磁场中拓扑物态的量子输运

拓扑物态包括拓扑绝缘体、拓扑半金属以及拓扑超导体.拓扑物态奇异的能带结构以及受拓扑保护的新奇表面态,使其具有了独特的输运性质.拓扑半金属作为物质的一种三维拓扑态具有无能隙的准粒子激发,根据导带和价带的接触类型分为外尔半金属、狄拉克半金属和节线半金属.本文以拓扑半金属为主回顾了在磁场下拓扑物态中量子输运的最新工作,在不同的磁场范围内分别给出了描述拓扑物态输运行为的主要理论.     

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.     

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.     

反铁磁半金属 EuCd2Pn2（Pn = As,Sb）中磁交换诱导的外尔态

由于丰富的拓扑量子效应及巨大的潜在应用价值,拓扑材料逐渐成为凝聚态物理前沿的研究材料体系。其中,作为与石墨烯具有相似电子结构的材料,三维拓扑半金属吸引了越来越多的研究兴趣。目前已知的拓扑半金属大多为非磁性的,而磁性拓扑半金属数量有限,与非磁性拓扑半金属相比较,研究开展的还比较少。磁性与拓扑之间的相互作用能够导致非常规的物理性质,如反常霍尔效应甚至量子反常霍尔效应等。此外,在一些具有特殊磁结构的拓扑半金属中,施加外磁场能够调制其自旋结构,从而影响其拓扑能带结构。在该综述中,笔者将详细介绍利用外磁场在 EuCd2Pn2 (Pn = As, Sb) 反铁磁半金属材料中通过调制自旋结构从而改变晶体结构对称性来诱导拓扑相变。此外,笔者也将简单介绍包括 GdPtBi 和 MnBi2Te4 在内的几个相关材料。该综述中讨论的外磁场调控的磁交换诱导的拓扑相变不仅有望应用于拓扑器件,也有助于为理解磁性与拓扑态之间的紧密关联提供新的线索,对于设计新的磁性拓扑材料有启发意义。综述最后,笔者对发展磁性拓扑半金属做了一些简单展望。     

Topological Nodal Line Semimetal in Non-Centrosymmetric PbTaS_2

Topological semimetals are a new type of matter with one-dimensional Fermi lines or zero-dimensional Weyl or Dirac points in momentum space. Here using first-principles calculations, we find that the non-centrosymmetric PbTaS2 is a topological nodal line semimetal. In the absence of spin-orbit coupling(SOC), one band inversion happens around a high symmetrical H point, which leads to forming a nodal line. The nodal line is robust and protected against gap opening by mirror reflection symmetry even with the inclusion of strong SOC. In addition, it also hosts exotic drumhead surface states either inside or outside the projected nodal ring depending on surface termination. The robust bulk nodal lines and drumhead-like surface states with SOC in PbTaS_2 make it a potential candidate material for exploring the freakish properties of the topological nodal line fermions in condensed matter systems.     

拓扑量子材料光电探测器研究进展

物质拓扑态的发现是近年来凝聚态物理和材料科学的重大突破。由于存在不同于常规半导体的特殊拓扑量子态(如狄拉克费米子、外尔费米子、马约拉纳费米子等),拓扑量子材料通常能表现出一些新颖的物理特性(如量子反常霍尔效应、三维量子霍尔效应、零带隙的拓扑态、超高的载流子迁移率等),因而在低能耗电子器件和宽光谱光电探测器件领域具有重要的研究价值。本文综述了拓扑量子材料的特性与制备方法以及在光电探测领域的发展现状,重点讨论了拓扑绝缘体与拓扑半金属宽光谱光电探测器的器件结构与性能,同时也对拓扑量子材料在光电探测器领域的发展前景进行了展望。     

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.     

Topological hierarchy matters — topological matters with superlattices of defects

Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states.In this paper,we review the defects effect in these topological states and study new types of topological matters — topological hierarchy matters.We find that both topological defects(quantized vortices) and non topological defects(vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects.These topological mid-gap states have nontrivial topological properties,including the nonzero Chern number and the gapless edge states.Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters.     

Low-energy electronic properties of a Weyl semimetal quantum dot

We investigate the low-energy electronic structure of a Weyl semimetal quantum dot(QD) with a simple model Hamiltonian with only two Weyl points. Distinguished from the semiconductor and topological insulator QDs, there exist both surface and bulk states near the Fermi level in Weyl semimetal QDs. The surface state, distributed near the side surface of the QD, contributes a circular persistent current, an orbital magnetic moment, and a chiral spin polarization with spin-current locking. There are always surface states even for a strong magnetic field, even though a given surface state gradually evolves into a Landau level with increasing magnetic field. It indicates that these unique properties can be tuned via the QD size. In addition, we show the correspondence to the electronic structures of a three-dimensional Weyl semimetal, such as Weyl point and Fermi arc. Because a QD has the largest surface-to-volume ratio, it provides a new platform to verify Weyl semimetal by separating and detecting the signals of surface states. Besides, the study of Weyl QDs is also necessary for potential applications in nanoelectronics.     

Topological nodal line semimetals predicted from first-principles calculations

Topological semimetals are newly discovered states of quantum matter, which have extended the concept of topological states from insulators to metals and attracted great research interest in recent years. In general, there are three kinds of topological semimetals, namely Dirac semimetals, Weyl semimetals, and nodal line semimetals. Nodal line semimetals can be considered as precursor states for other topological states. For example, starting from such nodal line states, the nodal line structure might evolve into Weyl points, convert into Dirac points, or become a topological insulator by introducing the spin–orbit coupling (SOC) or mass term. In this review paper, we introduce theoretical materials that show the nodal line semimetal state, including the all-carbon Mackay–Terrones crystal (MTC), anti-perovskite Cu₃PdN, pressed black phosphorus, and the CaP₃ family of materials, and we present the design principles for obtaining such novel states of matter.     

