A tunable topological insulator in the spin helical Dirac transport regime

Stochastically Broken Inversion Symmetry of Van der Waals Topological Insulator for Nanoscale Physically Unclonable Functions

Owing to the exotic state of quantum matter, topological insulators have emerged as a significant platform for new-generation functional devices. Among these topological insulators, tetradymites have received significant attention because of their van der Waals (vdW) structures and inversion symmetries. Although this inversion symmetry completely blocks exotic quantum phenomena, it should be broken down to facilitate versatile topological functionalities. Recently, a Janus structure is suggested for asymmetric out-of-plane lattice structures, terminating the heterogeneous atoms at two sides of the vdW structure. However, the synthesis of Janus structures has not been achieved commercially because of the imprecise control of the layer-by-layer growth, high-temperature synthesis, and low yield. To overcome these limitations, plasma sulfurization of vdW topological insulators has been presented, enabling stochastic inversion asymmetry. To take practical advantage of the random lattice distortion, physically unclonable functions (PUFs) have been suggested as applications of vdW Janus topological insulators. The sulfur dominance is experimentally demonstrated via X-ray photoelectron spectroscopy, hysteresis variation, cross-sectional transmission electron microscopy, and adhesion energy variation. In conclusion, it is envisioned that the vdW Janus topological insulators can provide an extendable encryption platform for randomized lattice distortion, offering on-demand stochastic inversion asymmetry via a single-step plasma sulfurization.

Spin logic enabled by current vector adder

In order to advance the silicon integrated circuit technology, researchers have been searching for memory and logic devices with new physical state variables other than charge. Spin logic device that adds one degree of freedom-electron spin to charge has been considered as a promising candidate due to its low power consumption, built-in memory, and high scalability. Here, we demonstrate that a new variable - current direction on the sample can be introduced into the spin logic operation. The current direction of the sample is considered as a vector. For the various input currents along different directions, the direction of vector sum (vector adder) determines the output and therefore can enable complex logic functions. We have realized the basic Boolean logic gates including AND, OR, NAND, NOR, and even complicated IMPLY in a single device and further constructed a full adder with only 2 devices.

Spin-dependent thermoelectric properties of a hybrid ferromagnetic metal/quantum dot/topological insulator junction

The thermoelectric properties of hybrid system based on a single-level quantum dot coupled to a ferromagnetic metallic lead and attached to the surface states of a three-dimensional topological insulator are theoretically investigated. On the surface of a three-dimensional topological insulator, massless helical Dirac fermions emerge. We calculate the thermoelectric coefficients, including electrical conductance, Seebeck coefficient (thermopower), heat conductance, and the figure of merit, using the nonequilibrium Green's function technique. The results are analyzed in terms of the emergence of new effects. The calculations are performed within the Hubbard I approximation concerning the dot's Coulomb interactions. Additionally, the spin-dependent coupling of the quantum dot to the ferromagnetic lead lifts the spin degeneracy of the dot's level, which influences the transport properties of the system. We incorporate this effect perturbatively to obtain the spin-dependent renormalization of the dot's level. We also consider the case of finite spin accumulation in the ferromagnetic electrode, which leads to spin thermoelectric effects.

Probing Berry Phase Effect in Topological Surface States

We have observed the Berry phase effect associated with interband coherence in topological surface states (TSSs) using two-color high-harmonic spectroscopy. This Berry phase accumulates along the evolution path of strong field-driven electron-hole quasiparticles in electronic bands with strong spin-orbit coupling. By introducing a secondary weak field, we perturb the evolution of Dirac fermions in TSSs and thus provide access to the Berry phase. We observe a significant shift in the oscillation phase of the even-order harmonics from the spectral interferogram. We reveal that such a modulation feature is linked to the geometric phase acquired in the nonperturbative dynamics of TSSs. Furthermore, we show that the overwhelming Berry phase effect can significantly deform the quantum paths of electron-hole pairs, thus enhancing the ability to harness electron spin using lightwaves in quantum materials with strong spin-orbit interactions.

Br-Vacancies Induced Variable Ranging Hopping Conduction in High-Order Topological Insulator Bi4Br4

The defects have a remarkable influence on the electronic structures and the electric transport behaviors of the matter, providing the additional means to engineering their physical properties. In this work, a comprehensive study on the effect of Br-vacancies on the electronic structures and transport behaviors in the high-order topological insulator Bi4Br4 is performed by the combined techniques of the scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), and physical properties measurement system along with the first-principle calculations. The STM results show the defects on the cleaved surface of a single crystal and reveal that the defects are correlated to the Br-vacancies with the support of the simulated STM images. The role of the Br-vacancies in the modulation of the band structures has been identified by ARPES spectra and the calculated energy-momentum dispersion. The relationship between the Br-vacancies and the semiconducting-like transport behaviors at low temperature has been established, implying a Mott variable ranging hopping conduction in Bi4Br4. The work not only resolves the unclear transport behaviors in this matter, but also paves a way to modulate the electric conduction path by the defects engineering.

Spin-Hall conductivity and optical characteristics of noncentrosymmetric quantum spin Hall insulators: the case of PbBiI

Quantum spin Hall insulators have attracted significant attention in recent years. Understanding the optical properties and spin Hall effect in these materials is crucial for technological advancements. In this study, we present theoretical analyses to explore the optical properties, Berry curvature and spin Hall conductivity of pristine and perturbed PbBiI using the linear combination of atomic orbitals and the Kubo formula. The system is not centrosymmetric and it is hosting at the same time Rashba spin-splitting and quantized spin Hall conductivity. Our calculations reveal that the electronic structure can be modified using staggered exchange fields and electric fields, leading to changes in the optical properties. Additionally, the spin Berry curvature and spin Hall conductivity are investigated as a function of the energy and temperature. The results indicate that due to the small dynamical spin Hall conductivity, generating an ac spin current in the PbBiI requires the use of external magnetic fields or magnetic materials.

