Novel topological insulators from crystalline symmetries

We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions (3D), these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the appearance of these topological states in both crystals with negligible spin–orbit coupling and a fourfold rotational symmetry, as well as in mirror-symmetric crystals with sizable spin–orbit interaction characterized by the so-called mirror Chern number. Finally, we also discuss similar topological crystalline states in one-dimensional (1D) insulators, such as nanowires or atomic chains, with mirror symmetry. There, the prime physical consequence of the non-trivial topology is the presence of quantized end charges.     

Topological crystalline insulators

The recent discovery of topological insulators has revived interest in the band topology of insulators. In this Letter, we extend the topological classification of band structures to include certain crystal point group symmetry. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces. These topological crystalline insulators are the counterpart of topological insulators in materials without spin-orbit coupling. Their band structures are characterized by new topological invariants. We hope this work will enlarge the family of topological phases in band insulators and stimulate the search for them in real materials.     

Majorana modes at the ends of superconductor vortices in doped topological insulators

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.     

Dephasing effects in topological insulators

Topological insulators, a class of typical topological materials in both two dimensions and three dimensions,are insulating in bulk and metallic at surface. The spin-momentum locked surface states and peculiar transport properties exhibit promising potential applications on quantum devices, which generate extensive interest in the last decade. Dephasing is the process of the loss of phase coherence, which inevitably exists in a realistic sample. In this review, we focus on recent progress in dephasing effects on the topological insulators. In general, there are two types of dephasing processes: normal dephasing and spin dephasing. In two-dimensional topological insulators, the phenomenologically numerical investigation shows that the longitudinal resistance plateaus is robust against normal dephasing but fragile with spin dephasing. Several microscopic mechanisms of spin dephasing are then discussed. In three-dimensional topological insulators, the helical surface states exhibit a helical spin texture due to the spin-momentum locking mechanism. Thus, normal dephasing has close connection to spin dephasing in this case, and gives rise to anomalous “gap-like” feature. Dephasing effects on properties of helical surface states are investigated.     

Pseudo topological insulators

We predict pseudo topological insulators that have been previously overlooked. We determine some conditions under which robust pseudo topological edge states appear and illustrate our idea on the Su–Schrieffer–Heeger (SSH) model with extra chiral symmetry breaking potentials. We discuss that pseudo topological insulating phase transition occurs without band gap closing.     

Topological insulator: Spintronics and quantum computations

Topological insulators are emergent states of quantum matter that are gapped in the bulk with timereversal symmetry-preserved gapless edge/surface states, adiabatically distinct from conventional materials. By proximity to various magnets and superconductors, topological insulators show novel physics at the interfaces, which give rise to two new areas named topological spintronics and topological quantum computation. Effects in the former such as the spin torques, spin-charge conversion, topological antiferromagnetic spintronics, and skyrmions realized in topological systems will be addressed. In the latter, a superconducting pairing gap leads to a state that supports Majorana fermions states, which may provide a new path for realizing topological quantum computation. Various signatures of Majorana zero modes/edge mode in topological superconductors will be discussed. The review ends by outlooks and potential applications of topological insulators. Topological superconductors that are fabricated using topological insulators with superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.     

Topological response theory of doped topological insulators

We generalize the topological response theory of three-dimensional topological insulators (TI) to metallic systems-specifically, doped TI with finite bulk carrier density and a time-reversal symmetry breaking field near the surface. We show that there is an inhomogeneity-induced Berry phase contribution to the surface Hall conductivity that is completely determined by the occupied states and is independent of other details such as band dispersion and impurities. In the limit of zero bulk carrier density, this intrinsic surface Hall conductivity reduces to the half-integer quantized surface Hall conductivity of TI. Based on our theory we predict the behavior of the surface Hall conductivity for a doped topological insulator with a top gate, which can be directly compared with experiments.     

