin Hall effect, protected transport of helical fermions, and topological superconductivity. Robust ferromagnetic order in correlated topological materials particularly attracts attention, as it can provide a versatile platform for novel quantum devices. Here, a singular Hall response arising from a unique band structure of flat topological nodal lines in combination with electron correlation in a van der Waals ferromagnetic semimetal, Fe3GaTe2, with a high Curie temperature of Tc = 347 K is reported. High anomalous Hall conductivity violating the conventional scaling, resistivity upturn at low temperature, and a large Sommerfeld coefficient are observed in Fe3GaTe2, which implies heavy fermion features in this ferromagnetic topological material. The scanning tunneling microscopy, circular dichroism in angle-resolved photoemission spectroscopy, and theoretical calculations support the original electronic features of the material. Thus, low-dimensional Fe3GaTe2 with electronic correlation, topology, and room-temperature ferromagnetic order appears to be a promising candidate for robust quantum devices.

Chirality-Driven Orbital Angular Momentum and Circular Dichroism in CoSi

Chiral crystals and molecules were recently predicted to form an intriguing platform for unconventional orbital physics. Here, we report the observation of chirality-driven orbital textures in the bulk electronic structure of CoSi, a prototype member of the cubic B20 family of chiral crystals. Using circular dichroism in soft x-ray angle-resolved photoemission, we demonstrate the formation of a bulk orbital-angular-momentum texture and monopolelike orbital-momentum locking that depends on crystal handedness. We introduce the intrinsic chiral circular dichroism, icCD, as a differential photoemission observable and a natural probe of chiral electron states. Our findings render chiral crystals promising for spin-orbitronics applications.

The Interaction of 2D Materials With Circularly Polarized Light

2D materials (2DMs), due to spin-valley locking degree of freedom, exhibit strongly bound exciton and chiral optical selection rules and become promising material candidates for optoelectronic and spin/valleytronic devices. Over the last decade, the manifesting of 2D materials by circularly polarized lights expedites tremendous fascinating phenomena, such as valley/exciton Hall effect, Moiré exciton, optical Stark effect, circular dichroism, circularly polarized photoluminescence, and spintronic property. In this review, recent advance in the interaction of circularly polarized light with 2D materials covering from graphene, black phosphorous, transition metal dichalcogenides, van der Waals heterostructures as well as small proportion of quasi-2D perovskites and topological materials, is overviewed. The confronted challenges and theoretical and experimental opportunities are also discussed, attempting to accelerate the prosperity of chiral light-2DMs interactions.

Spin-polarized spatially indirect excitons in a topological insulator

The exciton, a bound state of an electron and a hole, is a fundamental quasiparticle induced by coherent light-matter interactions in semiconductors. When the electrons and holes are in distinct spatial locations, spatially indirect excitons are formed with a much longer lifetime and a higher condensation temperature. One of the ultimate frontiers in this field is to create long-lived excitonic topological quasiparticles by driving exciton states with topological properties, to simultaneously leverage both topological effects and correlation^1,2. Here we reveal the existence of a transient excitonic topological surface state (TSS) in a topological insulator, Bi₂Te₃. By using time-, spin- and angle-resolved photoemission spectroscopy, we directly follow the formation of a long-lived exciton state as revealed by an intensity buildup below the bulk-TSS mixing point and an anomalous band renormalization of the continuously connected TSS in the momentum space. Such a state inherits the spin-polarization of the TSS and is spatially indirect along the z axis, as it couples photoinduced surface electrons and bulk holes in the same momentum range, which ultimately leads to an excitonic state of the TSS. These results establish Bi₂Te₃ as a possible candidate for the excitonic condensation of TSSs³ and, in general, opens up a new paradigm for exploring the momentum space emergence of other spatially indirect excitons, such as moiré and quantum well excitons^4-6, and for the study of non-equilibrium many-body topological physics.

Probing magnetic orbitals and Berry curvature with circular dichroism in resonant inelastic X-ray scattering

Resonant inelastic X-ray scattering (RIXS) can probe localized excitations at selected atoms in materials, including particle-hole transitions between the valence and conduction bands. These transitions are governed by fundamental properties of the corresponding Bloch wave functions, including orbital and magnetic degrees of freedom, and quantum geometric properties such as the Berry curvature. In particular, orbital angular momentum (OAM), which is closely linked to the Berry curvature, can exhibit a nontrivial momentum dependence. We demonstrate how information on such OAM textures can be extracted from the circular dichroism in RIXS. Based on accurate modeling with a first-principles treatment of the key ingredient-the light-matter interaction-we simulate dichroic RIXS spectra for the prototypical transition-metal dichalcogenide MoSe2 and the two-dimensional topological insulator 1T'-MoS2. Guided by an intuitive picture of the optical selection rules, we discuss how the momentum-dependent OAM manifests itself in the dichroic RIXS signal if one controls the momentum transfer. Our calculations are performed for typical experimental geometries and parameter regimes, and demonstrate the possibility of observing the predicted circular dichroism in forthcoming experiments. Thus, our work establishes a new avenue for observing Berry curvature and topological states in quantum materials.