Visualization of spin-polarized surface resonances in Pb-based ternary topological insulators

The formation of the topological surface state originates from bulk band inversion at the top of the valence band and the bottom of the conduction band. The transition between normal and topological insulators is known as a topological phase transition. Here we show spin-polarized electronic states of Pb-based ternary topological insulators Pb(Bi1-xSbx)2Te4 (x = 0.55, 0.70, 0.79) investigated by spin- and angle-resolved photoemission spectroscopy and first-principles calculations. We visualize a pair of spin-polarized surface resonances dispersing along the upper edge of projected bulk bands in occupied states. Interestingly, a branch of the spin-polarized surface resonances continuously connects to the topological surface state. The coexistence of the topological surface state and the spin-polarized surface resonances can be explained by considering the topological phase transition.

Topological Surface State Evolution in Bi2Se3 via Surface Etching

Topological insulators are materials that have an insulating bulk interior while maintaining gapless boundary states against back scattering. Bi2Se3 is a prototypical topological insulator with a Dirac-cone surface state around Γ. Here, we present a controlled methodology to gradually remove Se atoms from the surface Se-Bi-Se-Bi-Se quintuple layers, eventually forming bilayer-Bi on top of the quintuple bulk. Our method allows us to track the topological surface state and confirm its robustness throughout the surface modification. Importantly, we report a relocation of the topological Dirac cone in both real space and momentum space as the top surface layer transitions from quintuple Se-Bi-Se-Bi-Se to bilayer-Bi. Additionally, charge transfer among the different surface layers is identified. Our study provides a precise method to manipulate surface configurations, allowing for the fine-tuning of the topological surface states in Bi2Se3, which represents a significant advancement toward nanoengineering of topological states.

Efficiency improvement of spin-resolved ARPES experiments using Gaussian process regression

The experimental efficiency has been a central concern for time-consuming experiments. Spin- and angle-resolved photoemission spectroscopy (spin-resolved ARPES) is renowned for its inefficiency in spin-detection, despite its outstanding capability to directly determine the spin-polarized electronic properties of materials. Here, we investigate the potential enhancement of the efficiency of spin-resolved ARPES experiments through the integration of measurement informatics. We focus on a representative topological insulator Bi 2 Te 3 , which has well-understood spin-polarized electronic states. We employ Gaussian process regression (GPR) to assess the accumulation of spin polarization information using an indicator known as the GPR score. Our analyses based on the GPR model suggest that the GPR score can serve as a stopping criterion for spin-resolved ARPES experiments. This criterion enables us to conduct efficient spin-resolved ARPES experiments, significantly reducing the time costs by 5-10 times, compared to empirical stopping criteria.

Geometric Amplitude Accompanying Local Responses: Spinor Phase Information from the Amplitudes of Spin-Polarized STM Measurements

Solving the Hamiltonian of a system yields the energy dispersion and eigenstates. The geometric phase of the eigenstates generates many novel effects and potential applications. However, the geometric properties of the energy dispersion go unheeded. Here, we provide geometric insight into energy dispersion and introduce a geometric amplitude, namely, the geometric density of states (GDOS) determined by the Riemann curvature of the constant-energy contour. The geometric amplitude should accompany various local responses, which are generally formulated by the real-space Green's function. Under the stationary phase approximation, the GDOS simplifies the Green's function into its ultimate form. In particular, the amplitude factor embodies the spinor phase information of the eigenstates, favoring the extraction of the spin texture for topological surface states under an in-plane magnetic field through spin-polarized STM measurements. This work opens a new avenue for exploring the geometric properties of electronic structures and excavates the unexplored potential of spin-polarized STM measurements to probe the spinor phase information of eigenstates from their amplitudes.

Memristive switching in the surface of a charge-density-wave topological semimetal

Owing to the outstanding properties provided by nontrivial band topology, topological phases of matter are considered as a promising platform towards low-dissipation electronics, efficient spin-charge conversion, and topological quantum computation. Achieving ferroelectricity in topological materials enables the non-volatile control of the quantum states, which could greatly facilitate topological electronic research. However, ferroelectricity is generally incompatible with systems featuring metallicity due to the screening effect of free carriers. In this study, we report the observation of memristive switching based on the ferroelectric surface state of a topological semimetal (TaSe4)2I. We find that the surface state of (TaSe4)2I presents out-of-plane ferroelectric polarization due to surface reconstruction. With the combination of ferroelectric surface and charge-density-wave-gapped bulk states, an electric-switchable barrier height can be achieved in (TaSe4)2I-metal contact. By employing a multi-terminal-grounding design, we manage to construct a prototype ferroelectric memristor based on (TaSe4)2I with on/off ratio up to 103, endurance over 103 cycles, and good retention characteristics. The origin of the ferroelectric surface state is further investigated by first-principles calculations, which reveal an interplay between ferroelectricity and band topology. The emergence of ferroelectricity in (TaSe4)2I not only demonstrates it as a rare but essential case of ferroelectric topological materials, but also opens new routes towards the implementation of topological materials in functional electronic devices.

