Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, M. Z. Hasan
备注：
3 Figures, 18 pages, Submitted to NATURE PHYSICS in December 2008
最近的理论和实验表明，某些带绝缘体中的强自旋-轨道耦合效应可以产生量子物质的新相，即所谓的拓扑绝缘体，它可以表现出宏观纠缠效应。这样的系统具有二维表面状态，其电动力学性质不是由传统的麦克斯韦方程组描述的，而是由一个附加的轴子场描述的，最初提出来描述强相互作用的粒子。有人提出，具有单个自旋织构狄拉克锥的拓扑绝缘体与超导体的界面可以形成执行容错量子计算的最基本单元。在这里，我们提出了一个角度分辨光电子能谱研究和第一原理理论计算预测，揭示了第一次观察到这样的拓扑状态的物质具有一个单一的表面Dirac-cone实现自然发生的Bi $_2$ Se $_3$类材料。我们的研究结果，我们的理论预测和计算的支持，表明这类材料的未掺杂化合物可以作为长期寻求的拓扑器件，其中面内表面载流子输运将有一个纯粹的量子拓扑起源的母矩阵化合物。我们的研究进一步表明，未掺杂的化合物通过n到p掺杂达到即使在室温下也应该显示拓扑输运现象。
英文摘要：
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement effects. Such systems feature two-dimensional surface states whose electrodynamic properties are described not by the conventional Maxwell equations but rather by an attached axion field, originally proposed to describe strongly interacting particles. It has been proposed that a topological insulator with a single spin-textured Dirac cone interfaced with a superconductor can form the most elementary unit for performing fault-tolerant quantum computation. Here we present an angle-resolved photoemission spectroscopy study and first-principle theoretical calculation-predictions that reveal the first observation of such a topological state of matter featuring a single-surface-Dirac-cone realized in the naturally occurring Bi$_2$Se$_3$ class of materials. Our results, supported by our theoretical predictions and calculations, demonstrate that undoped compound of this class of materials can serve as the parent matrix compound for the long-sought topological device where in-plane surface carrier transport would have a purely quantum topological origin. Our study further suggests that the undoped compound reached via n-to-p doping should show topological transport phenomena even at room temperature.
Non-trivial spin-texture of the coaxial Dirac cones on the surface of topological crystalline insulator SnTe
本文采用第一性原理计算研究了拓扑晶体绝缘体SnTe的非平凡表面态及其自旋织构。[001]表面上的表面态色散呈现出四个Dirac-cone，中心位于镜面和表平面的相交处。我们提出了一个简单的模型，两个相互作用的同轴狄拉克锥来描述的表面态色散和相关的自旋纹理。虽然由于晶体和时间反转对称性，面外自旋极化为零，但由于两个同轴狄拉克锥的相互作用，面内自旋织构显示出螺旋性和一些扭曲，表明非平凡的镜像陈氏数为-2，不同于$Z_{2}$拓扑绝缘体（如Bi/Sb合金或Bi $_2$ Se $_3$）中的值-1。表面态色散和它的自旋织构将提供一种实验上可获得的方法来确定非平凡的镜像陈氏数。
The massless Dirac electrons found at topological insulator surfaces are thought to be influenced very little by weak, non-magnetic disorder. However, a resonance effect of strongly perturbing non-magnetic impurities has been theoretically predicted to change the dispersion and physical nature of low-energy quasiparticles, resulting in unique particle-like states that lack microscopic translational symmetry. Here we report the direct observation of impurities reshaping the surface Dirac cone of the model 3D topological insulator Bi2Se3. For the first time, a pronounced kink-like dispersion fea…
The protected surface states of topological insulators (TIs) form gapless Dirac cones corresponding non-degenerate eigenstates with helical spin polarisation. The presence of a warping term deforms the isotropic cone of the most simple model into snowflake Fermi surfaces as in Bi2Se3 and Bi2Te3. Their features have been identified in STM quasiparticle interference (QPI) experiments on isolated surfaces. Here we investigate the QPI spectrum for the TI thin-film geometry with finite tunnelling between the surface states. This leads to a dramatic change of spectrum due to gapping and a change in …
A flat band in fermionic system is a dispersionless single-particle state with a diverging effective mass and nearly zero group velocity. These flat bands are expected to support exotic properties in the ground state, which might be important for a wide range of promising physical phenomena. For many applications it is highly desirable to have such states in Dirac materials, but so far they have been reported only in non-magnetic Dirac systems. In this work we propose a realization of topologically protected spin-polarized flat bands generated by domain walls in planar magnetic topological ins…
Weak topological insulators possess a symmetry related set of Dirac-Weyl cones in the surface Brillouin zone, implying misorientation between the principle axis of the low energy manifold of the bulk and the surface normal. We show that this feature of weak topological insulators comes with a hidden richness of surface spin textures, and that by misorientation a helical texture can become an unusual hyperbolic spin texture. We illustrate this effect by comparison of the $M$-point and $Γ$-point Dirac-Weyl cones on the (111) surface of the crystalline topological insulator SnTe.