Large magnetoelectric resistance in the topological Dirac semimetal α-Sn

The spin-momentum locking of surface states in topological materials can produce a resistance that scales linearly with magnetic and electric fields. Such a bilinear magnetoelectric resistance (BMER) effect offers a new approach for information reading and field sensing applications, but the effects demonstrated so far are too weak or for low temperatures. This article reports the first observation of BMER effects in topological Dirac semimetals; the BMER responses were measured at room temperature and were substantially stronger than those reported previously. The experiments used topological Dirac semimetal α-Sn thin films grown on silicon substrates. The films showed BMER responses that are 10⁶ times larger than previously measured at room temperature and are also larger than those previously obtained at low temperatures. These results represent a major advance toward realistic BMER applications. Significantly, the data also yield the first characterization of three-dimensional Fermi-level spin texture of topological surface states in α-Sn.

Emergence of Fermi arcs due to magnetic splitting in an antiferromagnet

The Fermi surface plays an important role in controlling the electronic, transport and thermodynamic properties of materials. As the Fermi surface consists of closed contours in the momentum space for well-defined energy bands, disconnected sections known as Fermi arcs can be signatures of unusual electronic states, such as a pseudogap¹. Another way to obtain Fermi arcs is to break either the time-reversal symmetry² or the inversion symmetry³ of a three-dimensional Dirac semimetal, which results in formation of pairs of Weyl nodes that have opposite chirality⁴, and their projections are connected by Fermi arcs at the bulk boundary^3,5-12. Here, we present experimental evidence that pairs of hole- and electron-like Fermi arcs emerge below the Neel temperature (T_N) in the antiferromagnetic state of cubic NdBi due to a new magnetic splitting effect. The observed magnetic splitting is unusual, as it creates bands of opposing curvature, which change with temperature and follow the antiferromagnetic order parameter. This is different from previous theoretically considered^13,14 and experimentally reported cases^15,16 of magnetic splitting, such as traditional Zeeman and Rashba, in which the curvature of the bands is preserved. Therefore, our findings demonstrate a type of magnetic band splitting in the presence of a long-range antiferromagnetic order that is not readily explained by existing theoretical ideas.

Spiers Memorial Lecture: Prospects for photoelectron spectroscopy

An overview is presented of recent advances in photoelectron spectroscopy, focussing on advances in in situ and time-resolved measurements, and in extending the sampling depth of the technique. The future...

Orbital Complexity in Intrinsic Magnetic Topological Insulators MnBi_{4}Te_{7} and MnBi_{6}Te_{10}

Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the surface electronic structure of the magnetic van der Waals compounds MnBi_{4}Te_{7} and MnBi_{6}Te_{10}, the n=1 and 2 members of a modular (Bi_{2}Te_{3})_{n}(MnBi_{2}Te_{4}) series, which have attracted recent interest as intrinsic magnetic topological insulators. Combining circular dichroic, spin-resolved and photon-energy-dependent ARPES measurements with calculations based on density functional theory, we unveil complex momentum-dependent orbital and spin textures in the surface electronic structure and disentangle topological from trivial surface bands. We find that the Dirac-cone dispersion of the topologial surface state is strongly perturbed by hybridization with valence-band states for Bi_{2}Te_{3}-terminated surfaces but remains preserved for MnBi_{2}Te_{4}-terminated surfaces. Our results firmly establish the topologically nontrivial nature of these magnetic van der Waals materials and indicate that the possibility of realizing a quantized anomalous Hall conductivity depends on surface termination.

Disorder-Promoted Splitting in Quasiparticle Interference at Nesting Vectors

Inelastic interactions of quantum systems with the environment usually wash coherent effects out. In the case of Friedel oscillations, the presence of disorder leads to a fast decay of the oscillation amplitude. Here we show both experimentally and theoretically that in three-dimensional topological insulator Bi₂Te₃ there is a nesting-induced splitting of coherent scattering vectors which follows a peculiar evolution in energy. The effect becomes experimentally observable when the lifetime of quasiparticles shortens due to disorder. The amplitude of the splitting allows an evaluation of the lifetime of the electrons. A similar phenomenon should be observed in any system with a well-defined scattering vector regardless of its topological properties.

Angle, Spin, and Depth Resolved Photoelectron Spectroscopy on Quantum Materials

The role of X-ray based electron spectroscopies in determining chemical, electronic, and magnetic properties of solids has been well-known for several decades. A powerful approach is angle-resolved photoelectron spectroscopy, whereby the kinetic energy and angle of photoelectrons emitted from a sample surface are measured. This provides a direct measurement of the electronic band structure of crystalline solids. Moreover, it yields powerful insights into the electronic interactions at play within a material and into the control of spin, charge, and orbital degrees of freedom, central pillars of future solid state science. With strong recent focus on research of lower-dimensional materials and modified electronic behavior at surfaces and interfaces, angle-resolved photoelectron spectroscopy has become a core technique in the study of quantum materials. In this review, we provide an introduction to the technique. Through examples from several topical materials systems, including topological insulators, transition metal dichalcogenides, and transition metal oxides, we highlight the types of information which can be obtained. We show how the combination of angle, spin, time, and depth-resolved experiments are able to reveal "hidden" spectral features, connected to semiconducting, metallic and magnetic properties of solids, as well as underlining the importance of dimensional effects in quantum materials.

