Surface States Of Topological Insulators Research Articles

Spin-orbit torques due to extrinsic spin-orbit scattering of topological insulator surface states: out-of-plane magnetization

The origins of the spin-orbit torque (SOT) at ferromagnet/topological insulator interfaces are incompletely understood. The theory has overwhelmingly focussed on the Edelstein effect due to the surface states in the presence of a scalar scattering potential. We investigate here the contribution to the SOT due to extrinsic spin-orbit (SO) scattering of the surface states, focusing on the case of an out-of-plane magnetization. We show that SO scattering brings about a sizable renormalization of the field-like SOT, which exceeds 20 at larger strengths of the extrinsic SO parameter. The resulting SOT exhibits a maximum as a function of the Fermi energy, magnetization, and extrinsic SO strength. The field-like SOT decreases with increasing disorder strength, while the damping-like SOT is independent of the impurity density. With experimental observation in mind we also determine the role of extrinsic SO scattering on the anomalous Hall effect. Our results suggest extrinsic SO scattering is a significant contributor to the surface SOT stemming from the Edelstein effect when the magnetization is out of the plane.

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.

Interface Engineering Enabled Low Temperature Growth of Magnetic Insulator on Topological Insulator

AbstractCombining topological insulators (TIs) and magnetic materials in heterostructures is crucial for advancing spin‐based electronics. Magnetic insulators (MIs) can be deposited on TIs using the spin‐spray process, which is a unique nonvacuum, low‐temperature growth process. TIs have highly reactive surfaces that oxidize upon exposure to atmosphere, making it challenging to grow spin‐spray ferrites on TIs. In this work, it is demonstrated that a thin titanium capping layer on TI, followed by oxidation in atmosphere to produce a thin TiOx interfacial layer, protects the TI surface, without significantly compromising spin transport from the magnetic material across the TiOx to the TI surface states. First, it is demonstrated that in Bi2Te3/TiOx/Ni80Fe20 heterostructures, TiOx provides an excellent barrier against diffusion of magnetic species, yet maintains a large spin‐pumping effect. Second, the TiOx is also used as a protective capping layer on Bi2Te3, followed by the spin‐spray growth of the MI, NixZnyFe2O4 (NZFO). For the thinnest TiOx barriers, Bi2Te3/TiOx/NZFO samples have antiferromagnetic (AFM) disordered interfacial layer because of diffusion. With increasing TiOx barrier thickness, the diffusion is reduced, but still maintains strong interfacial magnetic exchange‐interaction. These experimental results demonstrate a novel method of low‐temperature growth of magnetic insulators on TIs enabled by interface engineering.

Observation of nonlinear planar Hall effect in magnetic-insulator–topological-insulator heterostructures

Interfacing topological insulators (TIs) with magnetic insulators (MIs) has been widely used to study the interaction between topological surface states and magnetism. Previous transport studies typically interpret the suppression of weak antilocalization or appearance of the anomalous Hall effect as signatures of magnetic proximity effect (MPE) imposed to TIs. Here, we report the observation of nonlinear planar Hall effect (NPHE) in Bi2Se3 films grown on MI thulium and yttrium iron garnet (TmIG and YIG) substrates, which is an order of magnitude larger than that in Bi2Se3 grown on nonmagnetic gadolinium gallium garnet (GGG) substrate. The nonlinear Hall resistance in TmIG/Bi2Se3 depends linearly on the external magnetic field, while that in YIG/Bi2Se3 exhibits an extra hysteresis loop around zero field. The magnitude of the NPHE is found to scale inversely with carrier density. We speculate the observed NPHE is related to the MPE-induced exchange gap opening and out-of-plane spin textures in the TI surface states, which may be used as an alternative transport signature of the MPE in MI/TI heterostructures.

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.