In the quantum Hall regime of graphene, antiferromagnetic and spin-polarized ferromagnetic states at the zeroth Landau level compete, leading to a canted antiferromagnetic state depending on the direction and magnitude of an applied magnetic field. Here, we investigate this transition at 2.7 K in graphene Hall bars that are proximity coupled to the ferrimagnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$. From nonlocal transport measurements, we demonstrate an induced magnetic exchange field in graphene, which lowers the magnetic field required to modulate the magnetic state in graphene. These results …
Novel Spin-texture on the warped Dirac-cone surface states in topological insulators
我们用第一性原理计算和模型哈密顿量研究了Bi 2 Te 3族三维拓扑绝缘体的表面态性质。当表面狄拉克锥由于菱形结构中的Dresselhaus自旋轨道耦合而翘曲时，自旋获得有限的面外分量。我们预测了一种新的面内自旋纹理的扭曲表面狄拉克锥的自旋不垂直于电子动量。我们的k.p模型计算表明，这种新型的面内自旋纹理需要高阶Dresselhaus自旋轨道耦合项。
We use the Dirac cone model to explore the high Chern number (C) phases that are realized in the magnetic-doped topological insulator (TI) multilayer structures by Zhao et al. [Nature 588, 419 (2020)]. The Chern number is calculated by capturing the evolution of the phase boundaries with the parameters and then the Chern number phase diagrams of the TI multilayer structures are obtained. The high-C behavior is attributed to the band inversion of the renormalized Dirac cones, along with which the spin polarization at the Γpoint will get increased. Moreover, another two TI multilayer structures …
New phase of matter usually emerges when a given symmetry breaks spontaneously, which can involve charge, spin, and valley degree of freedoms. Here, we report an observation of new correlated insulators evolved from spin polarized states to valley polarized states in AB-BA stacked twisted double bilayer graphene (TDBG). The transition of the isospin polarization is a result of the competition between spin and valley, driven by the displacement field (D). At a high field |D| > 0.7 V/nm, we observe valley polarized correlated insulators with a big Zeeman g factor of ~10, both at v = 2 in the moi…
We envision that quantum spin Hall effect should be observed in $(111)$-oriented thin films of SnSe and SnTe topological crystalline insulators. Using a tight-binding approach supported by first-principles calculations of the band structures we demonstrate that in these films the energy gaps in the two-dimensional band spectrum depend in an oscillatory fashion on the layer thickness. These results as well as the calculated topological invariant indexes and edge state spin polarizations show that for films ~20-40 monolayers thick a two-dimensional topological insulator phase appears. In this ra…
We propose to Floquet-engineer Dirac cones at the surface of a three-dimensional topological insulator. We show that a large tunability of the Fermi velocity can be achieved as a function of the polarization, direction and amplitude of the driving field. Using this external control, the Dirac cones in the quasienergy spectrum may become elliptic or massive, in accordance to experimental evidences. These results help us to understand the interplay of surface states and external ac driving fields in topological insulators. In our work we use the full Hamiltonian for the three-dimensional system …
We demonstrate theoretically that a strong high-frequency circularly polarized electromagnetic field can turn a two-dimensional periodic array of interconnected quantum rings into a topological insulator. The elaborated approach is applicable to calculate and analyze the electron energy spectrum of the array, the energy spectrum of the edge states and the corresponding electronic densities. As a result, the present theory paves the way to optical control of the topological phases in ring-based mesoscopic structures.
Spin-momentum locking in the surface mode of topological insulators (TI) leads to the surface accumulation of spin-polarized electrons caused by bias current flows through TI samples. Here, we demonstrate that scanning tunneling microscopy can be used to sense this surface spin-polarized electron accumulation. We present experimental results of this sensing for Sn-doped Bi$_2$Se$_3$ samples by employing Fe-coated W tips as well as non-magnetic W tips. We observe a linear increase in the spin-accumulation as a function of bias current through TI samples.
