Topological Insulator State Research Articles

Hinge states of second-order topological insulators as a Mach-Zehnder interferometer

Three-dimensional higher-order topological insulators can have topologically protected chiral modes propagating on their hinges. Hinges with two copropagating chiral modes can serve as a ``beam splitter'' between hinges with only a single chiral mode. Here we show how such a crystal, with Ohmic contacts attached to its hinges, can be used to realize a Mach-Zehnder interferometer. We present concrete calculations for a lattice model of a first-order topological insulator in a magnetic field, which, for a suitable choice of parameters, is an extrinsic second-order topological insulator with the required configuration of chiral hinge modes.

Characterizing the helical Andreev states of a second-order topological insulator

Characterizing the helical Andreev states of a second-order topological insulator

Direct Optical Probe of Magnon Topology in Two-Dimensional Quantum Magnets.

Controlling edge states of topological magnon insulators is a promising route to stable spintronics devices. However, to experimentally ascertain the topology of magnon bands is a challenging task. Here we derive a fundamental relation between the light-matter coupling and the quantum geometry of magnon states. This allows us to establish the two-magnon Raman circular dichroism as an optical probe of magnon topology in honeycomb magnets, in particular of the Chern number and the topological gap. Our results pave the way for interfacing light and topological magnons in functional quantum devices.

Quantum Floquet spectra of surface and bulk state of topological insulator

Topological insulator is a new class of material, which consists of insulating bulk and conducting surface state. In this study, we investigated the behaviour of bulk and surface state of topological insulator under a high frequency electromagnetic field, produce a kind of oscillation called as Floquet oscillation. We successfully identified the classical and quantum behavior of Floquet oscillation in the prospective of collapse revival spectra. This work shows the bulk and surface states behaviour of a topological insulator with the help of Floquet and Rabi frequency and describes the dominancy of Floquet oscillation in the low energy physics. Numerical simulation has been applied for verifying the Floquet approximation.

Spin transfer torques due to the bulk states of topological insulators.

Spin torques at topological insulator (TI)/ferromagnet interfaces have received considerable attention in recent years with a view towards achieving full electrical manipulation of magnetic degrees of freedom. The most important question in this field concerns the relative contributions of bulk and surface states to the spin torque, a matter that remains incompletely understood. Whereas the surface state contribution has been extensively studied, the contribution due to the bulk states has received comparatively little attention. Here we study spin torques due to TI bulk states and show that: (i) there is no spin-orbit torque due to the bulk states on a homogeneous magnetisation, in contrast to the surface states, which give rise to a spin-orbit torque via the well-known Edelstein effect. (ii) The bulk states give rise to a spin transfer torque (STT) due to the inhomogeneity of the magnetisation in the vicinity of the interface. This spin transfer torque, which has not been considered in TIs in the past, is somewhat unconventional since it arises from the interplay of the bulk TI spin-orbit coupling and the gradient of the monotonically decaying magnetisation inside the TI. Whereas we consider an idealised model in which the magnetisation gradient is small and the spin transfer torque is correspondingly small, we argue that in real samples the spin transfer torque should be sizable and may provide the dominant contribution due to the bulk states. We show that an experimental smoking gun for identifying the bulk states is the fact that the field-like component of the spin transfer torque generates a spin density with the same size but opposite sign for in-plane and out-of-plane magnetisations. This distinguishes them from the surface states, which are expected to give a spin density of a similar size and the same sign for both an in-plane and out-of-plane magnetisations.

Higher-Order Topological States in Photonic Thue-Morse Quasicrystals: Quadrupole Insulator and the Origin of Corner States

Corner states (CSs) in higher-order topological insulators (HOTIs) have recently been of great interest in both crystals and quasicrystals. In contrast to electronic systems, HOTIs have not been found in photonic quasicrystals (PQCs). Here, we systemically study the higher-order topology in the two-dimensional Thue-Morse photonic quasicrystals (TM PQCs). Not only the topological phase transition and the nontrivial CSs with fractional charge induced by multipole moments, but also another type of CSs are found due to the complex structure of TM PQCs near corners. The different origins of these CSs are also analyzed based on the tight-binding model. Our work opens the door to explore richer HOT physics beyond photonic crystals and the robustness of CSs in PQC shows the potential for applications.