Tailoring the surface and interface states in a three-dimensional fragile topological insulator with kagome lattice

Topological insulators, which are insulating in the bulk and conducting on the surface, have attracted great interest in recent years. The recently discovered topological surface and hinge states in three dimensions have provided promising methods for wave manipulation in classical systems. However, the combination of surface states and interface states has yet to be achieved in phononic crystals due to the missing topological surface states. Here, we experimentally demonstrate a fragile topological insulator with a bilayer kagome lattice. We observe the surface states in three different orientations and interface states formed by inversion of layer pseudospin sectors or bands. The combination of surface and interface states is investigated in $\mathsf{X}$-shaped waveguides. Our work may provide a platform for exploring unique acoustic applications based on surface or interface states.

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.

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.

High photodetection performance on vertically oriented topological insulator Sb2Te3/Silicon heterostructure

The coexistence of bulk electronic band gap and gapless surface states of topological insulators (TIs) opens up many new opportunities in optoelectronic devices. Here we demonstrate the synthesis and photodetection response of vertical Sb2Te3 nanoplate film grown on n-type Si substrates. The small bulk bandgap of Sb2Te3 and surface states conduction lead to effective light absorption and photocarrier transport. The device exhibits a significant photoresponse over a broad spectral range between 350 and 1400 ​nm. The switching speed and on/off ratio Iph/Id are estimated to be 3 ​ms and 5900, respectively, which are much better than those of other TI-based photodetectors. Given the simple device preparation and compatibility with silicon technology, the unconventional structure Sb2Te3/Si heterostructure holds great promise for high-performance optoelectronic applications.

Electrochemical biosensor based on topological insulator Bi2Se3 tape electrode for HIV-1 DNA detection.

A large-size Bi2Se3 tape electrode (BTE) was prepared by peeling off a 2 × 1 × 0.5cm high-quality single crystal. The feasibility of using the flexible BTE as an efficient bioplatform to load Au nanoparticles and probe DNA for HIV-1 DNA electrochemical sensing was explored. Differential pulse voltammetry (DPV) and electrochemical impedance spectroscopy (EIS) show that the resultant biosensor has a wide linear range from 0.1 fM to 1pM, a low detection limit of 50 aM, excellent selectivity, reproducibility and stability, and is superior to the pM DNA detection level of Pt-Au, graphene-AuNPs hybrid biosensors. This outstanding performance is attributed to the intrinsic surface state of Bi2Se3 topological insulator in facilitating electron transfer. Therefore, BTE electrochemical biosensor platform has great potential in the application for sensitive detection of DNA biomarkers.

Spin-Sensitive Epitaxial In2Se3 Tunnel Barrier in In2Se3/Bi2Se3 Topological van der Waals Heterostructure.

Current-generated spin arising from spin-momentum locking in topological insulator (TI) surface states has been shown to switch the magnetization of an adjacent ferromagnet (FM) via spin-orbit torque (SOT) with a much higher efficiency than heavy metals. However, in such FM/TI heterostructures, most of the current is shunted through the FM metal due to its lower resistance, and recent calculations have also shown that topological surface states can be significantly impacted when interfaced with an FM metal such as Ni and Co. Hence, placing an insulating layer between the TI and FM will not only prevent current shunting, therefore minimizing overall power consumption, but may also help preserve the topological surface states at the interface. Here, we report the van der Waals epitaxial growth of β-phase In2Se3 on Bi2Se3 by molecular beam epitaxy and demonstrate its spin sensitivity by the electrical detection of current-generated spin in Bi2Se3 surface states using a Fe/In2Se3 detector contact. Our density functional calculations further confirm that the linear dispersion and spin texture of the Bi2Se3 surface states are indeed preserved at the In2Se3/Bi2Se3 interface. This demonstration of an epitaxial crystalline spin-sensitive barrier that can be grown directly on Bi2Se3, and verification that it preserves the topological surface state, is electrically insulating and spin-sensitive, is an important step toward minimizing overall power consumption in SOT switching in TI/FM heterostructures in fully epitaxial topological spintronic devices.