Recently, a new quantum phase, the topological insulator, has been vividly investigated in a variety of materials. Its unique bandstructure allows for optical generation and control of spin-polarized currents based on the circular photogalvanic effect. In this paper, we generate and distinguish the different photocurrent contributions via the the polarization of the driving light wave. We discuss the helicity-dependent spin-polarized current and the polarization independent thermoelectric current as spatially resolved maps, focusing on the influence of the topological insulator/metallic contac…
We propose a different route to time-reversal invariant Weyl semimetals employing multilayer heterostructures comprising ordinary "trivial" insulators and nontrivial insulators with \textit{pairs} of protected Dirac cones on the surface. We consider both the case of weak topological insualtors, where surface Dirac cones are pinned to time-reversal invariant momenta, and of topological crystalline insulators with unpinned surface Dirac cones. For both realizations we explain phenomenologically how the proposed construction leads to the emergence of a Weyl semimetal phase. We further formulate e…
Control over topological insulator photocurrents with light polarization
三维拓扑绝缘体代表了一种新的量子相的物质与自旋极化的表面状态，是从反向散射的保护。这些表面态的静态电子性质已全面成像的光电子能谱和隧道光谱。理论家提出拓扑表面态也可以表现出新颖的电子对光的响应，例如拓扑量子相变和自旋极化电流。然而，光学驱动拓扑绝缘体脱离平衡的效果在很大程度上还没有被实验探索，也没有测量到光电流。在这里，我们表明，照射的拓扑绝缘体Bi 2 Se 3与圆偏振光产生的光电流，源于拓扑螺旋狄拉克费米子，反转的螺旋光反转的光电流的方向。我们还观察到一个光电流，是由光的线性偏振控制，并认为它也可能有一个拓扑表面态的起源。这种方法可以探测拓扑绝缘体的动态特性，并导致新的光自旋电子器件。
We report a systematic angle-resolved photoemission spectroscopy on topological insulator (TI) TlBi1-xSbxTe2 which is bulk insulating at 0.5 < x < 0.9 and undergoes a metal-insulator-metal transition with the Sb content x. We found that this transition is characterized by a systematic hole doping with increasing x, which results in the Fermi-level crossings of the bulk conduction and valence bands at x~ 0 and x~1, respectively. The Dirac point of the topological surface state is gradually isolated from the valence-band edge, accompanied by a sign reversal of Dirac carriers. We also found that …
We demonstrate that the charge-spin conversion efficiency of topological insulators (TI) can be experimentally determined by injecting spin-polarized tunneling electrons into a TI. Through a comparative study between bismuth selenide and bismuth antimony telluride, we verified the topological-surface-state origin of the observed giant spin signals. By injecting energetic electrons into bismuth selenide, we further studied the energy dependence of the effective spin polarization at the TI surface. The experimentally verified large spin polarization, as well as our calculations, provides new ins…
Spin-momentum locked (SML) topological surface state (TSS) provides exotic properties for spintronics applications. The spin-polarized current, which emerges owing to the SML, can be directly detected by performing spin potentiometric measurement. We observed spin-polarized current using a bulk insulating topological insulator (TI), Bi1.5Sb0.5Te1.7Se1.3, and Co as the ferromagnetic spin probe. The spin voltage was probed with varying the bias current, temperature, and gate voltage. Moreover, we observed non-local spin-polarized current, which is regarded as a distinguishing property of TIs. Th…
We theoretically predict two new classes of three-dimensional topological crystalline insulators (TCIs), which have an odd number of unpinned surface Dirac cones protected by crystal symmetries. The first class is protected by a single glide plane symmetry; the second class is protected by a composition of a twofold rotation and time-reversal symmetry. Both classes of TCIs are characterized by a quantized $π$ Berry phase associated with surface states and a $Z_2$ topological invariant associated with the bulk bands. In the presence of disorder, these TCI surface states are protected against lo…
A three-dimensional topological insulator features a two-dimensional surface state consisting of a single linearly-dispersive Dirac cone. Under broken time-reversal symmetry, the single Dirac cone is predicted to cause half-integer quantization of Hall conductance, which is a manifestation of the parity anomaly in quantum field theory. However, despite various observations of quantization phenomena, the half-integer quantization has been elusive because a pair of equivalent Dirac cones on two opposing surfaces are simultaneously measured in ordinary experiments. Here we demonstrate the half-in…
We investigate electromagnetic properties of a topological crystalline insulator (TCI) thin film under external electromagnetic fields. The TCI thin film is a topological insulator indexed by the mirror-Chern number. It is demonstrated that the gap closes together with the emergence of a pair of gapless cones carrying opposite chirarities by applying in-plane magnetic field. A pair of gapless points have opposite vortex numbers. This is a reminiscence of a pair of Weyl cones in 3D Weyl semimetal. We thus present an a magnetic-field induced semimetal-semiconductor transition in 2D material. Thi…
We report Coulomb blockade transport studies of semiconducting InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. Comparing experiment to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels. Results are consistent with zero-field spin splitting exceeding the induced superconducting gap. Energies of subgap states are tunable on either side of zero via electrostatic gates.