Observation of edge states derived from topological helix chains

Introducing the concept of topology has revolutionized materials classification, leading to the discovery of topological insulators and Dirac-Weyl semimetals1-3. One of the most fundamental theories underpinning topological materials is the Su-Schrieffer-Heeger (SSH) model4,5, which was developed in 1979-decades before the recognition of topological insulators-to describe conducting polymers. Distinct from the vast majority of known topological insulators with two and three dimensions1-3, the SSH model predicts a one-dimensional analogue of topological insulators, which hosts topological bound states at the endpoints of a chain4-8. To establish this unique and pivotal state, it is crucial to identify the low-energy excitations stemming from bound states, but this has remained unknown in solids because of the absence of suitable platforms. Here we report unusual electronic states that support the emergent bound states in elemental tellurium, the single helix of which was recently proposed to realize an extended version of the SSH chain9,10. Using spin- and angle-resolved photoemission spectroscopy with a micro-focused beam, we have shown spin-polarized in-gap states confined to the edges of the (0001) surface. Our density functional theory calculations indicate that these states are attributed to the interacting bound states originating from the one-dimensional array of SSH tellurium chains. Helices in solids offer a promising experimental platform for investigating exotic properties associated with the SSH chain and exploring topological phases through dimensionality control.

Effect of an external/internal magnetic field on the photocurrent in Py-topological insulator heterojunction Ni80Fe20/TI (Bi2Te3/Bi2Se3/Bi2Te2Se)/p-Si devices

This study demonstrates the fabrication and study of a permalloy (Py)/topological insulator heterojunction, i.e., the Ni80Fe20/TI(Bi2Te3/Bi2Se3/Bi2Te2Se)/p-Si heterojunction, for spintronic device applications at room temperature. In this work, the forward current values, under the absence of a magnetic field, for Ni80Fe20/Bi2Te2Se/p-Si, Ni80Fe20/Bi2Se3/p-Si, and Ni80Fe20/Bi2Te3/p-Si heterojunctions were 12.7 μA, 8.7 μA, and 6.85 μA, respectively; while in the presence of a magnetic field, the corresponding values were 10.8 μA, 7.6 μA, and 4.47 μA, respectively. Such reductions in current were attributed to an increase in the resistance of the p-n junction diode due to Lorentz force and a magnetoresistance effect, which was also verified using magneto-transport measurements. This resulted in a modification of the space charge shape and an increase in the potential barrier. Along with this, the magnetic field also affected the diffusion length, leading to a reduction in the current. Such a phenomenon enables the development of durable devices with improved reliability and longevity under harsh environments. The special features of topological edge states in the presence of a magnetic field can be used for sophisticated sensing applications. The future applications will likely lead to the emergence of other novel applications across disciplines such as computing, health, materials science, and energy harvesting.

Topological spin textures in electronic non-Hermitian systems

Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification of observables. However, their counterpart in solid-state electronic systems in equilibrium remains unmasked although highly desired, where a variety of materials are available, calculations are solidly founded, and accurate spectroscopic techniques can be applied. We demonstrate that, in the surface state of a topological insulator with spin-dependent relaxation due to magnetic impurities, highly nontrivial topological soliton spin textures appear in momentum space. Such spin-channel phenomena are delicately related to the type of non-Hermiticity and correctly reveal the most robust non-Hermitian features detectable spectroscopically. Moreover, the distinct topological soliton objects can be deformed to each other, mediated by topological transitions driven by tuning across a critical direction of doped magnetism. These results not only open a solid-state avenue to exotic spin patterns via spin- and angle-resolved photoemission spectroscopy, but also inspire non-Hermitian dissipation engineering of spins in solids.

Observation of Emergent Superconductivity in the Topological Insulator Ta2Pd3Te5 via Pressure Manipulation

Topological insulators offer significant potential to revolutionize diverse fields driven by nontrivial manifestations of their topological electronic band structures. However, the realization of superior integration between exotic topological states and superconductivity for practical applications remains a challenge, necessitating a profound understanding of intricate mechanisms. Here, we report experimental observations for a novel superconducting phase in the pressurized second-order topological insulator candidate Ta2Pd3Te5, and the high-pressure phase maintains its original ambient pressure lattice symmetry up to 45 GPa. Our in situ high-pressure synchrotron X-ray diffraction, electrical transport, infrared reflectance, and Raman spectroscopy measurements, in combination with rigorous theoretical calculations, provide compelling evidence for the association between the superconducting behavior and the densified phase. The electronic state change around 20 GPa was found to modify the topology of the Fermi surface directly, which synergistically fosters the emergence of robust superconductivity. In-depth comprehension of the fascinating properties exhibited by the compressed Ta2Pd3Te5 phase is achieved, highlighting the extraordinary potential of topological insulators for exploring and investigating high-performance electronic advanced devices under extreme conditions.

On the topological surface states of the intrinsic magnetic topological insulator Mn-Bi-Te family

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.

Laser-based angle-resolved photoemission spectroscopy with micrometer spatial resolution and detection of three-dimensional spin vector

We have developed a state-of-the-art apparatus for laser-based spin- and angle-resolved photoemission spectroscopy with micrometer spatial resolution (µ-SARPES). This equipment is realized by the combination of a high-resolution photoelectron spectrometer, a 6 eV laser with high photon flux that is focused down to a few micrometers, a high-precision sample stage control system, and a double very-low-energy-electron-diffraction spin detector. The setup achieves an energy resolution of 1.5 (5.5) meV without (with) the spin detection mode, compatible with a spatial resolution better than 10 µm. This enables us to probe both spatially-resolved electronic structures and vector information of spin polarization in three dimensions. The performance of µ-SARPES apparatus is demonstrated by presenting ARPES and SARPES results from topological insulators and Au photolithography patterns on a Si (001) substrate.

Probing Spin-Dependent Ballistic Charge Transport at Single-Nanometer Length Scales

The coherent transport of charge and spin is a key requirement of future devices for quantum computing and communication. Scattering at defects or impurities may significantly reduce the coherence of quantum-mechanical states, thereby affecting the device functionality. While numerous methods exist to experimentally assess charge transport, the real-space detection of a material's ballistic spin transport properties with nanometer resolution remains a challenge. Here we report on a novel approach that utilizes a combination of spin-polarized scanning tunneling microscopy (SP-STM) and the recently introduced molecular nanoprobe (MONA) technique. It relies on the local injection of spin-polarized charge carriers from a magnetic STM tip and their detection by a single surface-deposited phthalocyanine molecule via reversible electron-induced tautomerization events. Based on the particular electronic structure of the Rashba alloy BiAg2, which is governed by a spin-momentum-locked surface state, we prove that the current direction inverses upon tip magnetization reversal.

