Direct evidence for the dirac-cone topological surface states in the ternary chalcogenide TlBiSe₂

We have performed angle-resolved photoemission spectroscopy on TlBiSe?, which is a member of the ternary chalcogenides theoretically proposed as candidates for a new class of three-dimensional topological insulators. We found direct evidence for a nontrivial surface metallic state showing an "X"-shaped energy dispersion within the bulk-band gap. The present result unambiguously establishes that TlBiSe? is a strong topological insulator with a single Dirac cone at the Brillouin-zone center. The observed bulk-band gap of 0.35 eV is the largest among known topological insulators, making TlBiSe? the most promising material for studying room-temperature topological phenomena.     

Experimental realization of a three-dimensional topological insulator phase in ternary chalcogenide TlBiSe₂

We report the first observation of a topological surface state on the (111) surface of the ternary chalcogenide TlBiSe? by angle-resolved photoemission spectroscopy. By tuning the synchrotron radiation energy we reveal that it features an almost ideal Dirac cone with the Dirac point well isolated from bulk continuum states. This suggests that TlBiSe? is a promising material for realizing quantum topological transport.     

Sizable band gap in organometallic topological insulator

Based on first principle calculation when Ceperley–Alder and Perdew–Burke–Ernzerh type exchange-correlation energy functional were adopted to LSDA and GGA calculation, electronic properties of organometallic honeycomb lattice as a two-dimensional topological insulator was calculated. In the presence of spin–orbit interaction bulk band gap of organometallic lattice with heavy metals such as Au, Hg, Pt and Tl atoms were investigated. Our results show that the organometallic topological insulator which is made of Mercury atom shows the wide bulk band gap of about ∼120 meV. Moreover, by fitting the conduction and valence bands to the band-structure which are produced by Density Functional Theory, spin–orbit interaction parameters were extracted. Based on calculated parameters, gapless edge states within bulk insulating gap are indeed found for finite width strip of two-dimensional organometallic topological insulators.     

Intrinsic magnetic topological materials

Topological states of matter possess bulk electronic structures categorized by topological invariants and edge/surface states due to the bulk-boundary correspondence. Topological materials hold great potential in the development of dissipationless spintronics, information storage and quantum computation, particularly if combined with magnetic order intrinsically or extrinsically. Here, we review the recent progress in the exploration of intrinsic magnetic topological materials, including but not limited to magnetic topological insulators, magnetic topological metals, and magnetic Weyl semimetals. We pay special attention to their characteristic band features such as the gap of topological surface state, gapped Dirac cone induced by magnetization (either bulk or surface), Weyl nodal point/line and Fermi arc, as well as the exotic transport responses resulting from such band features. We conclude with a brief envision for experimental explorations of new physics or effects by incorporating other orders in intrinsic magnetic topological materials.     

Two-dimensional topological insulators with large bulk energy gap

Two-dimensional(2D) topological insulators(TTs,or quantum spin Hall insulators) are special insulators that possess bulk 2D electronic energy gap and time-reversal symmetry protected one-dimensional(1D) edge state.Carriers in the edge state have the property of spin-momentum locking,enabling dissipation-free conduction along the 1D edge.The existence of 2D TIs was confirmed by experiments in semiconductor quantum wells.However,the 2D bulk gaps in those quantum wells are extremely small,greatly limiting potential application in future electronics and spintronics.Despite this limitation,2D TIs with a large bulk gap attracted plenty of interest.In this paper,recent progress in searching for TIs with a large bulk gap is reviewed briefly.We start by introducing some theoretical predictions of these new materials and then discuss some recent important achievements in crystal growth and characterization.     

Photogalvanic effects in topological insulators

We discuss optical absorption in topological insulators and study possible photoelectric effects theoretically. We found that absorption of circularly polarized electromagnetic waves in two-dimensional topological insulators results in electric current in the conducting 1D edge channels, the direction of the current being determined by the light polarization. We suggest two ways of inducing such a current: due to magnetic dipole electron transitions stimulated by irradiation of frequency below the bulk energy gap, and due to electric dipole transitions in the bulk at frequencies larger than the energy gap with subsequent capture of the photogenerated carriers on conducting edge states.     

Bulk band gap and surface state conduction observed in voltage-tuned crystals of the topological insulator Bi2Se3

We report a transport study of exfoliated few monolayer crystals of topological insulator Bi2Se3 in an electric field effect geometry. By doping the bulk crystals with Ca, we are able to fabricate devices with sufficiently low bulk carrier density to change the sign of the Hall density with the gate voltage V(g). We find that the temperature T and magnetic field dependent transport properties in the vicinity of this V(g) can be explained by a bulk channel with activation gap of approximately 50 meV and a relatively high-mobility metallic channel that dominates at low T. The conductance (approximately 2×7e2/h), weak antilocalization, and metallic resistance-temperature profile of the latter lead us to identify it with the protected surface state. The relative smallness of the observed gap implies limitations for electric field effect topological insulator devices at room temperature.     