Topological insulators (TIs) are a new class of quantum materials that exhibit spin momentum locking (SML) of massless Dirac fermions in the surface states. Usually optical methods, such as angle and spin-resolved photoemission spectroscopy, have been employed to observe the helical spin polarization in the surface states of three-dimensional (3D) TIs up to room temperatures. Recently, spin polarized surface currents in 3D TIs were detected by electrical methods using ferromagnetic (FM) contacts in a lateral spin-valve measurement geometry. However, probing the spin texture with such electrica…
Topological crystalline insulators are materials in which the crystalline symmetry leads to topologically protected surface states with a chiral spin texture, rendering them potential candidates for spintronics applications. Using scanning tunneling spectroscopy, we uncover the existence of one-dimensional (1D) midgap states at odd-atomic surface step edges of the three- dimensional topological crystalline insulator (Pb,Sn)Se. A minimal toy model and realistic tight- binding calculations identify them as spin-polarized flat bands connecting two Dirac points. This non-trivial origin provides th…
We derive the spin texture of a weak topological insulator via a supersymmetric approach that includes the roles of the bulk gap edge states and surface band bending. We find the spin texture can take one of four forms: (i) helical, (ii) hyperbolic, (iii) hedgehog, with spins normal to the Dirac-Weyl cone of the surface state, and (iv) hyperbolic hedgehog. Band bending determines the winding number in the case of a helical texture, and for all textures can be used to tune the spin texture polarization to zero. For the weak topological insulator SnTe, we show that inclusion of band bending is c…
Linearly Polarized Light-Induced Anomalous Hall Effect and Topological Phase Transitions in an Altermagnetic Topological Insulator
National Laboratory of Solid State Microstructures and School of Physics, Nanjing University（南京大学固体微结构物理学院）；College of Science, China University of Petroleum (East China)（中国石油大学（华东）理学院）；Jiangsu Physical Science Research Center（江苏省物理科学研究院）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学量子信息科学与技术江苏省重点实验室）
We study thermoelectric transport in ultrathin topological insulators under the application of circularly polarized off-resonant light of frequency Ω and amplitude A. We derive analytical expressions for the band structure, orbital magnetization Morb, and the thermal (\k{appa}xy) and Nernst (αxy) conductivities. Reversing the light polarization from right to left leads to an exchange of the conduction and valence bands of the symmetric and antisymmetric surface states and to a sign change in Morb,αxy, and \k{appa}xy. Varying the sample thickness or A/Ω leads to a strong enhancement of Morb and…
Chirally stacked $N$-layer graphene is a semimetal with $\pm p^N$ band-touching at two nonequivalent corners in its Brillioun zone. We predict that an off-resonant circularly polarized light (CPL) drives chirally stacked $N$-layer graphene into a Floquet Chern Insulators (FCIs), a.k.a. quantum anomalous Hall insulators, with tunable high Chern number $C_F=\pm N$ and large gaps. A topological phase transition between such a FCI and a valley Hall (VH) insulator with high valley Chern number $C_v=\pm N$ induced by a voltage gate can be engineered by the parameters of the CPL and voltage gate. We …
We propose a class of photonic Floquet topological insulators based on staggered helical lattices and an efficient numerical method for calculating their Floquet bandstructure. The lattices support anomalous Floquet topological insulator phases with vanishing Chern number and tunable topological transitions. At the critical point of the topological transition, the bandstructure hosts a single unpaired Dirac cone, which yields a variety of unusual transport effects: a discrete analogue of conical diffraction, weak antilocalization not limited by intervalley scattering, and suppression of Anders…
A time-reversal invariant topological insulator occupying a Euclidean half-space determines a 'Quaternionic' self-adjoint Fredholm family. We show that the discrete spectrum data for such a family is geometrically encoded in a non-trivial 'Real' gerbe. The gerbe invariant, rather than a naïve counting of Dirac points, precisely captures how edge states completely fill up the bulk spectral gap in a topologically protected manner.