A computational investigation of topological insulator Bi2Se3 film

Topological insulators have a bulk band gap like an ordinary insulator and conducting states on their edge or surface which are formed by spin–orbit coupling and protected by time-reversal symmetry. We report theoretical analyses of the electronic properties of three-dimensional topological insulator Bi₂Se₃ film on different energies. We choose five different energies (–123, –75, 0, 180, 350 meV) around the Dirac cone (–113 meV). When energy is close to the Dirac cone, the properties of wave function match the topological insulator’s hallmark perfectly. When energy is far way from the Dirac cone, the hallmark of topological insulator is broken and the helical states disappear. The electronic properties of helical states are dug out from the calculation results. The spin-momentum locking of the helical states are confirmed. A 3-fold symmetry of the helical states in Brillouin zone is also revealed. The penetration depth of the helical states is two quintuple layers which can be identified from layer projection. The charge contribution on each quintuple layer depends on the energy, and has completely different behavior along K and M direction in Brillouin zone. From orbital projection, we can find that the maximum charge contribution of the helical states is p_z orbit and the charge contribution on p_yand p_x orbits have 2-fold symmetry.     

Topological magnetic insulators with corundum structure

Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap are protected by time-reversal symmetry. When a proper kind of antiferromagnetic long-range order is established in a topological insulator, the system supports axionic excitations. In this Letter, we study theoretically the electronic states in a transition metal oxide of corundum structure, in which both spin-orbit interaction and electron-electron interaction play crucial roles. A tight-binding model analysis predicts that materials with this structure can be strong topological insulators. Because of the electron correlation, an antiferromagnetic order may develop, giving rise to a topological magnetic insulator phase with axionic excitations.     

Measurement of an exceptionally weak electron-phonon coupling on the surface of the topological insulator Bi2Se3 using angle-resolved photoemission spectroscopy

Gapless surface states on topological insulators are protected from elastic scattering on nonmagnetic impurities which makes them promising candidates for low-power electronic applications. However, for widespread applications, these states should have to remain coherent at ambient temperatures. Here, we studied temperature dependence of the electronic structure and the scattering rates on the surface of a model topological insulator, Bi2Se3, by high-resolution angle-resolved photoemission spectroscopy. We found an extremely weak broadening of the topological surface state with temperature and no anomalies in the state's dispersion, indicating exceptionally weak electron-phonon coupling. Our results demonstrate that the topological surface state is protected not only from elastic scattering on impurities, but also from scattering on low-energy phonons, suggesting that topological insulators could serve as a basis for room-temperature electronic devices.     

拓扑绝缘体表面态的STM研究

文章主要介绍了利用扫描隧道显微镜对拓扑绝缘体表面态进行的一系列研究工作,包括拓扑绝缘体表面态的电子驻波以及拓扑表面态的朗道量子化现象.这些工作对于拓扑绝缘体基本性质的确立以及深入理解具有十分重要的意义.     

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.     

Proximity effects in topological insulator heterostructures

Topological insulators （Tls） are bulk insulators that possess robust helical conducting states along their interfaces with conventional insulators. A tremendous research effort has recently been devoted to TI-based heterostructures, in which con- ventional proximity effects give rise to a series of exotic physical phenomena. This paper reviews our recent studies on the potential existence of topological proximity effects at the interface between a topological insulator and a normal insu- lator or other topologically trivial systems. Using first-principles approaches, we have realized the tunability of the vertical location of the topological helical state via intriguing dual-proximity effects. To further elucidate the control parameters of this effect, we have used the graphene-based heterostructures as prototypical systems to reveal a more complete phase diagram. On the application side of the topological helical states, we have presented a catalysis example, where the topo- logical helical state plays an essential role in facilitating surface reactions by serving as an effective electron bath, These discoveries lay the foundation for accurate manipulation of the real space properties of the topological helical state in TI- based heterostructures and pave the way for realization of the salient functionality of topological insulators in future device applications.     

Robustness of topologically protected surface states in layering of Bi2Te3 thin films

Bulk Bi2Te3 is known to be a topological insulator. We investigate surface states of Bi2Te3(111) thin films of one to six quintuple layers using density-functional theory including spin-orbit coupling. We construct a method to identify topologically protected surface states of thin film topological insulators. Applying this method to Bi2Te3 thin films, we find that the topological nature of the surface states remains robust with the film thickness and that the films of three or more quintuple layers have topologically nontrivial surface states, which agrees with experiments.     