Emergent Z_2 topological invariant and robust helical edge states in two-dimensional topological metals

In this work, we study the effects of disorder on topological metals that support a pair of helical edge modes deeply embedded inside the gapless bulk states. Strikingly, we predict that a quantum spin Hall(QSH) phase can be obtained from such topological metals without opening a global band gap. To be specific, disorder can lead to a pair of robust helical edge states which is protected by an emergent Z_2 topological invariant, giving rise to a quantized conductance plateau in transport measurements. These results are instructive for solving puzzles in various transport experiments on QSH materials that are intrinsically metallic. This work also will inspire experimental realization of the QSH effect in disordered topological metals.     

Li(Na)AuS体系拓扑绝缘体材料的能带结构

在拓扑领域中发现可以通过大数据搜索拓扑绝缘体,使得此领域对材料的探索转变为对材料性质的研究.半Heusler合金体系是非平庸拓扑绝缘体材料的重要载体.通过全势线性缀加平面波方法计算Li(Na)AuS体系拓扑绝缘体材料的能带结构.采用各种关联泛函计算LiAuS的平衡晶格常数,发现得到的能带图均为具有反带结构的拓扑绝缘体,而且打开了自然带隙.较小的单轴应力破坏立方结构后也破坏了此类拓扑绝缘体的自然带隙,通过施加单轴拉应力直到四方结构的平衡位置时,系统带隙值约为0.2 eV,这与立方结构平衡位置得到的带隙结果一致.运用同族元素替代的手段,实现了在保证材料拓扑绝缘体性质的同时,不改变立方结构,在体系的平衡晶格常数下使得材料的带隙打开,从而提高了实验合成拓扑绝缘体材料的可行性.     

Holographic correspondence in topological superconductors

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.     

Topological Dirac surface states in ternary compounds GeBi2Te4, SnBi2Te4 and Sn0.571Bi2.286Se4

Using high-resolution angle-resolved and time-resolved photoemission spectroscopy, we have studied the low-energy band structures in occupied and unoccupied states of three ternary compounds GeBi₂Te₄, SnBi₂Te₄ and Sn_0.571Bi_2.286Se₄ near the Fermi level. In previously confirmed topological insulator GeBi₂Te₄ compounds, we confirmed the existence of the Dirac surface state and found that the bulk energy gap is much larger than that in the first-principles calculations. In SnBi₂Te₄ compounds, the Dirac surface state was observed, consistent with the first-principles calculations, indicating that it is a topological insulator. The experimental detected bulk gap is a little bit larger than that in calculations. In Sn_0.571Bi_2.286Se₄ compounds, our measurements suggest that this nonstoichiometric compound is a topological insulator although the stoichiometric SnBi₂Se₄ compound was proposed to be topological trivial.     

Ternary thallium-based semimetal chalcogenides Tl-V-VI<Subscript>2</Subscript> as a new class of three-dimensional topological insulators

The results of the theoretical investigation of the bulk and surface electronic structures of Tl-V-VI₂ compounds, where V is the Bi or Sb semimetal and VI is the Se or Te chalcogen, are reported. It has been shown that these compounds are three-dimensional topological insulators. Both a topologically protected surface state, which forms a Dirac cone at the $ \bar \Gamma $ \bar \Gamma point, and occupied surface states, which are localized in the band gap, are present on the surface of these compounds.     

Elastic scattering of surface states on three-dimensional topological insulators

Topological insulators as a new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states protected by the time-reversal symmetry. We propose that the interference patterns caused by the elastic scattering of defects or impurities are dominated by the surface states at the extremal points on the constant energy contour. Within such a formalism, we summarize our recent theoretical investigations on the elastic scattering of topological surface states by various imperfections, including non-magnetic impurities, magnetic impurities, step edges, and various other defects, in comparison with the recent related experiments in typical topological materials such as BiSb alloys, Bi2Te3, and Bi2Se3 crystals.     