Ultrafast evolution of bulk, surface and surface resonance states in photoexcited [Formula: see text]

We use circular dichroism (CD) in time- and angle-resolved photoemission spectroscopy (trARPES) to measure the femtosecond charge dynamics in the topological insulator (TI) [Formula: see text]. We detect clear CD signatures from topological surface states (TSS) and surface resonance (SR) states. In time-resolved measurements, independently from the pump polarization or intensity, the CD shows a dynamics which provides access to the unexplored electronic evolution in unoccupied states of [Formula: see text]. In particular, we are able to disentangle the unpolarized electron dynamics in the bulk states from the spin-textured TSS and SR states on the femtosecond timescale. Our study demonstrates that photoexcitation mainly involves the bulk states and is followed by sub-picosecond transport to the surface. This provides essential details on intra- and interband scattering in the relaxation process of TSS and SR states. Our results reveal the significant role of SRs in the subtle ultrafast interaction between bulk and surface states of TIs.

Quantum frequency doubling in the topological insulator Bi2Se3

The nonlinear Hall effect due to Berry curvature dipole (BCD) induces frequency doubling, which was recently observed in time-reversal-invariant materials. Here we report novel electric frequency doubling in the absence of BCD on a surface of the topological insulator Bi₂Se₃ under zero magnetic field. We observe that the frequency-doubling voltage transverse to the applied ac current shows a threefold rotational symmetry, whereas it forbids BCD. One of the mechanisms compatible with the symmetry is skew scattering, arising from the inherent chirality of the topological surface state. We introduce the Berry curvature triple, a high-order moment of the Berry curvature, to explain skew scattering under the threefold rotational symmetry. Our work paves the way to obtain a giant second-order nonlinear electric effect in high mobility quantum materials, as the skew scattering surpasses other mechanisms in the clean limit.

Berry curvature dipole (BCD) leads to the nonlinear Hall effect manifested as a frequency doubling in topological materials. Here, the authors report electric frequency doubling in the absence of BCD and magnetic field on a surface of Bi₂Se₃ due to skew scattering arising from inherent chirality of the topological surface states.

Revealing Hidden Orbital Pseudospin Texture with Time-Reversal Dichroism in Photoelectron Angular Distributions

We performed angle-resolved photoemission spectroscopy (ARPES) of bulk 2H-WSe_{2} for different crystal orientations linked to each other by time-reversal symmetry. We introduce a new observable called time-reversal dichroism in photoelectron angular distributions (TRDAD), which quantifies the modulation of the photoemission intensity upon effective time-reversal operation. We demonstrate that the hidden orbital pseudospin texture leaves its imprint on TRDAD, due to multiple orbital interference effects in photoemission. Our experimental results are in quantitative agreement with both the tight-binding model and state-of-the-art fully relativistic calculations performed using the one-step model of photoemission. While spin-resolved ARPES probes the spin component of entangled spin-orbital texture in multiorbital systems, we unambiguously demonstrate that TRDAD reveals its orbital pseudospin texture counterpart.

Relation between spin-orbit induced spin polarization, Fano-effect and circular dichroism in soft x-ray photoemission

A Feynman diagram analysis of photoemission probabilities suggests a relation between two final-state spin polarization effects, the optical spin-orientation originating from the interaction with circularly polarized light ([Formula: see text], Fano effect) and the spin polarization induced by the spin-orbit scattering ([Formula: see text], Mott effect). The analysis predicts that [Formula: see text] is proportional to the product of [Formula: see text] and the circular dichroism in the angular distribution (CDAD) of photoelectrons. To confirm this prediction, the spin polarization of photoelectrons excited by soft x-ray radiation from initial spin-degenerate bulk states of tungsten using time-of-flight momentum microscopy with parallel spin detection has been measured. By measurement of four independent photoemission intensities for two opposite spin directions and opposite photon helicity, CDAD, Fano, and Mott effect are distinguished. The results confirm the prediction from the Feynman diagram analysis.

Dirac fermions and flat bands in the ideal kagome metal FeSn

A kagome lattice of 3d transition metal ions is a versatile platform for correlated topological phases hosting symmetry-protected electronic excitations and magnetic ground states. However, the paradigmatic states of the idealized two-dimensional kagome lattice-Dirac fermions and flat bands-have not been simultaneously observed. Here, we use angle-resolved photoemission spectroscopy and de Haas-van Alphen quantum oscillations to reveal coexisting surface and bulk Dirac fermions as well as flat bands in the antiferromagnetic kagome metal FeSn, which has spatially decoupled kagome planes. Our band structure calculations and matrix element simulations demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals, and evidence that the coexisting Dirac surface state realizes a rare example of fully spin-polarized two-dimensional Dirac fermions due to spin-layer locking in FeSn. The prospect to harness these prototypical excitations in a kagome lattice is a frontier of great promise at the confluence of topology, magnetism and strongly correlated physics.

Quantization in Chiral Higher Order Topological Insulators: Circular Dichroism and Local Chern Marker

The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual features related to quantization. First, we show that circular dichroism is quantized to an integer or zero depending on the orientation of the sample. This probe locates the hinge states, and can be used to distinguish different types of chiral HOTIs. Second, we find that the average of the local Chern marker over a single surface, an observable related to the surface Hall conductivity known to be quantized in the infinite slab geometry, is nonuniversal for a finite surface. This is due to a nonuniversal contribution of the hinge states, previously unaccounted for, that distinguishes surfaces of chiral HOTIs from Chern insulators. Our findings are relevant to establish higher order topology in systems such as the axion insulator candidate EuIn_{2}As_{2}, and cold atomic realizations.

