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.     

Effect of atomic impurities on the helical surface states of the topological insulator Bi2Te3

The effect of atomic impurities including N, O, Na, Ti and Co on the surface states of the topological insulator (TI) Bi(2)Te(3) is studied using pseudopotential first principles methods. The robustness of the TI surface states is particularly investigated against magnetic and non-magnetic atomic adsorption by calculating the electronic band structure, charge transfer, and magnetic moments. Interestingly, it is found that a non-magnetic nitrogen atom has produced a residual magnetic moment and opens a gap in the surface states whereas Na and O atoms preserve the Dirac-like dispersion. The charge transfer from the adatoms produces an electric dipole field that causes Rashba splitting in the surface bands. For atomic impurities with 3d orbitals (Ti and Co), the TI surface states are destroyed and two spin-resolved resonance peaks are developed near the Fermi level in the DOS.     

Surface Majorana flat bands in j=3/2 superconductors with singlet-quintet mixing

Recent experiments [Science Advances 4 eaao4513(2018)] have revealed the evidence of nodal-line superconductivity in half-Heusler superconductors, e.g., YPt Bi. Theories have suggested the topological nature of such nodal-line superconductivity and proposed the existence of surface Majorana flat bands on the(111) surface of half-Heusler superconductors.Due to the divergent density of states of the surface Majorana flat bands, the surface order parameter and the surface impurity play essential roles in determining the surface properties. We study the effect of the surface order parameter and the surface impurity on the surface Majorana flat bands of half-Heusler superconductors based on the Luttinger model. To be specific, we consider the topological nodal-line superconducting phase induced by the singlet-quintet pairing mixing, classify all the possible translationally invariant order parameters for the surface states according to irreducible representations of C_(3v)point group, and demonstrate that any energetically favorable order parameter needs to break the time-reversal symmetry. We further discuss the energy splitting in the energy spectrum of surface Majorana flat bands induced by different order parameters and non-magnetic or magnetic impurities. We propose that the splitting in the energy spectrum can serve as the fingerprint of the pairing symmetry and mean-field order parameters. Our theoretical prediction can be examined in the future scanning tunneling microscopy experiments.     

Half-metallic ferromagnetism in I2-VI compounds with non-magnetic dopants

First-principles calculations based on the tight-binding linear muffin-tin orbital (TB-LMTO) method were performed to investigate the occurrence of spin polarization in the alkali metal oxides (M₂O) [M: Li, Na, K, Rb] in antifluorite (anti- CaF₂-type) structure with non-magnetic (N, P, As, Sb and Bi) dopants. The calculations reveal that non-magnetic substitutional doping at anion site can induce stable half-metallic ferromagnetic ground state in I₂-VI compounds. Total energy calculations show that the antifluorite ferromagnetic state is energetically more stable than the antifluorite non-magnetic state at equilibrium volume. Ground state properties such as equilibrium lattice constant and bulk modulus were calculated. The calculated magnetic moment is found to be 1.00 μ_B per dopant atom. The magnetic moment is mainly contributed by p orbitals of dopant atom.     

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.     

Stable nontrivial Z2 topology in ultrathin Bi (111) films: a first-principles study

Recently, there have been intense efforts in searching for new topological insulator materials. Based on first-principles calculations, we find that all the ultrathin Bi (111) films are characterized by a nontrivial Z(2) number independent of the film thickness, without the odd-even oscillation of topological triviality as commonly perceived. The stable nontrivial Z(2) topology is retained by the concurrent band gap inversions at multiple time-reversal-invariant k points with the increasing film thickness and associated with the intermediate interbilayer coupling of the Bi film. Our calculations further indicate that the presence of metallic surface states in thick Bi (111) films can be effectively removed by surface adsorption.     

Impurity effect on weak antilocalization in the topological insulator Bi2Te3

We study the weak antilocalization (WAL) effect in topological insulator Bi(2)Te(3) thin films at low temperatures. The two-dimensional WAL effect associated with surface carriers is revealed in the tilted magnetic field dependence of magnetoconductance. Our data demonstrate that the observed WAL is robust against deposition of nonmagnetic Au impurities on the surface of the thin films, but it is quenched by the deposition of magnetic Fe impurities which destroy the π Berry phase of the topological surface states. The magnetoconductance data of a 5 nm Bi(2)Te(3) film suggests that a crossover from symplectic to unitary classes is observed with the deposition of Fe impurities.     