Revealing the Interplay between Strong Field Selection Rules and Crystal Symmetries

Symmetries are ubiquitous in condensed matter physics, playing an important role in the appearance of different phases of matter. Nonlinear light matter interactions serve as a coherent probe for resolving symmetries and symmetry breaking via their link to selection rules of the interaction. In the extreme nonlinear regime, high harmonic generation (HHG) spectroscopy offers a unique spectroscopic approach to study this link, probing the crystal spatial properties with high sensitivity while opening new paths for selection rules in the XUV regime. In this Letter we establish an advanced HHG polarimetry scheme, driven by a multicolor strong laser field, to observe the structural symmetries of solids and their interplay with the HHG selection rules. By controlling the crystal symmetries, we resolve nontrivial polarization states associated with new spectral features in the HHG spectrum. Our scheme opens new opportunities in resolving the symmetries of quantum materials, as well as ultrafast light driven symmetries in condensed matter systems.

Electron- versus Spin-Phonon Coupling Governs the Temperature-Dependent Carrier Dynamics in the Topological Insulator Bi2Te3

Ultrafast charge and spin dynamics have immense effects on the applications of topological insulators (TIs). By performing spin-adiabatic nonadiabatic molecular dynamics simulations in the presence of electron-phonon (e-ph) and spin-phonon couplings, we investigate temperature-dependent intra- and interband charge and spin relaxation dynamics via the bulk and surface paths in the three-dimensional TI Bi2Te3. The e-ph coupling dominates charge relaxation in the bulk path, and the relaxation rate is positively correlated with temperature due to the large energy gaps and weak spin polarization. Conversely, the relaxation dynamics exhibits an opposite temperature dependence in the surface path because of electron re-excitation and spin mismatching induced by spin-phonon coupling, which arises from small energy gaps and strong spin polarization. The two mechanisms rationalize the charge carriers being long-lived in the bulk and surface phases at low and room temperature, respectively. Additionally, strong thermal fluctuations of the topological states' magnetic moments destroy the spin-momentum locking and trigger backscattering at room temperature.

Magnetotransport Signatures of Superconducting Cooper Pairs Carried by Topological Surface States in Bismuth Selenide

As topological insulators (TIs) are becoming increasingly intriguing, the community is exploring transformative applications that require interfacing TIs with other materials such as ferromagnets or superconductors. Herein, we report on the manifestations of superconducting electrons carried by topological surface states (TSS) in Bi2Se3 films. As key signatures of TSS-carried Cooper pairs, we uncover the hysteresis of magnetoresistance (MR) and the switching behavior of anisotropic magnetoresistance (AMR). For in-plane fields perpendicular to the injected current, AMR shows negative switching (resistance drop) when the contacts become superconducting, which is consistent with a cooperative Zeeman effect enabled by the spin-momentum locking of TSS. The MR and AMR behaviors are robust, occurring reliably in multiple samples, from different sources, and with different defect concentrations. Our findings can guide novel developments in superconductor/TI quantum devices relying on supercurrent detection as well as lead to more refined transport signatures of Majorana zero-modes in the future.

Exploiting the Close-to-Dirac Point Shift of the Fermi Level in the Sb2Te3/Bi2Te3 Topological Insulator Heterostructure for Spin-Charge Conversion

Properly tuning the Fermi level position in topological insulators is of vital importance to tailor their spin-polarized electronic transport and to improve the efficiency of any functional device based on them. Here, we report the full in situ metal organic chemical vapor deposition (MOCVD) and study of a highly crystalline Bi2Te3/Sb2Te3 topological insulator heterostructure on top of large area (4″) Si(111) substrates. The bottom Sb2Te3 layer serves as an ideal seed layer for the growth of highly crystalline Bi2Te3 on top, also inducing a remarkable shift of the Fermi level to place it very close to the Dirac point, as visualized by angle-resolved photoemission spectroscopy. To exploit such ideal topologically protected surface states, we fabricate the simple spin-charge converter Si(111)/Sb2Te3/Bi2Te3/Au/Co/Au and probe the spin-charge conversion (SCC) by spin pumping ferromagnetic resonance. A large SCC is measured at room temperature and is interpreted within the inverse Edelstein effect, thus resulting in a conversion efficiency of λIEEE ∼ 0.44 nm. Our results demonstrate the successful tuning of the surface Fermi level of Bi2Te3 when grown on top of Sb2Te3 with a full in situ MOCVD process, which is highly interesting in view of its future technology transfer.

Giant Spin-Orbit Torque in Sputter-Deposited Bi Films

Bismuth (Bi) has the strongest spin-orbit coupling among non-radioactive elements and is thus a promising material for efficient charge-to-spin conversion. However, previous electrical detections have reported controversial results for the conversion efficiency. In this study, an optical detection of a spin-orbit torque is reported in a Bi/CoFeB bilayer with a polycrystalline texture of (012) and (003). Taking advantage of the optical detection, spin-orbit torque is accurately separated from the Oersted field and achieves a giant damping-like torque efficiency of +0.5, verifying efficient charge-to-spin conversion. This study also demonstrates a field-like torque efficiency of -0.1. For the mechanism of the charge-to-spin conversion, the bulk spin Hall effect and the interface Rashba-Edelstein effect are considered.