Time-resolved XUV ARPES with tunable 24-33 eV laser pulses at 30 meV resolution

High harmonic generation of ultrafast laser pulses can be used to perform angle-resolved photoemission spectroscopy (ARPES) to map the electronic band structure of materials with femtosecond time resolution. However, currently it is difficult to reach high momenta with narrow energy resolution. Here, we combine a gas phase extreme ultraviolet (XUV) femtosecond light source, an XUV monochromator, and a time-of-flight electron analyzer to develop XUV-based time-resolved ARPES. Our technique can produce tunable photon energy between 24-33 eV with an unprecedented energy resolution of 30 meV and time resolution of 200 fs. This technique enables time-, energy- and momentum-resolved investigation of the nonequilibrium dynamics of electrons in materials with a full access to their first Brillouin zone. We evaluate the performance of this setup through exemplary measurements on various quantum materials, including WTe₂, WSe₂, TiSe₂, and Bi₂Sr₂CaCu₂O_8+δ.

Topological electronic structure and Rashba effect in Bi thin layers: theoretical predictions and experiments

The goal of the present review is to cross-compare theoretical predictions with selected experimental results on bismuth thin films exhibiting topological properties and a strong Rashba effect. The theoretical prediction that a single free-standing Bi(1 1 1) bilayer is a topological insulator has triggered a large series of studies of ultrathin Bi(1 1 1) films grown on various substrates. Using selected examples we review theoretical predictions of atomic and electronic structure of Bi thin films exhibiting topological properties due to interaction with a substrate. We also survey experimental signatures of topological surface states and Rashba effect, as obtained mostly by angle- and spin-resolved photoelectron spectroscopy.

Nonlinear Planar Hall Effect

An intriguing property of a three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new type of Hall effect in a 3D TI Bi_{2}Se_{3} film. The Hall resistance scales linearly with both the applied electric and magnetic fields and exhibits a π/2 angle offset with respect to its longitudinal counterpart, in contrast to the usual angle offset of π/4 between the linear planar Hall effect and the anisotropic magnetoresistance. This novel nonlinear planar Hall effect originates from the conversion of a nonlinear transverse spin current to a charge current due to the concerted actions of spin-momentum locking and time-reversal symmetry breaking, which also exists in a wide class of noncentrosymmetric materials with a large span of magnitude. It provides a new way to characterize and utilize the nonlinear spin-to-charge conversion in a variety of topological quantum materials.

Three-Dimensional Topological Insulator Bi2Te3/Organic Thin Film Heterojunction Photodetector with Fast and Wideband Response from 450 to 3500 Nanometers

In the pursuit of broadband photodetection materials from visible to mid-IR region, the fresh three-dimensional topological insulators (3D TIs) are theoretically predicted to be a promising candidate due to its Dirac-like stable surface state and high absorption rate. In this work, a self-powered inorganic/organic heterojunction photodetector based on n-type 3D TIs Bi₂Te₃ combined with p-type pentacene thin film was designed and fabricated. Surprisingly, it was found that the Bi₂Te₃/pentacene heterojunction photodetector exhibited a fast and wideband response from 450 to 3500 nm. The optimized responsivity of photodetector reached 14.89 A/W, along with the fast response time of 1.89 ms and the ultrahigh external quantum efficiency of 2840%. Moreover, at the mid-IR 3500 nm, our devices demonstrated a responsivity of 1.55 AW^-1, which was several orders of magnitude higher than that of previous 3D TIs photodetector. These excellent properties indicate that the inorganic/organic heterojunction, that is, the combination of 3D TIs with organic materials, is an exciting structure for high performance photodetectors in the wideband detection region. On account of the fact that the device is constructed on mica substrate, this work also represents a potential scenario for flexible optoelectronic devices.

Optically tunable spin texture of the surface state for Bi2Se3 and SmB6 topological insulators

The spin texture of the surface state for topological insulators can be manipulated by the polarization of light, which might play a potential role in the applications in spintronics. However, the study so far in this direction mainly focuses on the classical light-topological-insulators interactions; TIs coupled to quantized light remains barely explored. In this paper, we develop a formalism to deal with this issue of spin texture of the surface state for topological insulators (for example Bi₂Se₃ and SmB₆) irradiated by a quantum field, and we find that the coupling between an electron and a single-mode quantum field modulates only the arrow length that represents the spin polarization of a topological surface state. Specifically, when the photon number of a single-mode quantum field is fixed, the azimuth angle between the quantum light and the material surface manipulates the spin textures along the constant energy contour rotating (clockwise or counterclockwise) around the high symmetry point, and the polar angle controls the magnitude of the spin polarization. These results are quite different from the situation where an external field is not applied to an electron in a crystal or where a classical external field is utilized to control the spin polarization of a photoemitted electron in a vacuum. Our results have potential applications in quantum optics and condensed-matter physics.