类石墨烯复杂晶胞光子晶体中的确定性界面态

拓扑绝缘体是当前凝聚态物理领域研究的热点问题.利用石墨烯材料的特殊能带特性来实现拓扑输运特性在设计下一代电子和能谷电子器件方面具有较广泛的应用前景.基于光子与电子的类比,利用光子拓扑材料实现了确定性界面态;构建了具有C_(6v)。对称性的类似石墨烯结构的的光子晶体复杂晶格;通过多种方式降低晶格对称性来获得具有C_(3v),C_3,C_(2v)和C_2对称的晶体,从而打破能谷简并实现全光子带隙结构;将体拓扑性质不同的两种光子晶体摆放在一起,在此具有反转体能带性质的界面上,实现了具有单向传输特性的拓扑确定性界面态的传输.利用光子晶体结构的容易加工性,可以简便地调控拓扑界面态控制光的传播,可为未来光拓扑绝缘体的研究提供良好的平台.     

Z(2) topological insulators in ultracold atomic gases

We describe how optical dressing can be used to generate band structures for ultracold atoms with nontrivial Z(2) topological order. Time-reversal symmetry is preserved by simple conditions on the optical fields. We first show how to construct optical lattices that give rise to Z(2) topological insulators in two dimensions. We then describe a general method for the construction of three-dimensional Z(2) topological insulators. A central feature of our approach is a new way to understand Z(2) topological insulators starting from the nearly free electron limit.     

Electronic properties of SnTe-class topological crystalline insulator materials

The rise of topological insulators in recent years has broken new ground both in the conceptual cognition of condensed matter physics and the promising revolution of the electronic devices.It also stimulates the explorations of more topological states of matter.Topological crystalline insulator is a new topological phase,which combines the electronic topology and crystal symmetry together.In this article,we review the recent progress in the studies of SnTe-class topological crystalline insulator materials.Starting from the topological identifications in the aspects of the bulk topology,surface states calculations,and experimental observations,we present the electronic properties of topological crystalline insulators under various perturbations,including native defect,chemical doping,strain,and thickness-dependent confinement effects,and then discuss their unique quantum transport properties,such as valley-selective filtering and helicity-resolved functionalities for Dirac fermions.The rich properties and high tunability make SnTe-class materials promising candidates for novel quantum devices.     

Studies on the electronic structures of three-dimensional topological insulators by angle resolved photoemission spectroscopy

Three-dimensional (3D) topological insulators represent a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The unusual surface states of topological insulators rise from the nontrivial topology of their electronic structures as a result of strong spin-orbital coupling. In this review, we will briefly introduce the concept of topological insulators and the experimental method that can directly probe their unique electronic structure: angle resolved photoemission spectroscopy (ARPES). A few examples are then presented to demonstrate the unique band structures of different families of topological insulators and the unusual properties of the topological surface states. Finally, we will briefly discuss the future development of topological quantum materials.     

Identifying Two-Dimensional <Emphasis Type="Italic">Z</Emphasis><Subscript>2</Subscript> Antiferromagnetic Topological Insulators

We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate Néel antiferromagnet, where staggered magnetization breaks the symmetry with respect to both elementary translation and time reversal, but retains their product as a symmetry. In contrast to the so-called Z₂ topological insulators, an exhaustive characterization of antiferromagnetic topological phases with the help of topological invariants has been missing. We analyze a simple model of an antiferromagnetic topological insulator and chart its phase diagram, using a recently proposed criterion for centrosymmetric systems [13]. We then adapt two methods, originally designed for paramagnetic systems, and make antiferromagnetic topological phases manifest. The proposed methods apply far beyond the particular examples treated in this work, and admit straightforward generalization. We illustrate this by two examples of non-centrosymmetric systems, where no simple criteria have been known to identify topological phases. We also present, for some cases, an explicit construction of edge states in an antiferromagnetic topological insulator.