Two-dimensional non-Abelian topological insulators and the corresponding edge/corner states from an eigenvector frame rotation perspective

We propose the concept of two-dimensional (2D) non-Abelian topological insulators which can explain the energy distributions of the edge states and corner states in systems with parity-time symmetry. From the viewpoint of non-Abelian band topology, we establish the constraints on the 2D Zak phase and polarization. We demonstrate that the corner states in some 2D systems can be explained as the boundary mode of the one-dimensional edge states arising from the multiband non-Abelian topology of the system. We also propose the use of the off-diagonal Berry phase as complementary information to assist the prediction of edge states in non-Abelian topological insulators. Our work provides an alternative approach to study edge and corner modes and this idea can be extended to three-dimensional systems.

Superlattices of Gadolinium and Bismuth Based Thallium Dichalcogenides as Potential Magnetic Topological Insulators.

Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics.

Low Power In-Memory Computation with Reciprocal Ferromagnet/Topological Insulator Heterostructures.

The surface state of a 3D topological insulator (3DTI) is a spin-momentum locked conductive state, whose large spin hall angle can be used for the energy-efficient spin-orbit torque based switching of an overlying ferromagnet (FM). Conversely, the gated switching of the magnetization of a separate FM in or out of the TI surface plane can turn on and off the TI surface current. By exploiting this reciprocal behavior, we can use two FM/3DTI heterostructures to design an integrated 1-transistor 1-magnetic tunnel junction random access memory unit (1T1MTJ RAM) for an ultra low power Processing-in-Memory (PiM) architecture. Our calculation involves combining the Fokker-Planck equation with the Nonequilibrium Green Function (NEGF) based flow of conduction electrons and Landau-Lifshitz-Gilbert (LLG) based dynamics of magnetization. Our combined approach allows us to connect device performance metrics with underlying material parameters, which can guide proposed experimental and fabrication efforts.

Electron transport, transverse and longitudinal magnetoresistance, and Shubnikov–de Haas oscillations in Bi0.83Sb0.17 topological insulator semiconductor wires

The paper describes results of experimental studies of the dependence of the resistance, transverse and longitudinal magnetoresistance, as well as the Shubnikov–de Haas (SdH) oscillations of Bi0.83Sb0.17 semiconductor single-crystal wires with diameters of (75–1100) nm, as a function of the thickness, in a temperature range of (3.1–300) K at magnetic fields of up to 14 T. The wires were prepared by liquid-phase casting. It has been found that the temperature dependences of the resistance of wires with d < 0.5 m have two regions exhibiting a semiconductor and a metallic behavior of the resistance, the two regions being separated by a maximum, which is shifted to the high-temperature region with a decrease in the wire diameter d. It has been revealed that the energy gap E increases by a factor of 2 with a decrease in wire diameter d, due to the occurrence of the quantum size effect. The “metallic” behavior of conductivity is attributed to surface states characteristic of topological insulators, which is most clearly evident in thin wires at temperatures of T < 50 K. It has been shown that, in the presence of a uniform magnetic field H, the field dependences of the longitudinal and transverse magnetoresistance in quasi-one-dimensional systems can undergo a significant change depending on the ratio of quantum wire radius to the magnetic length R = (ch/eH)1/2, as well as on the decrease in the mean free path of carriers due to scattering on the wire surface. The SdH oscillation periods exhibit anomalies that are typical neither to bulk Bi1xSbx samples nor to semimetallic wires based on Bi1xSbx alloys. This fact points to the essential role of surface states of topological insulators in 1D-systems, which lead to the occurrence of new effects that are not characteristic of other systems.

Comprehensive Insight into p-Type Bi2Te3-Based Thermoelectrics near Room Temperature.