Development of deflector mode for spin-resolved time-of-flight photoemission spectroscopy

Spin- and angle-resolved photoemission spectroscopy ("spin-ARPES") is a powerful technique for probing the spin degree-of-freedom in materials with nontrivial topology, magnetism, and strong correlations. Spin-ARPES faces severe experimental challenges compared to conventional ARPES attributed to the dramatically lower efficiency of its detection mechanism, making it crucial for instrumentation developments that improve the overall performance of the technique. In this paper, we demonstrate the functionality of our spin-ARPES setup based on time-of-flight spectroscopy and introduce our recent development of an electrostatic deflector mode to map out spin-resolved band structures without sample rotation. We demonstrate the functionality by presenting the spin-resolved spectra of the topological insulator Bi2Te3 and describe in detail the spectrum calibrations based on numerical simulations. By implementing the deflector mode, we minimize the need for sample rotation during measurements, hence improving the overall efficiency of experiments on small or inhomogeneous samples.

Room Temperature Spin-to-Charge Conversion in Amorphous Topological Insulating Gd-Alloyed BixSe1-x/CoFeB Bilayers

Disordered topological insulator (TI) films have gained intense interest by benefiting from both the TI's exotic transport properties and the advantage of mass production by sputtering. Here, we report on the clear evidence of spin-charge conversion (SCC) in amorphous Gd-alloyed BixSe1-x (BSG)/CoFeB bilayers fabricated by sputtering, which could be related to the amorphous TI surface states. Two methods have been employed to study SCC in BSG (tBSG = 6-16 nm)/CoFeB(5 nm) bilayers with different BSG thicknesses. First, spin pumping is used to generate a spin current in CoFeB and detect SCC by the inverse Edelstein effect (IEE). The maximum SCC efficiency (SCE) is measured to be as large as 0.035 nm (IEE length λIEE) in a 6 nm thick BSG sample, which shows a strong decay when tBSG increases due to the increase of BSG surface roughness. The second method is THz time-domain spectroscopy, which reveals a small tBSG dependence of SCE, validating the occurrence of a pure interface state-related SCC. Furthermore, our angle-resolved photoemission spectroscopy data show dispersive two-dimensional surface states that cross the bulk gap until the Fermi level, strengthening the possibility of SCC due to the amorphous TI states. Our studies provide a new experimental direction toward the search for topological systems in amorphous solids.

Giant and Tunable Out-of-Plane Spin Polarization of Topological Antimonene

Topological insulators are bulk insulators with metallic and fully spin-polarized surface states displaying Dirac-like band dispersion. Due to spin-momentum locking, these topological surface states (TSSs) have a predominant in-plane spin polarization in the bulk fundamental gap. Here, we show by spin-resolved photoemission spectroscopy that the TSS of a topological insulator interfaced with an antimonene bilayer exhibits nearly full out-of-plane spin polarization within the substrate gap. We connect this phenomenon to a symmetry-protected band crossing of the spin-polarized surface states. The nearly full out-of-plane spin polarization of the TSS occurs along a continuous path in the energy-momentum space, and the spin polarization within the gap can be reversibly tuned from nearly full out-of-plane to nearly full in-plane by electron doping. These findings pave the way to advanced spintronics applications that exploit the giant out-of-plane spin polarization of TSSs.

Monolayer Superconductivity and Tunable Topological Electronic Structure at the Fe(Te,Se)/Bi2 Te3 Interface

The interface between 2D topological Dirac states and an s-wave superconductor is expected to support Majorana-bound states (MBS) that can be used for quantum computing applications. Realizing these novel states of matter and their applications requires control over superconductivity and spin-orbit coupling to achieve spin-momentum-locked topological interface states (TIS) which are simultaneously superconducting. While signatures of MBS have been observed in the magnetic vortex cores of bulk FeTe_0.55 Se_0.45 , inhomogeneity and disorder from doping make these signatures unclear and inconsistent between vortices. Here superconductivity is reported in monolayer (ML) FeTe_1-y Se_y (Fe(Te,Se)) grown on Bi₂ Te₃ by molecular beam epitaxy (MBE). Spin and angle-resolved photoemission spectroscopy (SARPES) directly resolve the interfacial spin and electronic structure of Fe(Te,Se)/Bi₂ Te₃ heterostructures. For y = 0.25, the Fe(Te,Se) electronic structure is found to overlap with the Bi₂ Te₃ TIS and the desired spin-momentum locking is not observed. In contrast, for y = 0.1, reduced inhomogeneity measured by scanning tunneling microscopy (STM) and a smaller Fe(Te,Se) Fermi surface with clear spin-momentum locking in the topological states are found. Hence, it is demonstrated that the Fe(Te,Se)/Bi₂ Te₃ system is a highly tunable platform for realizing MBS where reduced doping can improve characteristics important for Majorana interrogation and potential applications.

Exchange-Driven Intermixing of Bulk and Topological Surface States by Chiral Excitons in Bi_{2}Se_{3}

Topological surface states (TSS) in the prototypical topological insulator (TI) Bi_{2}Se_{3} are frequently characterized using optical probes, but electron-hole interactions and their effect on surface localization and optical response of the TSS remain unexplored. Here, we use ab initio calculations to understand excitonic effects in the bulk and surface of Bi_{2}Se_{3}. We identify multiple series of chiral excitons that exhibit both bulk and TSS character, due to exchange-driven mixing. Our results address fundamental questions about the degree to which electron-hole interactions can relax the topological protection of surface states and dipole selection rules for circularly polarized light in TIs by elucidating the complex intermixture of bulk and surface states excited in optical measurements and their coupling to light.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

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.