Modification of the Hybridization Gap by Twisted Stacking of Quintuple Layers in a Three-Dimensional Topological Insulator Thin Film

Twisting the stacking of layered materials leads to rich new physics. A three-dimensional topological insulator film hosts two-dimensional gapless Dirac electrons on top and bottom surfaces, which, when the film is below some critical thickness, will hybridize and open a gap in the surface state structure. The hybridization gap can be tuned by various parameters such as film thickness and inversion symmetry, according to the literature. The three-dimensional strong topological insulator Bi(Sb)Se(Te) family has layered structures composed of quintuple layers(QLs) stacked together by van der Waals interaction. Here we successfully grow twistedly stacked Sb_2Te_3 QLs and investigate the effect of twist angels on the hybridization gaps below the thickness limit. It is found that the hybridization gap can be tuned for films of three QLs, which may lead to quantum spin Hall states.Signatures of gap-closing are found in 3-QL films. The successful in situ application of this approach opens a new route to search for exotic physics in topological insulators.     

金属表面Rashba自旋轨道耦合作用研究进展

自旋轨道耦合是电子自旋与轨道相互作用的桥梁, 它提供了利用外电场来调控电子的轨道运动、进而调控电子自旋状态的可能. 固体材料中有很多有趣的物理现象, 例如磁晶各向异性、自旋霍尔效应、拓扑绝缘体等, 都与自旋轨道耦合密切相关. 在表面/界面体系中, 由于结构反演不对称导致的自旋轨道耦合称为Rashba自旋轨道耦合, 它最早在半导体材料中获得研究, 并因其强度可由栅电压灵活调控而备受关注, 成为电控磁性的重要物理基础之一. 继半导体材料后, 金属表面成为具有Rashba自旋轨道耦合作用的又一主流体系. 本文以Au(111), Bi(111), Gd(0001)等为例综述了磁性与非磁性金属表面Rashba自旋轨道耦合的研究进展, 讨论了表面电势梯度、原子序数、表面态波函数的对称性, 以及表面态中轨道杂化等因素对金属表面Rashba自旋轨道耦合强度的影响. 在磁性金属表面, 同时存在Rashba自旋轨道耦合作用与磁交换作用, 通过Rashba自旋轨道耦合可能实现电场对磁性的调控. 最后, 阐述了外加电场和表面吸附等方法对金属表面Rashba自旋轨道耦合的调控. 基于密度泛函理论的第一性原理计算和角分辨光电子能谱测量是金属表面Rashba自旋轨道耦合的两大主要研究方法, 本文综述了这两方面的研究结果, 对金属表面Rashba自旋轨道耦合进行了深入全面的总结和分析.     

Mixed Type of the Magnetic Order in Intrinsic Magnetic Topological Insulators Mn(Bi,Sb)2Te4

JETP Letters - It is known that Mn(Bi1 – xSbx)2Te4 is an intrinsic magnetic topological insulator, where the Dirac point can be localized at the Fermi level by substituting Bi atoms for Sb...     

Electronic Properties of Defects Induced by H Irradiation in Tantalum Phosphide

Tantalum phosphide(TaP) is predicted to be a kind of topological semimetal. Several defects of TaP induced by H irradiation are studied by the density functional theory. Electronic dispersion curves and density of states of these defects are reported. Various defects have different impacts on the topological properties. Weyl point positions are not affected by most defects. The H atom can tune the Fermi level as an interstitial. The defect of substitutional H on P site does not affect the topological properties. P and Ta vacancies of concentration 1/64 as well as the defect of substitutional H on Ta site destruct part of the Weyl points.     

Bi(110)薄膜在NbSe_2衬底上的扫描隧道显微镜研究

二维拓扑绝缘体因其特殊的能带结构带来的新奇物理性质,成为近年来凝聚态物理的研究热点.尤其是在引入超导电性之后,二维拓扑绝缘体中可能存在马约拉纳费米子(Majorana fermion),因此在量子计算方面具有重大应用前景.在Bi(111)薄膜被证实为二维拓扑绝缘体之后, Bi(110)薄膜引起了广泛关注,然而其拓扑性质还存在争议.本文利用分子束外延技术在室温低生长速率环境下成功制备出了高质量的单晶Bi(110)薄膜.通过扫描隧道显微镜测量发现,薄膜以约8个原子层厚度为分界,从双层生长转变为单层生长模式.结合隧道谱测量发现,在NbSe_2衬底上生长的Bi(110)薄膜因为近邻效应而具有明显的超导性质,但并未显示出拓扑边缘态的存在.此外,对薄膜中特殊的量子阱态现象也进行了讨论.     