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.     

Nodal Topological Phases in s-wave Superfluid of Ultracold Fermionic Gases

The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid.In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines,which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.     

磁性材料的磁结构、磁畴结构和拓扑磁结构

首先简要地介绍了磁性材料中磁结构、磁畴结构和拓扑磁结构以及相互之间的关系. 一方面, 磁畴结构由材料的磁结构、内禀磁性和微结构因素决定; 另一方面, 磁畴结构决定了材料磁化和退磁化过程以及技术磁性. 拓扑学与材料物理、材料性能的联系越来越紧密. 最近的研究兴趣集中在一些拓扑磁性组态, 如涡旋、磁泡、麦纫、斯格米子等. 研究发现这些拓扑磁结构的拓扑性质与磁性能密切相关. 然后从尺寸效应、缺陷、晶界三个方面介绍国际学术界在磁结构、磁畴结构和拓扑磁结构方面的进展. 最后介绍了在稀土永磁薄膜材料的微观结构、磁畴结构和磁性能关系、交换耦合纳米盘中的拓扑磁结构及其动力学行为方面的工作. 通过对文献的评述, 得到以下结论: 开展各向异性纳米复合稀土永磁材料的研究对更好地利用稀土资源具有重要的意义. 可以有目的地改变材料的微结构, 可控地进行磁性材料的磁畴工程, 最终获得优秀的磁性能. 拓扑学的概念正在应用于越来越多的学科领域, 在越来越多的材料中发现拓扑学的贡献. 研究磁畴结构、拓扑磁性基态或者激发态的形成规律以及动力学行为对理解量子拓扑相变以及其他与拓扑相关的物理效应是十分重要的. 也会帮助理解不同拓扑学态之间相互作用的物理机制及其与磁性能之间的关系, 同时拓展拓扑学在新型磁性材料中的应用.     

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.     

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.     

Weak antilocalization and interaction-induced localization of Dirac and Weyl Fermions in topological insulators and semimetals

Weak localization and antilocalization are quantum transport phenomena that arise from the quantum interference in disordered metals.At low temperatures,they can give distinct temperature and magnetic field dependences in conductivity,allowing the symmetry of the system to be explored.In the past few years,they have also been observed in newly emergent topological materials,including topological insulators and topological semimetals.In contrast from the conventional electrons,in these new materials the quasiparticles are described as Dirac or Weyl fermions.In this article,we review our recent efforts on the theories of weak antilocalization and interaction-induced localization for Dirac and Weyl fermions in topological insulators and topological semimetals.     

Topological properties of Sb(111) surface: A first-principles study

First-principles calculations based on the density functional theory were performed to systematically study the electronic properties of the thin film of antimony in (111) orientation. By considering the spin-orbit interaction, for stoichiometric surface, the topological states keep robust for six-bilayer case, and can be recovered in the three-bilayer film, which are guaranteed by time-reversal symmetry and inverse symmetry. For reduced surface doped by non-magnetic Bi or magnetic Mn atom, localized three-fold symmetric features can be identified. Moreover, band structures show that the non-trivial topological states stand for non-magnetic substitutional Bi atom, while can be eliminated by adsorbed or substitutional magnetic Mn atom.     

Topology of a parity-time symmetric non-Hermitian rhombic lattice

We investigate the topological properties of a trimerized parity–time(PT)symmetric non-Hermitian rhombic lattice.Although the system is PT-symmetric,the topology is not inherited from the Hermitian lattice;in contrast,the topology can be altered by the non-Hermiticity and depends on the couplings between the sublattices.The bulk–boundary correspondence is valid and the Bloch bulk captures the band topology.Topological edge states present in the two band gaps and are predicted from the global Zak phase obtained through the Wilson loop approach.In addition,the anomalous edge states compactly localize within two diamond plaquettes at the boundaries when all bands are flat at the exceptional point of the lattice.Our findings reveal the topological properties of the??PT-symmetric non-Hermitian rhombic lattice and shed light on the investigation of multi-band non-Hermitian topological phases.     

外尔半金属及其输运特性

外尔半金属是继石墨烯以及拓扑绝缘体之后的又一个研究热点。相比于后两者,外尔半金 属独特的三维无能隙线性色散能带结构使得它有很多奇特的性质,如：手性反常、手性磁效应、 反弱局域化、手性朗道能级和负磁阻效应等。实际样品中无序总是不可避免的,所以考虑无序对 体系的影响是很有必要的。我们回顾了无序下第一类以及第二类外尔半金属的相变特性,并获得 了完整的相图,这些无序诱导的相变丰富了拓扑安德森绝缘体和安德森金属绝缘体相变的物理内 涵。我们同样回顾了长程短程无序影响下的第一类外尔半金属体系的输运,发现了一种不能采用 玻尔兹曼输运方程来描述的输运过程。我们介绍Imbert-Fedorov 位移这一光学中的效应在外尔 半金属中的实现,这为更好地应用外尔半金属提供了更多的可能性,随后采用波包散射,我们解 释了外尔半金属中的超高载流子迁移率问题的原因,最后我们给出一个简要的总结。     

Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.