Bi2Te3 is a well-recognized material for its unique properties in diverse thermoelectric applications near room temperature. The considerable efforts on Bi2Te3-based alloys have been extremely extensive in recent years, and thus the latest breakthroughs in high-performance p-type (Bi, Sb)2Te3 alloys are comprehensively reviewed to further implement applications. Effective strategies to further improve the thermoelectric performance are summarized from the perspective of enhancing the power factor and minimizing the lattice thermal conductivity. Furthermore, the surface states of topological insulators are investigated to provide a possibility of advancing (Bi, Sb)2Te3 thermoelectrics. Finally, future challenges and outlooks are overviewed. This review will provide potential guidance toward designing and developing high-efficient Bi2Te3-based and other thermoelectrics.

Mini-review of interesting properties in Mn2CoAl bulk and films.

Heusler compounds exhibit many interesting properties, such as high thermopower, magnetocaloric properties, and even topological insulator states. Heusler Mn2CoAl alloy has been experimentally and theoretically proposed as a promising spin-gapless semiconductor with novel electronic, magnetic, spintronic, transport, and topological properties. Furthermore, the spin-gapless semiconducting-like behaviors are also predicted in Mn2CoAl films by measuring the transport and magnetic properties. This mini-review systematically summarizes the interesting properties of Mn2CoAl bulk and Mn2CoAl-based films. This mini-review is hoped to guide further experimental investigations and applications in the particular scientific community.

Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators.

In intrinsic magnetic topological insulators, Dirac surface-state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here, we use molecular beam epitaxy to grow intrinsic MnBi2Te4 thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that, in high defect regions, the Dirac mass gap collapses. Ab initio and coupled Dirac cone model calculations provide insight into the microscopic origin of the correlation between defect density and spatial gap variations. This work provides unambiguous identification of the Dirac mass gap in MnBi2Te4 and, by revealing the microscopic origin of its gap variation, establishes a material design principle for realizing exotic states in intrinsic magnetic topological insulators.

Robustness of helical edge states under edge reconstruction

The helical edge states of time-reversal invariant two-dimensional topological insulators are protected against backscattering in idealized models. In more realistic scenarios with a shallow confining potential at the sample boundary, additional strongly interacting edge states may arise, that could interfere with the topological protection of edge conduction. We find that interaction effects within the reconstructed edges are well described by the Luttinger liquid model. While interactions between this Luttinger liquid and the helical edge states can in principle give rise to dynamical spin polarization and the breaking of time-reversal symmetry, we demonstrate that random spin-orbit coupling strongly suppresses such dynamical spin polarization, resulting in the persistence of near quantized edge conduction.

Copper migration and surface oxidation of in ambient pressure environments

Chemical modifications such as intercalation can be used to modify surface properties or to further functionalize the surface states of topological insulators (TIs). Using ambient pressure x-ray photoelectron spectroscopy, we report copper migration in , which occurs on a timescale of hours to days after initial surface cleaving. The increase in near-surface copper proceeds along with the oxidation of the sample surface and large changes in the selenium content. These complex changes are further modeled with core-level spectroscopy simulations, which suggest a composition gradient near the surface which develops with oxygen exposure. Our results shed light on a new phenomenon that must be considered for intercalated TIs—and intercalated materials in general—that surface chemical composition can change when specimens are exposed to ambient conditions.

Emergent topological states via digital (001) oxide superlattices

Oxide heterostructures exhibit many intriguing properties. Here we provide design principles for inducing multiple topological states in (001) (AMO3)1/(AM′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AM^{\\prime}$$\\end{document}O3)1 oxide superlattices. Aided by first-principles calculations and model analysis, we show that a (SrMO3)1/(SrM′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M^{\\prime}$$\\end{document}O3)1 superlattice (M = Nb, Ta and M′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M^{\\prime}$$\\end{document} = Rh, Ir) is a strong topological insulator with Z2 index (1;001). More remarkably, a (SrMoO3)1/(SrIrO3)1 superlattice exhibits multiple coexisting topological insulator (TI) and topological Dirac semi-metal (TDS) states. The TDS state has a pair of type-II Dirac points near the Fermi level and symmetry-protected Dirac node lines. The surface TDS Dirac cone is sandwiched by two surface TI Dirac cones in the energy-momentum space. The non-trivial topological properties arise from the band inversion between d orbitals of two dissimilar transition metal atoms and a particular parity property of (001) superlattice geometry. Our work demonstrates how to induce non-trivial topological states in (001) perovskite oxide heterostructures by rational design.