Ultrafast Surface State Spin-Carrier Dynamics in the Topological Insulator Bi_{2}Te_{2}Se

Topological insulators are promising candidates for optically driven spintronic devices, because photoexcitation of spin polarized surface states is governed by angular momentum selection rules. We carry out femtosecond midinfrared spectroscopy on thin films of the topological insulator Bi_{2}Te_{2}Se, which has a higher surface state conductivity compared to conventionally studied Bi_{2}Se_{3} and Bi_{2}Te_{3}. Both charge and spin dynamics are probed utilizing circularly polarized light. With a sub-band-gap excitation, clear helicity-dependent dynamics is observed only in thin (<20  nm) flakes. On the other hand, such dependence is observed for both thin and thick flakes with above-band-gap excitation. The helicity dependence is attributed to asymmetric excitation of the Dirac-like surface states. The observed long-lasting asymmetry over 10 ps even at room temperature indicates low backscattering of surface state carriers which can be exploited for spintronic devices.

Functions to map photoelectron distributions in a variety of setups in angle-resolved photoemission spectroscopy

The distribution of photoelectrons acquired in angle-resolved photoemission spectroscopy can be mapped onto the energy-momentum space of the Bloch electrons in the crystal. The explicit forms of the mapping function f depend on the configuration of the apparatus as well as on the type of the photoelectron analyzer. We show that the existence of the analytic forms of f^-1 is guaranteed in a variety of setups. The variety includes the case when the analyzer is equipped with a photoelectron deflector. Thereby, we provide a demonstrative mapping program implemented by an algorithm that utilizes both f and f^-1. The mapping methodology is also usable in other spectroscopic methods such as momentum-resolved electron-energy loss spectroscopy.

Strong Linear Dichroism in Spin-Polarized Photoemission from Spin-Orbit-Coupled Surface States

A comprehensive understanding of spin-polarized photoemission is crucial for accessing the electronic structure of spin-orbit coupled materials. Yet, the impact of the final state in the photoemission process on the photoelectron spin has been difficult to assess in these systems. We present experiments for the spin-orbit split states in a Bi-Ag surface alloy showing that the alteration of the final state with energy may cause a complete reversal of the photoelectron spin polarization. We explain the effect on the basis of ab initio one-step photoemission theory and describe how it originates from linear dichroism in the angular distribution of photoelectrons. Our analysis shows that the modulated photoelectron spin polarization reflects the intrinsic spin density of the surface state being sampled differently depending on the final state, and it indicates linear dichroism as a natural probe of spin-orbit coupling at surfaces.

Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients ensure the possibility of the odd-frequency pairing: (1) the topological surface states, (2) the induced pair potential, and (3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac point in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary, the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.

Spin injection and helicity control of surface spin photocurrent in a three dimensional topological insulator

A three-dimensional (3D) topological insulator (TI) is a unique quantum phase of matter with exotic physical properties and promising spintronic applications. However, surface spin current in a common 3D TI remains difficult to control and the out-of-plane spin texture is largely unexplored. Here, by means of surface spin photocurrent in Bi₂Te₃ TI devices driven by circular polarized light, we identify the subtle effect of the spin texture of the topological surface state including the hexagonal warping term on the surface current. By exploring the out-of-plane spin texture, we demonstrate spin injection from GaAs to TI and its significant contribution to the surface current, which can be manipulated by an external magnetic field. These discoveries pave the way to not only intriguing new physics but also enriched spin functionalities by integrating TI with conventional semiconductors, such that spin-enabled optoelectronic devices may be fabricated in such hybrid structures.

Surface spin current in a 3D topological insulator (TI) remains difficult to control and the out-of-plane spin texture is largely unexplored. Here, the authors identify subtle effect of the spin texture on surface photocurrent and demonstrate controlled spin injection from a semiconductor to a TI.

Tunable Magnetic Anisotropy from Higher-Harmonics Exchange Scattering on the Surface of a Topological Insulator

We show that higher-harmonics exchange scattering from a magnetic adatom on the surface of a three dimensional topological insulator leads to a magnetic anisotropy whose magnitude and sign may be tuned by adjusting the chemical potential of the helical surface band. As the chemical potential moves from the Dirac point towards the surface band edge, the surface normal is found to change from a magnetic easy to a hard axis. Hexagonal warping is shown to diminish the region with easy axis anisotropy, and to suppress the anisotropy altogether. This indirect contribution can be comparable in magnitude to the intrinsic term arising from crystal field splitting and atomic spin-orbit coupling, and its tunability with the chemical potential makes the two contributions experimentally discernible, and endows this source of anisotropy with potentially interesting magnetic functionality.

Surface Kondo effect and non-trivial metallic state of the Kondo insulator YbB12

A synergistic effect between strong electron correlation and spin–orbit interaction has been theoretically predicted to realize new topological states of quantum matter on Kondo insulators (KIs), so-called topological Kondo insulators (TKIs). One TKI candidate has been experimentally observed on the KI SmB₆(001), and the origin of the surface states (SS) and the topological order of SmB₆ has been actively discussed. Here, we show a metallic SS on the clean surface of another TKI candidate YbB₁₂(001) using angle-resolved photoelectron spectroscopy. The SS shows temperature-dependent reconstruction corresponding to the Kondo effect observed for bulk states. Despite the low-temperature insulating bulk, the reconstructed SS with c–f hybridization is metallic, forming a closed Fermi contour surrounding on the surface Brillouin zone and agreeing with the theoretically expected behaviour for SS on TKIs. These results demonstrate the temperature-dependent holistic reconstruction of two-dimensional states localized on KIs surface driven by the Kondo effect.