Structural, electronic and magnetic properties of the Mnben Ni(110) c(2×2) surface alloy

Using first-principles total energy method, we study the structural, the electronic and the magnetic properties of the MnNi(110) c(2×2) surface alloy. Paramagnetic, ferromagnetic, and antiferromagnetic surfaces in the top layer and the second layer are considered. It turns out that the substitutional alloy in the outermost layer with ferromagnetic surface is the most stable in all cases. The buckling of the Mn–Ni(110) c(2×2) surface alloy in the top layer is as large as 0.26á(1á=0.1 n13) and the weak rippling is 0.038 AA in the third layer, in excellent agreement with experimental results. It is proved that the magnetism of Mn can stabilize this surface alloy. Electronic structures show a large magnetic splitting for the Mn atom, which is slightly higher than that of Mn–Ni(100) c(2×2) surface alloy (3.41 eV) due to the higher magnetic moment. A large magnetic moment for the Mn atom is predicted to be 3.81 μ_B. We suggest the ferromagnetic order of the Mn moments and the ferromagnetic coupling to the Ni substrate, which confirms the experimental results. The magnetism of Mn is identified as the driving force of the large buckling and the work-function change. The comparison with the other magnetic surface alloys is also presented and some trends are predicted.     

Dopant-assisted concentration enhancement of substitutional Mn in Si and Ge

The influence of p- and n-type electronic dopants on Mn incorporation in bulk Si and Ge is studied using first-principles calculations within density functional theory. In Si, it is found that the site preference of a single Mn atom is reversed from interstitial to substitutional in the presence of a neighboring n-type dopant. In Ge, a Mn atom is more readily incorporated into the lattice when an n-type dopant is present in its immediate neighborhood, forming a stable Mn-dopant pair with both impurities at substitutional sites. A detailed analysis of the magnetic exchange interactions between such pairs reveals a new type of magnetic anisotropy in both systems.     

Photoemission spectroscopy of magnetic and nonmagnetic impurities on the surface of the Bi2Se3 topological insulator

Dirac-like surface states on surfaces of topological insulators have a chiral spin structure that suppresses backscattering and protects the coherence of these states in the presence of nonmagnetic scatterers. In contrast, magnetic scatterers should open the backscattering channel via the spin-flip processes and degrade the state's coherence. We present angle-resolved photoemission spectroscopy studies of the electronic structure and the scattering rates upon the adsorption of various magnetic and nonmagnetic impurities on the surface of Bi2Se3, a model topological insulator. We reveal a remarkable insensitivity of the topological surface state to both nonmagnetic and magnetic impurities in the low impurity concentration regime. Scattering channels open up with the emergence of hexagonal warping in the high-doping regime, irrespective of the impurity's magnetic moment.     

Surface structures formed by individual adsorption and coadsorption of Mn and Bi on Cu(0 0 1), studied by LEED

We have studied the individual adsorption of Mn and Bi, and their coadsorption on Cu(0 0 1) by low-energy electron diffraction (LEED). For Mn, we have determined the c(2 × 2) structure formed at 300 K, whose structure had been determined by several methods. We reconfirmed by a tensor LEED analysis that it is a substitutional structure and that a previously reported large corrugation (0.30 Å) between substitutional Mn and remaining surface Cu atoms coincides perfectly with the present value. In the individual adsorption of Bi, we have found a c(4 × 2) structure, which is formed by cooling below ∼250 K a surface prepared by Bi deposition of ∼0.25 ML coverage at 300 K where streaky half-order LEED spots appear. The c(4 × 2) structure has been determined by the tensor LEED analysis at 130 K and it is a substitutional structure. In the coadsorption, we found a c(6 × 4) structure, which has been determined by the tensor LEED analysis. It is very similar to the previously determined structure of the c(6 × 4) formed by coadsorption of Mg and Bi, and embedded MnBi₄ clusters are arranged in the top Cu layer instead of MgBi₄. Large lateral displacements of Bi atoms in the c(6 × 4)-(Mn + Bi) suggest that the Mn atoms undergo the size-enhancement caused by their large magnetic moment.     

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.     

Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3

We report the THz response of thin films of the topological insulator Bi2Se3. At low frequencies, transport is essentially thickness independent showing the dominant contribution of the surface electrons. Despite their extended exposure to ambient conditions, these surfaces exhibit robust properties including narrow, almost thickness-independent Drude peaks, and an unprecedentedly large polarization rotation of linearly polarized light reflected in an applied magnetic field. This Kerr rotation can be as large as 65° and can be explained by a cyclotron resonance effect of the surface states.     

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.