Magnetic moiré surface states and flat Chern bands in topological insulators

We propose the magnetic moir\'e surface states of topological insulators as a platform for time-reversal symmetry breaking flat Chern bands. We construct a generic continuum model of Dirac electrons with a single Dirac cone moving in a time-reversal symmetry breaking periodic potential containing minimal parameters. The Zeeman-type moir\'e potentials generically gap out the moir\'e surface Dirac cones and give rise to isolated flat Chern minibands with Chern number $\ifmmode\pm\else\textpm\fi{}1$. Interestingly, the bandwidth of such isolated flat minibands is insensitive to the twisting angle, which originates from the completely flat band of the $p$ orbitals on the honeycomb lattice. This result provides a promising platform for realizing time-reversal breaking correlated topological phases and circumvents two main experimental difficulties in correlated states with twisted graphene: that the bandwidth varies rapidly with angle as well as the moir\'e disorder. Furthermore, in a ${C}_{6}$ periodic potential, with the interplay of the scalar potential and the Zeeman moir\'e potential, the $\mathrm{\ensuremath{\Gamma}}$-valley moir\'e surface electrons simulate two-dimensional honeycomb lattice physics, leading to emergent moir\'e surface Dirac cones as well as the Haldane model.

Nonlinear Hybrid Surface-Defect States in Defective Bi2Se3

Surface-states of topological insulators are assumed to be robust against non-magnetic defects in the crystal. However, recent theoretical models and experiments indicate that even non-magnetic defects can perturb these states. Our first-principles calculations demonstrate that the presence of Se vacancies in Bi$_2$Se$_3$, has a greater impact than a mere n-doping of the structure, which would just shift the Fermi level relative to the Dirac point. We observe the emergence of a non-linear band pinned near the Fermi level, while the Dirac cone shifts deeper into the valence band. We attribute these features in the bandstructure to the interaction between the surface and defect states, with the resulting hybridization between these states itself depending on the position and symmetry of the Se vacancy relative to the surfaces. Our results bring us a step closer to understanding the exotic physics emerging from defects in Bi$_2$Se$_3$ that remained unexplored in prior studies.

Emergent optical plasmons at the surface of a doped three-dimensional topological insulator

The conduction electrons in the topologically nontrivial surface states of three-dimensional topological insulators have been actively exploited to exhibit emergent exotic properties and functionalities. The existence of a trivial two-dimensional electron gas near the surface has also been widely established, stemming from surface carrier doping of the topological insulators. Here we investigate theoretically the coupling between the electrons in the topological surface states and two-dimensional electron gas, and reveal that the helical nature of the former can be effectively shared with the latter through proximity effect. Next we examine the collective modes of the combined system and predict an optical plasmon mode rooted in the enhanced interband transitions of the nontrivial bands with the same helicity. The emergence of the interband transitions also introduce pronounced variations in the Dirac plasmon mode of the topological surface states, characterized by its gapped feature. These findings may find important applications in plasmonic and spintronic devices.

Ultrafast dynamics of Dirac surface and bulk photocarriers in topological-insulator bismuth telluride nanocrystals using terahertz spectroscopy

Unlike conventional semiconductors, Dirac fermions in surface states of topological insulators (TIs) exhibit many fascinating electronic properties relevant for several optoelectronic and spintronic applications. We investigate the relaxation dynamics of photoexcited carriers in bismuth telluride (${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$) nanocrystals---a prominent candidate among the three-dimensional (3D) topological insulators, using ultrafast time resolved terahertz (THz) spectroscopy. Upon photoexcitation using an 800 nm pump pulse, we observe a decrease in the THz transmission due to the absorption of THz radiation by the photoexcited carriers. The time evolution of the real part of pump induced conductivity [$\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})=\phantom{\rule{4pt}{0ex}}{\ensuremath{\sigma}}_{\text{pump}}{\phantom{\rule{4pt}{0ex}}}_{\text{on}}({\ensuremath{\tau}}_{\text{pp}})\ensuremath{-}{\ensuremath{\sigma}}_{\text{pump}}{\phantom{\rule{4pt}{0ex}}}_{\text{off}}$] with respect to the pump-probe delay time (${\ensuremath{\tau}}_{\text{pp}}$), exhibits a sign change from positive to negative as carriers relax back to their equilibrium distribution, which is also evident from the spectral signatures of $\mathrm{\ensuremath{\Delta}}\ensuremath{\sigma}(\ensuremath{\omega})$, measured at various ${\ensuremath{\tau}}_{\text{pp}}$. While the positive sign of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$ is attributed to the contribution from the semiconducting bulk states, the negative sign of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$ at longer delay times is shown to arise from the Dirac surface states of TIs due to increased scattering rate of photoexcited charge carriers. We model the differential conductivity spectrum [$\mathrm{\ensuremath{\Delta}}\ensuremath{\sigma}(\ensuremath{\omega})$] and the transient dynamics [$\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}_{R}({\ensuremath{\tau}}_{\text{pp}})$] quantitatively using the Boltzmann transport equation applied to the surface and bulk states. This includes the energy dependence of scattering rates along with the dynamics of hot electron temperature (${T}_{e}$) evaluated in a self-consistent manner. Such an approach enables us to understand various scattering mechanisms associated with the photoexcited carriers both in Dirac surface as well as in bulk electronic states.