Topological state in Kondo insulators has been provoked in SmB₆, but the origin of surface states and topological order remain elusive. Here, Hagiwara et al. report temperature dependent reconstruction of a metallic surface state on the (001) surface of YbB₁₂ driven by Kondo effect and discuss its origin from topology.

Pressure-induced phase transition in Bi2Se3 at 3 GPa: electronic topological transition or not?

In recent years, a low pressure transition around P3 GPa exhibited by the A2B3-type 3D topological insulators is attributed to an electronic topological transition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi2Se3) using Raman spectroscopy at pressure up to 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P2.4 GPa followed by structural transitions at ∼ 10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated Z2 invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition.

Pressure-induced electronic topological transition in Sb2S3

We report the high-pressure vibrational properties and a pressure-induced electronic topological transition in the wide bandgap semiconductor Sb2S3 (E g  =  1.7-1.8 eV) using Raman spectroscopy, resistivity and x-ray diffraction (XRD) studies. In this report, high-pressure Raman spectroscopy and resistivity studies of Sb2S3 have been carried out to 22 GPa and 11 GPa, respectively. We observed the softening of phonon modes [Formula: see text], [Formula: see text] and B 2g and a sharp anomaly in their line widths at 4 GPa. The resistivity studies corroborate this anomaly around similar pressures. The changes in resistivity as well as Raman line widths can be ascribed to the strong phonon-phonon coupling, indicating clear evidence of isostructural electronic topological transition in Sb2S3. The previously reported pressure dependence of a/c ratio plot obtained also showed a minimum at ~5 GPa consistent with our high-pressure Raman and resistivity results.

Spin-orbit coupling at surfaces and 2D materials

Spin-orbit interaction gives rise to a splitting of surface states via the Rashba effect, and in topological insulators it leads to the existence of topological surface states. The resulting k(//) momentum separation between states with the opposite spin underlies a wide range of new phenomena at surfaces and interfaces, such as spin transfer, spin accumulation, spin-to-charge current conversion, which are interesting for fundamental science and may become the basis for a breakthrough in the spintronic technology. The present review summarizes recent theoretical and experimental efforts to reveal the microscopic structure and mechanisms of spin-orbit driven phenomena with the focus on angle and spin-resolved photoemission and scanning tunneling microscopy.

Surface state photoelectrons in topological insulators: Green's function approach

We compute the photoemission intensity and polarization for the surface states in topological insulators. Due to the chirality and linear energy dispersion the effective electron-photon coupling is normalized by the tunneling amplitude (τ) into the vacuum. We investigate a chiral Dirac Hamiltonian for different cases: helical, Zeeman and warping, allowing us to study spin textures. Using the Green's function formalism we obtain exact results for the emitted photoelectrons to second order in the laser field. The number of emitted photoelectrons is sensitive to the laser coherent state intensity whereas the photoelectron polarization is sensitive to the surface topology of electronic states and incoming photon polarization.

Signature of Strong Spin-Orbital Coupling in the Large Nonsaturating Magnetoresistance Material WTe2

We report the detailed electronic structure of WTe2 by high resolution angle-resolved photoemission spectroscopy. We resolved a rather complicated Fermi surface of WTe2. Specifically, there are in total nine Fermi pockets, including one hole pocket at the Brillouin zone center Γ, and two hole pockets and two electron pockets on each side of Γ along the Γ-X direction. Remarkably, we have observed circular dichroism in our photoemission spectra, which suggests that the orbital angular momentum exhibits a rich texture at various sections of the Fermi surface. This is further confirmed by our density-functional-theory calculations, where the spin texture is qualitatively reproduced as the conjugate consequence of spin-orbital coupling. Since the spin texture would forbid backscatterings that are directly involved in the resistivity, our data suggest that the spin-orbit coupling and the related spin and orbital angular momentum textures may play an important role in the anomalously large magnetoresistance of WTe2. Furthermore, the large differences among spin textures calculated for magnetic fields along the in-plane and out-of-plane directions also provide a natural explanation of the large field-direction dependence on the magnetoresistance.

Scattering times and surface conductivity of Dirac fermions in a 3D topological insulator film with localised impurities

The zero gap surface states of a 3D-topological insulator host highly mobile Dirac fermions with spin locked to the momentum. The high mobility attributed to the absence of back scattering is reduced in the presence of impurities on the surface. In particular, we discuss and compare scattering times for localised impurities on the surface, scattering between states of opposite helicity located on different surfaces coupled through a hybridisation potential and the role of magnetic impurities. Magnetic impurities give rise to an additional spin suppression factor. The role of warped bands and their influence on topological factors that can enhance the overall surface mobility is examined. Finally, employing a linearised Boltzmann equation approach, surface conductivity calculations for Dirac fermions in a 3D TI is outlined.