Topological insulators are candidates to open up a novel route in spin based electronics. Different to traditional ferromagnetic materials, where the carrier spin-polarization and magnetization are based on the exchange interaction, the spin properties in topological insulators are based on the coupling of spin- and orbit interaction connected to its momentum. Specific ways to control the spin-polarization with light have been demonstrated: the energy momentum landscape of the Dirac cone provides spin-momentum locking of the charge current and its spin. The directionality of spin and momentum,…
Inducing Lifshitz transition by extrinsic doping of surface bands in topological crystalline insulator Pb$_{1-x}$Sn$_{x}$Se
研究了窄隙半导体Pb $_{1-x}$ Sn $_{x}$ Se在其岩盐结构相中的拓扑保护表面态，x=0.45、0.23、0.15和0。角分辨光电子能谱学的本质上p掺杂的样品显示出两个狄拉克锥，偏心的时间反转不变点X的表面布里渊区的所有，但x=0的样品的明确指示。碱金属的吸附逐渐使表面带充满电子，驱动x>0拓扑晶体绝缘体系统通过Lifshitz转变，并从空穴到电子的费米表面。x>0样品中的电子掺杂带显示出狄拉克锥的完整构型，也证实了表面带的电子-空穴对称性。
Generation of an anomalous linearly dispersing spin-polarized band in Bi-based topological insulators
University of Regensburg（雷根斯堡大学）；New Technologies – Research Centre of the University of West Bohemia（西波希米亚大学新技术研究中心）；Technical University of Munich（慕尼黑工业大学）；Elettra-Sincrotrone Trieste（的里雅斯特电子同步加速器中心）；Physikalisch-Technische Bundesanstalt（德国物理技术研究院）
We discuss the magnetic and topological properties of bulk crystals and quasi-two-dimensional thin films formed by stacking intrinsic magnetized topological insulator ( for example Mn(Sb$_{x}$Bi$_{1-x}$)$_2$X$_4$ with X = Se,Te, including MnBi$_2$Te$_4$) septuple layers and topological insulator quintuple layers in arbitrary order. Our analysis makes use of a simplified model that retains only Dirac-cone degrees of freedom on both surfaces of each septuple or quintuple layer. We demonstrate the model's applicability and estimate its parameters by comparing with {\it ab initio } density-functio…
The results of scanning tunneling microscopy experiments using iron-coated tungsten tips and current-carrying bismuth selenide ($Bi_2Se_3$) samples are reported. Asymmetry in tunneling currents with respect to the change in the direction of bias currents through $Bi_2Se_3$ samples has been observed. It is argued that this asymmetry is the manifestation of surface spin-polarized electron accumulation caused by the ninety-degree electron spin-momentum locking in the topologically protected surface current mode. It is demonstrated that the manifestation of surface spin-polarized electron accumula…
Site-polarized Mott phases competing with a correlated metal in twisted WSe$_2$
University of Hamburg（汉堡大学）；The Hamburg Centre for Ultrafast Imaging（汉堡超快成像中心）；University of Würzburg（维尔茨堡大学）；Max Planck Institute for the Structure and Dynamics of Matter（物质结构与动力学马普研究所）；RWTH Aachen University（亚琛工业大学）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Tsientang Institute for Advanced Study, Zhejiang（浙江大学前沿技术研究院（紫江））；Songshan Lake Materials Laboratory（松山湖材料实验室）
In recent years, a class of solid state materials, called three-dimensional topological insulators, has emerged. In the bulk, a topological insulator behaves like an ordinary insulator with a band gap. At the surface, conducting gapless states exist showing remarkable properties such as helical Dirac dispersion and suppression of backscattering of spin-polarized charge carriers. The characterization and control of the surface states via transport experiments is often hindered by residual bulk contributions yet at cryogenic temperatures. Here, we show that surface currents in Bi2Se3 can be cont…