Nonlinear optical absorption and photocurrents in topological insulators

Theory of optical absorption of linearly and circularly polarized light in surface and edge states in topological insulators is developed for a nonlinear in light intensity regime. The absorbance for surface states and the absorption width for the edge states both decease as $1/\sqrt{I}$ at high light intensity $I$. Elastic scattering of the photoexcited electrons and holes is taken into account. The absorption bleaching at high intensity is shown to be strongly suppressed by the elastic scattering. The linear-circular dichroism of one- and two-photon absorption in surface states, emerging in the nonlinear in intensity regime, decreases due to the elastic scattering of photocarriers. Absorption in the edge states of two-dimensional topological insulators also depends on the elastic scattering rate being suppressed when it is stronger that the energy relaxation rate. The linear dichroism - a dependence of the absorption length on the polarization plane orientation - is studied at arbitrary light intensities. We show that a degree of the linear dichroism is governed by the ratio of the elastic and inelastic relaxation times. The photocurrents generated in the edge states by both linearly and circularly polarized light change their intensity dependencies from the linear one at low $I$ to the $\propto \sqrt{I}$ at high intensities. The variation of the photocurrents with both polarization and intensity are strongly dependent on the elastic scattering rate. The considered effects can be observed in THz frequency range at laser intensities used in modern experiments.

In-gap states of vortices at the surface of a topological insulator

By solving the Bogoliubov–de Gennes equations we study fermion bound states in the core of a vortex of a two-dimensional superconductor. The metallic surface states of a strong topological insulator become superconducting via proximity effect with an s-wave superconductor. The strong spin-orbit coupling locks the spin perpendicular to the momentum (Rashba interaction) giving rise to a zero-energy Majorana state. We investigate the case of a large first excitation energy of the order of the superconducting gap (Δ∞), i.e. for the Fermi level close to the apex of the Dirac cone. We obtain the local density of states (LDOS) for the bulk and the bound states. The particle-hole symmetry is broken in the LDOS for up-spin as a consequence of the spin-orbit coupling and the chirality of the vortex. On the other hand, the down-spin LDOS is particle-hole symmetric. The spin-polarization of the bound state peaks is studied in detail. We present a waterfall-like spectrum that shows that for a distance less than 3 times the coherence length ξ from the core, the bound states can be observed.

Bilinear magnetoresistance in topological insulators: Role of magnetic disorder

Bilinear magnetoresistance is a nonlinear transport phenomenon that scales linearly with the electric and magnetic fields, and appears in nonmagnetic systems with strong spin–orbit coupling, such as topological insulators (TIs). Using the semiclassical Boltzmann theory and generalized relaxation time approximation, we consider in detail the bilinear magnetoresistance in an effective model describing surface states of three-dimensional topological insulators. We show that the presence of magnetic impurities remarkably modifies the BMR signal. In general, scattering on magnetic impurities reduces magnitude of BMR. Apart from this, an additional modulation of the angular dependence of BMR appears when the spin-dependent component of the impurity potential dominates the scalar one.