Topological Insulator Metamaterials

Confinement of electromagnetic fields at the subwavelength scale via metamaterial paradigms is an established method to engineer light-matter interaction in most common material systems, from insulators to semiconductors and from metals to superconductors. In recent years, this approach has been extended to the realm of topological materials, providing a new avenue to access nontrivial features of their electronic band structure. In this review, we survey various topological material classes from a photonics standpoint, including crystal growth and lithographic structuring methods. We discuss how exotic electronic features such as spin-selective Dirac plasmon polaritons in topological insulators or hyperbolic plasmon polaritons in Weyl semimetals may give rise to unconventional magneto-optic, nonlinear, and circular photogalvanic effects in metamaterials across the visible to infrared spectrum. Finally, we dwell on how these effects may be dynamically controlled by applying external perturbations in the form of electric and magnetic fields or ultrafast optical pulses. Through these examples and future perspectives, we argue that topological insulator, semimetal and superconductor metamaterials are unique systems to bridge the missing links between nanophotonic, electronic, and spintronic technologies.

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.

Direct Observation of the Topological Surface State in the Topological Superconductor 2M-WS2

The quantum spin Hall (QSH) effect has attracted extensive research interest because of the potential applications in spintronics and quantum computing, which is attributable to two conducting edge channels with opposite spin polarization and the quantized electronic conductance of 2e²/h. Recently, 2M-WS₂, a new stable phase of transition metal dichalcogenides with a 2M structure showing a layer configuration identical to that of the monolayer 1T' TMDs, was suggested to be a QSH insulator as well as a superconductor with a critical transition temperature of around 8 K. Here, high-resolution angle-resolved photoemission spectroscopy (ARPES) and spin-resolved ARPES are applied to investigate the electronic and spin structure of the topological surface states (TSS) in the superconducting 2M-WS₂. The TSS exhibit characteristic spin-momentum-locking behavior, suggesting the existence of long-sought nontrivial Z2 topological states therein. We expect that 2M-WS₂ with coexisting superconductivity and TSS might host the promising Majorana bound states.

Quantum Transport and Magnetism of Dirac Electrons in Solids

The relativistic Dirac equation covers the fundamentals of electronic phenomena in solids and as such it effectively describes the electronic states of the topological insulators like Bi_{2}Se_{3} and Bi_{2}Te_{3}. Topological insulators feature gapless surface states and, moreover, magnetic doping and resultant ferromagnetic ordering break time-reversal symmetry to realize quantum anomalous Hall and Chern insulators. Here, we focus on the bulk and investigate the mutual coupling of electronic and magnetic properties of Dirac electrons. Without carrier doping, spiral magnetic orders cause a ferroelectric polarization through the spin-orbit coupling. In a doped metallic state, the anisotropic magnetoresistance arises without uniform magnetization. We find that electric current induces uniform magnetization and conversely an oscillating magnetic order induces electric current. Our model provides a coherent and unified description of all those phenomena. The mutual control of electric and magnetic properties demonstrates implementations of antiferromagnetic spintronics. We also discuss the stoichiometric magnetic topological insulator MnBi_{2}Te_{4}.

Synthetic Pseudo-Spin-Hall effect in acoustic metamaterials

While vector fields naturally offer additional degrees of freedom for emulating spin, acoustic pressure field is scalar in nature, and it requires engineering of synthetic degrees of freedom by material design. Here we experimentally demonstrate the control of sound waves by using two types of engineered acoustic systems, where synthetic pseudo-spin emerges either as a consequence of the evanescent nature of the field or due to lattice symmetry. First, we show that evanescent sound waves in perforated films possess transverse angular momentum locked to their propagation direction which enables their directional excitation. Second, we demonstrate that lattice symmetries of an acoustic kagome lattice also enable a synthetic transverse pseudo-spin locked to the linear momentum, enabling control of the propagation of modes both in the bulk and along the edges. Our results open a new degree of control of radiation and propagation of acoustic waves thus offering new design approaches for acoustic devices.

Controlling emission and propagation of acoustic waves offers new design opportunities for acoustic devices. Here the authors demonstrate such controls thanks to the emergence of a synthetic pseudo-spin in two-dimensional acoustic metamaterial.

Spontaneous Ferromagnetism Induced Topological Transition in EuB_{6}

The interplay between various symmetries and electronic bands topology is one of the core issues for topological quantum materials. Spontaneous magnetism, which leads to the breaking of time-reversal symmetry, has been proven to be a powerful approach to trigger various exotic topological phases. In this Letter, utilizing the combination of angle-resolved photoemission spectroscopy, magneto-optical Kerr effect microscopy, and first-principles calculations, we present the direct evidence on the realization of the long-sought spontaneous ferromagnetism induced topological transition in soft ferromagnetic EuB_{6}. Explicitly, we reveal the topological transition is from Z_{2}=1 topological insulator in paramagnetic state to χ=1 magnetic topological semimetal in low temperature ferromagnetic state. Our results demonstrate that the simple band structure near the Fermi level and rich topological phases make EuB_{6} an ideal platform to study the topological phase physics.

N-band photonic Hopf insulators based on 2D microring lattices

Hopf insulators are topological insulators whose topological behavior arises from the nontrivial mapping from a 3D sphere to a 2D sphere, known as the Hopf map. The Hopf map, typically encountered in the study of spinor and Skyrmion systems, is classified topologically by an integer invariant called the Hopf index. Here we show that, owing to the periodic circulation of light inside each microring, a 2D lattice of microring resonators can emulate an N-band photonic Hopf insulator with nontrivial Hopf index. In particular, we show by numerical computation and direct analytical proof that the N-band Hopf index of the microring lattice is identical to its winding number. The result shows that the Hopf index is an alternative topological invariant for classifying 2D microring photonic lattices and establishes a correspondence between the Hopf insulator phase and the anomalous Floquet insulator phase of the lattice. More generally, our work shows that 2D microring lattices can provide a versatile nanophotonic platform for studying non-Abelian topological photonic systems.