Point-contact tunneling spectroscopy between a Nb tip and an ideal topological insulator Sn-doped Bi_(1.1)Sb_(0.9)Te_2S

The lightly Sn-doped Bi_(1.1)Sb_(0.9)Te_2S is a good material to investigate the pure topological surface state because the bulk bands are far away from the Fermi level. By measuring point-contact tunneling spectra on the topological insulator Bi_(1.08)Sn_(0.02)Sb_(0.9)Te_2S samples with a superconducting Nb tip, we observed the suppression of differential conductance near zero bias, instead of the enhancement due to Andreev reflection on the spectra. The fitting to the measured spectrum results in a superconducting gap of more than 4 meV, and this value is much larger than the superconducting gap of the bulk Nb. The gaped feature exists at temperatures even above the critical temperature of bulk Nb, and is visible when the magnetic field is as large as 9 T at 3 K. We argue that such behaviors may be related to the pressure induced superconductivity by the tip in the junction area, or just some novel phenomena arising from the junction between an s-wave superconductor and an ideal topological insulator.     

单轴压力下Ge2X2Te5(X=Sb,Bi)薄膜拓扑相变的第一性原理研究

随着拓扑绝缘体的发现, 材料拓扑物性的研究成为凝聚态物理研究的热点领域. 本文基于第一性原理计算, 研究了化合物Ge₂X₂Te₅ (X=Sb, Bi) 的块体结构和二维单层和双层薄膜结构的拓扑物性, 以及单双层薄膜在垂直方向单轴压力下的拓扑量子相变. 研究发现, A型原子序列排列的这两种化合物都是拓扑绝缘体, 其单层薄膜都是普通金属, 而双层薄膜都是拓扑金属, 单层和双层薄膜在单轴加压过程中都没有发生拓扑量子相变; 这两种化合物的B型原子序列的晶体是普通绝缘体, 其所对应的薄膜, Ge₂Sb₂Te₅单层是普通金属, 双层薄膜和Ge₂Bi₂Te₅的单层和双层薄膜均为普通绝缘体, 但是在单轴加压过程中B 型原子序列所对应的单层和双层薄膜都转变为拓扑金属.     

Z2 topological order and the quantum spin Hall effect

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.     

Interface-induced topological phase and doping-modulated bandgap of two-dimensioanl graphene-like networks

Biphenylene is a new topological material that has attracted much attention recently. By amplifying its size of unit cell, we construct a series of planar structures as homogeneous carbon allotropes in the form of polyphenylene networks. We first use the low-energy effective model to prove the topological three periodicity for these allotropes. Then, through first-principles calculations, we show that the topological phase has the Dirac point. As the size of per unit cell increases, the influence of the quaternary rings decreases, leading to a reduction in the anisotropy of the system, and the Dirac cone undergoes a transition from type II to type I. We confirm that there are two kinds of non-trivial topological phases with gapless and gapped bulk dispersion. Furthermore, we add a built-in electric field to the gapless system by doping with B and N atoms, which opens a gap for the bulk dispersion. Finally, by manipulating the built-in electric field, the dispersion relations of the edge modes will be transformed into a linear type. These findings provide a hopeful approach for designing the topological carbon-based materials with controllable properties of edge states.     

Direct measurement of the out-of-plane spin texture in the Dirac-cone surface state of a topological insulator

We have performed spin- and angle-resolved photoemission spectroscopy of Bi(2)Te(3) and present the first direct evidence for the existence of the out-of-plane spin component on the surface state of a topological insulator. We found that the magnitude of the out-of-plane spin polarization on a hexagonally deformed Fermi surface of Bi(2)Te(3) reaches maximally 25% of the in-plane counterpart, while such a sizable out-of-plane spin component does not exist in the more circular Fermi surface of TlBiSe(2), indicating that the hexagonal deformation of the Fermi surface is responsible for the deviation from the ideal helical spin texture. The observed out-of-plane polarization is much smaller than that expected from the existing theory, suggesting that an additional ingredient is necessary for correctly understanding the surface spin polarization in Bi(2)Te(3).     

Quantum Hall effect from the topological surface states of strained bulk HgTe

We report transport studies on a three-dimensional, 70-nm-thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semimetallic HgTe, which thus becomes a three-dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states.     

Stanene: A good platform for topological insulator and topological superconductor

Two dimensional (2D) topological insulators (TIs) and topological superconductors (TSCs) have been intensively studied for recent years due to their great potential for dissipationless electron transportation and fault-tolerant quantum computing, respectively. Here we focus on stanene, the tin analogue of graphene, to give a brief review of their development as a candidate for both 2D TI and TSC. Stanene is proposed to be a TI with a large gap of 0.3 eV, and its topological properties are sensitive to various factors, e.g., the lattice constants, chemical functionalization and layer thickness, which offer various methods for phase tunning. Experimentally, the inverted gap and edge states are observed recently, which are strong evidences for TI. In addition, stanene is also predicted to be a time reversal invariant TSC by breaking inversion symmetry, supporting helical Majorana edge modes. The layer-dependent superconductivity of stanene is recently confirmed by both transport and scanning tunneling microscopy measurements. This review gives a detailed introduction to stanene and its topological properties and some prospects are also discussed.