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.

Photo-induced inverse spin Hall effect of the top and bottom Dirac surface states of three-dimensional topological insulators Sb2Te3

Inverse spin Hall effect (ISHE) provides an important way to manipulate and detect spin current via spin–orbit coupling. However, it is difficult to distinguish the ISHE of the top and bottom surface states of topological insulators (TIs). Photo-induced inverse spin Hall effect (PISHE) is a powerful tool to investigate the ISHE of the Dirac surface states of TIs. In this work, PISHE of three-dimensional topological insulators Sb 2 Te 3 with a thickness of 7 and 30 quintuple layer (QL) has been investigated. It is revealed that both of the PISHE currents of the top and bottom surface states are observed in the 7-QL and the 30-QL samples. Besides, a model has been developed to separate the PISHE current of the top and bottom surface states. It is found that the PISHE currents of the top and bottom surface states of the Sb 2 Te 3 films almost do not change with temperature in the range of 77 to 300 K. It is demonstrated that the PISHE current changes linearly with light power, which agrees well with the theoretical model. This study provides a method utilizing circularly polarized light to manipulate and detect the ISHE of the top and bottom surface states of three-dimensional topological insulators. • Both of the PISHE currents of the top and bottom surface states are observed in the 7-QL and the 30-QL Sb 2 Te 3 films. • A model has been developed to separate the PISHE current of the top and bottom surface states. • The PISHE currents of the top and bottom surface states of the Sb 2 Te 3 films almost do not change with temperature in the range of 77 to 300 K.

Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice

In a first-order topological phase with sublattice degrees of freedom, a change in the boundary sublattice termination has no effect on the existence of gapless boundary states in dimensions higher than one. However, such a change may strongly affect the physical properties of those boundary states. Motivated by this observation, we perform a systematic study of the impact of sublattice terminations on the boundary physics on the two-dimensional kagome lattice. We find that the energies of the Dirac points of helical edge states in two-dimensional first-order topological kagome insulators sensitively depend on the terminating sublattices at the edge. Remarkably, this property admits the realization of a time-reversal invariant second-order topological superconducting phase with highly controllable Majorana Kramers pairs at the corners and sublattice domain walls by putting the topological kagome insulator in proximity to a $d$-wave superconductor. Moreover, substituting the $d$-wave superconductor with a conventional $s$-wave superconductor, we find that highly controllable Majorana zero modes can also be realized at the corners and sublattice domain walls if an in-plane Zeeman field is additionally applied. Our study reveals promising platforms to implement highly controllable Majorana zero modes.

Gate-Tunable Anomalous Hall Effect in a 3D Topological Insulator/2D Magnet van der Waals Heterostructure

We demonstrate advantages of samples made by mechanical stacking of exfoliated van der Waals materials for controlling the topological surface state of a three-dimensional topological insulator (TI) via interaction with an adjacent magnet layer. We assemble bilayers with pristine interfaces using exfoliated flakes of the TI BiSbTeSe2 and the magnet Cr2Ge2Te6, thereby avoiding problems caused by interdiffusion that can affect interfaces made by top-down deposition methods. The samples exhibit an anomalous Hall effect (AHE) with abrupt hysteretic switching. For the first time in samples composed of a TI and a separate ferromagnetic layer, we demonstrate that the amplitude of the AHE can be tuned via gate voltage with a strong peak near the Dirac point. This is the signature expected for the AHE due to Berry curvature associated with an exchange gap induced by interaction between the topological surface state and an out-of-plane-oriented magnet.