DFT-1/2 method applied to 3D topological insulators

In this paper, we present results and describe the methodology of application of DFT-1/2 method for five three-dimensional topological insulators materials that have been extensively studied in last years: Bi₂Se₃, Bi₂Te₃, Sb₂Te₃, CuTlSe₂and CuTlS₂. There are many differences between the results of simple DFT calculations and quasiparticle energy correction methods for these materials, especially for band dispersion in the character band inversion region. The DFT-1/2 leads to quite accurate results not only for band gaps, but also for the shape and atomic character of the bands in the neighborhood of the inversion region as well as the topological invariants, essential quantities to describe the topological properties of materials. The methodology is efficient and ease to apply for the different approaches used to obtain the topological invariantZ₂, with the benefit of not increasing the computational cost in comparison with standard DFT, possibilitating its application for materials with a high number of atoms and complex systems.

Observation of Dirac Hierarchy in Three-Dimensional Acoustic Topological Insulators

Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy comprising an eightfold bulk DC, a fourfold surface DC, and a twofold hinge DC, associated with a hierarchy of topological phases including first-order to third-order three-dimensional (3D) topological insulators, using the same 3D base lattice. Here, we report the first experimental observation of the Dirac hierarchy in 3D acoustic TIs. Using acoustic measurements, we unambiguously reveal that lifting of multifold DCs in each hierarchy can induce two-dimensional topological surface states with a fourfold DC in a first-order 3D TI, one-dimensional topological hinge states with a twofold DC in a second-order 3D TI, and zero-dimensional topological corner states in a third-order 3D TI. Our Letter not only expands the fundamental research scope of Dirac physics, but also opens up a new route for multidimensional robust wave manipulation.

Energy-Saving Pathways for Thermoelectric Nanomaterial Synthesis: Hydrothermal/Solvothermal, Microwave-Assisted, Solution-Based, and Powder Processing

The pillars of Green Chemistry necessitate the development of new chemical methodologies and processes that can benefit chemical synthesis in terms of energy efficiency, conservation of resources, product selectivity, operational simplicity and, crucially, health, safety, and environmental impact. Implementation of green principles whenever possible can spur the growth of benign scientific technologies by considering environmental, economical, and societal sustainability in parallel. These principles seem especially important in the context of the manufacture of materials for sustainable energy and environmental applications. In this review, the production of energy conversion materials is taken as an exemplar, by examining the recent growth in the energy-efficient synthesis of thermoelectric nanomaterials for use in devices for thermal energy harvesting. Specifically, "soft chemistry" techniques such as solution-based, solvothermal, microwave-assisted, and mechanochemical (ball-milling) methods as viable and sustainable alternatives to processes performed at high temperature and/or pressure are focused. How some of these new approaches are also considered to thermoelectric materials fabrication can influence the properties and performance of the nanomaterials so-produced and the prospects of developing such techniques further.

Unveiling the hybridization between the Cr-impurity-mediated flat band and the Rashba-split state of the α-Au/Si(111) surface

Adsorption of foreign atoms onto 2D materials can either lead to ordinary electron doping or the emergence of new electronic effects including topology, superconductivity, and quantum anomalous Hall and Kondo states. We have investigated the effect of Cr doping on the electronic structure of the α-Au/Si(111)- surface and its adsorbate-modified family. It has been found that below a critical coverage of ∼0.05 monolayer, Cr adatoms penetrate beneath the Au and topmost Si layers and induce the occupied resonance flat band in the electronic spectrum as revealed by angle-resolved photoelectron spectroscopy. Further deposition of Cr leads to the growth of the 3D islands spoiling the surface homogeneity. Using density functional theory calculations, we have disclosed the effects of Cr doping on the electronic band structure and revealed the nature of hybridization between the Cr-induced magnetic-split band and the Au-induced Rashba-split surface state. We believe that the synthesized 2D phases and electronic effects produced by magnetic atom doping in the ultimate two-dimensional limit will stimulate further investigations related to the highly correlated phases and will find practical applications in nanoelectronic devices.

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.

Carrier Injection Observed by Interface-Enhanced Raman Scattering from Topological Insulators on Gold Substrates

The electron-phonon interaction at the interface between topological insulator (TI), namely, Bi₂Se₃ and Bi₂Te₃ two-dimensional (2D) nanoflakes, to a gold substrate as a function of TI flake thickness is studied by means of Raman scattering. We reveal the presence of interface-enhanced Raman scattering and a strong phonon renormalization induced by carriers injected from the gold substrate to the topological surface in contact. We derive the change of the electron-phonon coupling showing a nearly linear behavior as a function of layer thickness. The strongly nonlinear change of the Raman scattering cross section as a function of flake thickness can be associated with band bending effects at the metal-TI interface. Our results provide spectroscopic evidence for a strongly modified band structure in the first few quintuple layers of Bi₂Se₃ and Bi₂Te₃ in contact with gold.

An Efficient Dopant for Introducing Magnetism into Topological Insulator Bi2Se3

In this work, we obtained an effective way to introduce magnetism into topological insulators, and successfully fabricated single crystal C-Bi₂Se₃. The structural, electrical and magnetic properties of non-magnetic element X (B, C and N) doped at Bi, Se1, Se2 and VDW gap sites of Bi₂Se₃ were studied by the first principles. It is shown that the impurity bands formed inside the bulk inverted energy gap near the Fermi level with C doping Bi₂Se₃. Due to spin-polarized ferromagnetic coupling, the time inversion symmetry of Bi₂Se₃ is destroyed. Remarkably, C is the most effective dopant because of the magnetic moment produced by doping at all positions. The experiment confirmed that the remnant ferromagnetism Mr is related to the C concentration. Theoretical calculations and experiments confirmed that carbon-doped Bi₂Se₃ is ferromagnetic, which provides a plan for manipulating topological properties and exploring spintronic applications.