Hierarchical spin-orbital polarization of a giant Rashba system

The Rashba effect is one of the most striking manifestations of spin-orbit coupling in solids and provides a cornerstone for the burgeoning field of semiconductor spintronics. It is typically assumed to manifest as a momentum-dependent splitting of a single initially spin-degenerate band into two branches with opposite spin polarization. Combining polarization-dependent and resonant angle-resolved photoemission measurements with density functional theory calculations, we show that the two "spin-split" branches of the model giant Rashba system BiTeI additionally develop disparate orbital textures, each of which is coupled to a distinct spin configuration. This necessitates a reinterpretation of spin splitting in Rashba-like systems and opens new possibilities for controlling spin polarization through the orbital sector.

RETRACTED: Observation of chiral currents at the magnetic domain boundary of a topological insulator

A magnetic domain boundary on the surface of a three-dimensional topological insulator is predicted to host a chiral edge state, but direct demonstration is challenging. We used a scanning superconducting quantum interference device to show that current in a magnetized topological insulator heterostructure (EuS/Bi2Se3) flows at the edge when the Fermi level is gate-tuned to the surface band gap. We further induced micrometer-scale magnetic structures on the heterostructure and detected a chiral edge current at the magnetic domain boundary. The chirality of the current was determined by magnetization of the surrounding domain, and its magnitude by the local chemical potential rather than the applied current. Such magnetic structures provide a platform for detecting topological magnetoelectric effects and may enable progress in quantum information processing and spintronics.

The evaluation of non-topological components in Berry phase and momentum relaxation time in a gapped 3D topological insulator

The zero gap surface states of a 3D-topological insulator host Dirac fermions with spin locked to the momentum. The gap-less Dirac fermions exhibit electronic behaviour different from those predicted in conventional materials. While calculations based on a simple linear dispersion can account for observed experimental patterns, a more accurate description of the physics of these systems and a better agreement between experimental data theoretical results can be obtained by including higher order k terms in the Hamiltonian. In this work, in presence of a time reversal symmetry breaking external magnetic field and higher order warping term, alteration to the topologically ordained Berry phase of (2n + 1)π, momentum relaxation time, and the magneto-conductivity tensors is established. The relation between scattering times and the deviations to topological Berry phase of π is also emphasized.

Photoemission Circular Dichroism and Spin Polarization of the Topological Surface States in Ultrathin Bi2Te3 Films

Circular dichroism (CD) observed by photoemission, being sensitive to the orbital and spin angular momenta of the electronic states, is a powerful probe of the nontrivial surface states of topological insulators, but the experimental results thus far have eluded a comprehensive description. We report a study of Bi2Te3 films with thicknesses ranging from one quintuple layer (two-dimensional limit) to 12 layers (bulk limit) over a wide range of incident photon energy. The data show complex variations in magnitude and sign reversals, which are nevertheless well described by a theoretical calculation including all three photoemission mechanisms: dipole transition, surface photoemission, and spin-orbit coupling. The results establish the nontrivial connection between the spin-orbit texture and CD.

Contact effects in thin 3D-topological insulators: how does the current flow?

The effect of different contact configurations (semi-infinite extended-channel, normal metal and ferromagnetic metal) on quantum transport through thin Bi2Se3 three-dimensional (3D) topological insulator (TI) slab (channel) has been investigated through Non-Equilibrium Green Function. The issue of contact dependent current flow and distribution across quintuple layers of 3D-TI has been addressed in this work and applied to expound the explanation for recent experimental work on electrical detection of spin-momentum locking on topological surface for long channel device. A theoretical model is propounded to develop a microscopic understanding of transport in 3D-TI in which contact type and magnetization concur with helical surface states of the TI channel to manifest seemingly counter-intuitive current distribution across layers. The quantum transport calculations for short channel devices with magnetic source and drain contacts postulate negative surface current for anti-phase magnetization whose axis is transverse to both current and quintuple layers. For in-phase magnetization at the two terminals, it is shown that observations can change fundamentally to result in anomalous current distribution. Such results are explained to stem from the confinement of 3D-TI between ferromagnetic contacts along the transport direction. A simple mechanism to validate topological insulators via quantum transport experiments has also been suggested.

Ultrafast helicity control of surface currents in topological insulators with near-unity fidelity

In recent years, a class of solid-state materials, called three-dimensional topological insulators, has emerged. In the bulk, a topological insulator behaves like an ordinary insulator with a band gap. At the surface, conducting gapless states exist showing remarkable properties such as helical Dirac dispersion and suppression of backscattering of spin-polarized charge carriers. The characterization and control of the surface states via transport experiments is often hindered by residual bulk contributions. Here we show that surface currents in Bi₂Se₃ can be controlled by circularly polarized light on a picosecond timescale with a fidelity near unity even at room temperature. We reveal the temporal separation of such ultrafast helicity-dependent surface currents from photo-induced thermoelectric and drift currents in the bulk. Our results uncover the functionality of ultrafast optoelectronic devices based on surface currents in topological insulators.

Bulk contributions to transport measurements often inhibit the study of the surface states of topological insulators. Here, Kastl et al. demonstrate high-fidelity helicity-dependent photocurrents in the surface states of Bi₂Se₃, controlled via circularly polarized light with a picosecond time-resolution.