Fabrication and Characterization of a Self-Powered n-Bi2Se3/p-Si Nanowire Bulk Heterojunction Broadband Photodetector

In the present study, vacuum evaporation method is used to deposit Bi2Se3 film onto Si nanowires (NWs) to form bulk heterojunction for the first time. Its photodetector is self-powered, its detection wavelength ranges from 390 nm to 1700 nm and its responsivity reaches its highest value of 84.3 mA/W at 390 nm. In comparison to other Bi2Se3/Si photodetectors previously reported, its infrared detection length is the second longest and its response speed is the third fastest. Before the fabrication of the photodetector, we optimized the growth parameter of the Bi2Se3 film and the best Bi2Se3 film with atomic steps could finally be achieved. The electrical property measurement conducted by the physical property measurement system (PPMS) showed that the grown Bi2Se3 film was n-type conductive and had unique topological insulator properties, such as a metallic state, weak anti-localization (WAL) and linear magnetic resistance (LMR). Subsequently, we fabricated Si NWs by the metal-assisted chemical etching (MACE) method. The interspace between Si NWs and the height of Si NWs could be tuned by Ag deposition and chemical etching times, respectively. Finally, Si NWs fabricated with the Ag deposition time of 60 s and the etching time of 10 min was covered by the best Bi2Se3 film to be processed for the photodetector. The primary n-Bi2Se3/p-Si NWs photodetector that we fabricated can work in a self-powered mode and it has a broadband detection range and fast response speed, which indicates that it can serve as a promising silicon-based near- and mid-infrared photodetector.

A Class of Magnetic Topological Material Candidates with Hypervalent Bi Chains

The link between crystal and electronic structure is crucial for understanding structure-property relations in solid-state chemistry. In particular, it has been instrumental in understanding topological materials, where electrons behave differently than they would in conventional solids. Herein, we identify 1D Bi chains as a structural motif of interest for topological materials. We focus on Sm₃ZrBi₅, a new quasi-one-dimensional (1D) compound in the Ln₃MPn₅ (Ln = lanthanide; M = metal; Pn = pnictide) family that crystallizes in the P6₃/mcm space group. Density functional theory calculations indicate a complex, topologically nontrivial electronic structure that changes significantly in the presence of spin-orbit coupling. Magnetic measurements show a quasi-1D antiferromagnetic structure with two magnetic transitions at 11.7 and 10.7 K that are invariant to applied field up to 9 T, indicating magnetically frustrated spins. Heat capacity, electrical, and thermoelectric measurements support this claim and suggest complex scattering behavior in Sm₃ZrBi₅. This work highlights 1D chains as an unexplored structural motif for identifying topological materials, as well as the potential for rich physical phenomena in the Ln₃MPn₅ family.

Revisiting the van der Waals Epitaxy in the Case of (Bi0.4Sb0.6)2Te3 Thin Films on Dissimilar Substrates

Ultrathin films of the ternary topological insulator (Bi0.4Sb0.6)2Te3 are fabricated by molecular beam epitaxy. Although it is generally assumed that the ternary topological insulator tellurides grow by van der Waals epitaxy, our results show that the influence of the substrate is substantial and governs the formation of defects, mosaicity, and twin domains. For this comparative study, InP (111)A, Al2O3 (001), and SrTiO3 (111) substrates were selected. While the films deposited on lattice-matched InP (111)A show van der Waals epitaxial relations, our results point to a quasi-van der Waals epitaxy for the films grown on substrates with a larger lattice mismatch.

All topological bands of all nonmagnetic stoichiometric materials

Topological quantum chemistry and symmetry-based indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy (E_F). We report the implementation of a publicly accessible catalog of stable and fragile topology in all of the bands both at and away from E_F in the 96,196 processable entries in the Inorganic Crystal Structure Database. Our calculations, which represent the completion of the symmetry-indicated band topology of known nonmagnetic materials, have enabled the discovery of repeat-topological and supertopological materials, including rhombohedral bismuth and Bi₂Mg₃. We find that 52.65% of all materials are topological at E_F, roughly two-thirds of bands across all materials exhibit symmetry-indicated stable topology, and 87.99% of all materials contain at least one stable or fragile topological band.

Nonequilibrium topological spin textures in momentum space

Optically excited systems can host unprecedented phenomena and reveal key information. The spin-channel physics in the photoexcited dynamics of quantum matter remains largely unexplored. This study finds the topological surface state under contemporary time-resolved pump-probe spectroscopy an exceptionally capable platform in this regard. Spin signals exhibit interesting tornado-like spiral patterns, and the unusual topological optical activity can be indicative of spintronic applications. This exemplifies a purely nonequilibrium topological winding phenomenon, where all the hidden helicity factors in the light–matter-coupled system are robustly encoded. These results open a direction of nonequilibrium topological spin states in quantum materials.

Nonequilibrium quantum dynamics of many-body systems is the frontier of condensed matter physics; recent advances in various time-resolved spectroscopic techniques continue to reveal rich phenomena. Angle-resolved photoemission spectroscopy (ARPES) as one powerful technique can resolve electronic energy, momentum, and spin along the time axis after excitation. However, dynamics of spin textures in momentum space remains mostly unexplored. Here, we demonstrate theoretically that the photoexcited surface state of genuine or magnetically doped topological insulators shows intriguing topological spin textures (i.e., tornado-like patterns) in the spin-resolved ARPES. We systematically reveal its origin as a unique nonequilibrium photoinduced topological winding phenomenon. As all intrinsic and extrinsic topological helicity factors of both material and light are embedded in a robust and delicate manner, the tornado patterns not only allow a remarkable tomography of such important system information, but also enable various unique dichroic topological switchings of the momentum-space spin texture. These results open a direction of nonequilibrium topological spin states in quantum materials.