Topological surface state enhanced photothermoelectric effect in Bi2Se3 nanoribbons

The photothermoelectric effect in topological insulator Bi2Se3 nanoribbons is studied. The topological surface states are excited to be spin-polarized by circularly polarized light. Because the direction of the electron spin is locked to its momentum for the spin-helical surface states, the photothermoelectric effect is significantly enhanced as the oriented motions of the polarized spins are accelerated by the temperature gradient. The results are explained based on the microscopic mechanisms of a photon induced spin transition from the surface Dirac cone to the bulk conduction band. The as-reported enhanced photothermoelectric effect is expected to have potential applications in a spin-polarized power source.

Angle-resolved photoemission spectroscopy study on the surface states of the correlated topological insulator YbB6

YbB₆ is recently predicted to be a moderately correlated topological insulator, which provides a playground to explore the interplay between correlation and topological properties. With angle-resolved photoemission spectroscopy, we directly observed almost linearly dispersive bands around the time-reversal invariant momenta and with negligible k_z dependence, consistent with odd number of surface states crossing the Fermi level in a Z₂ topological insulator. Circular dichroism photoemission spectra suggest that these in-gap states possess chirality of orbital angular momentum, which is related to the chiral spin texture, further indicative of their topological nature. The observed insulating gap of YbB₆ is about 100 meV, larger than that found by theoretical calculations. Our results present strong evidence that YbB₆ is a correlated topological insulator and provide a foundation for further studies of this promising material.

Observation of possible topological in-gap surface states in the Kondo insulator SmB6 by photoemission

SmB₆, a well-known Kondo insulator, exhibits a transport anomaly at low temperature. This anomaly is usually attributed to states within the hybridization gap. Recent theoretical work and transport measurements suggest that these in-gap states could be ascribed to topological surface states, which would make SmB₆ the first realization of topological Kondo insulator. Here by performing angle-resolved photoemission spectroscopy experiments, we directly observe several dispersive states within the hybridization gap of SmB₆. These states show negligible k_z dependence, which indicates their surface origin. Furthermore, we perform photoemission circular dichroism experiments, which suggest that the in-gap states possess chirality of the orbital angular momentum. These states vanish simultaneously with the hybridization gap at around 150 K. Together, these observations suggest the possible topological origin of the in-gap states.

The Kondo insulator samarium hexaboride exhibits low-temperature transport anomalies, which might be due to topological surface states. Here Jiang et al. perform angle-resolved photoemission and its circular dichroism measurements, which suggest that the anomalies might be of topological origin.

Identification of helicity-dependent photocurrents from topological surface states in Bi2Se3 gated by ionic liquid

Dirac-like surface states on surfaces of topological insulators have a chiral spin structure with spin locked to momentum, which is interesting in physics and may also have important applications in spintronics. In this work, by measuring the tunable helicity-dependent photocurrent (HDP), we present an identification of the HDP from the Dirac-like surface states at room temperature. It turns out that the total HDP has two components, one from the Dirac-like surface states, and the other from the surface accumulation layer. These two components have opposite directions. The clear gate tuning of the electron density as well as the HDP signal indicates that the surface band bending and resulted surface accumulation are successfully modulated by the applied ionic liquid gate, which provides a promising way to the study of the Dirac-like surface states and also potential applications in spintronic devices.

Photoelectron spin-polarization control in the topological insulator Bi2Se3

We study the manipulation of the spin polarization of photoemitted electrons in Bi2Se3 by spin- and angle-resolved photoemission spectroscopy. General rules are established that enable controlling the photoelectron spin-polarization. We demonstrate the ± 100% reversal of a single component of the measured spin-polarization vector upon the rotation of light polarization, as well as full three-dimensional manipulation by varying experimental configuration and photon energy. While a material-specific density-functional theory analysis is needed for the quantitative description, a minimal yet fully generalized two-atomic-layer model qualitatively accounts for the spin response based on the interplay of optical selection rules, photoelectron interference, and topological surface-state complex structure. It follows that photoelectron spin-polarization control is generically achievable in systems with a layer-dependent, entangled spin-orbital texture.

Dirac cone with helical spin polarization in ultrathin α-Sn(001) films

Spin-split two-dimensional electronic states have been observed on ultrathin Sn(001) films grown on InSb(001) substrates. Angle-resolved photoelectron spectroscopy (ARPES) performed on these films revealed Dirac-cone-like linear dispersion around the Γ¯ point of the surface Brillouin zone, suggesting nearly massless electrons belonging to 2D surface states. The states disperse across a band gap between bulklike quantum well states in the films. Moreover, both circular dichroism of ARPES and spin-resolved ARPES studies show helical spin polarization of the Dirac-cone-like surface states, suggesting a topologically protected character as in a bulk topological insulator (TI). These results indicate that a quasi-3D TI phase can be realized in ultrathin films of zero-gap semiconductors.

Observation of Floquet-Bloch states on the surface of a topological insulator

The unique electronic properties of the surface electrons in a topological insulator are protected by time-reversal symmetry. Circularly polarized light naturally breaks time-reversal symmetry, which may lead to an exotic surface quantum Hall state. Using time- and angle-resolved photoemission spectroscopy, we show that an intense ultrashort midinfrared pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topological insulator to form Floquet-Bloch bands. These photon-dressed surface bands exhibit polarization-dependent band gaps at avoided crossings. Circularly polarized photons induce an additional gap at the Dirac point, which is a signature of broken time-reversal symmetry on the surface. These observations establish the Floquet-Bloch bands in solids and pave the way for optical manipulation of topological quantum states of matter.