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.     

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.     

Photoinduced Weyl semimetal phase and anomalous Hall effect in a three-dimensional topological insulator

Motivated by the fact that Weyl fermions can emerge in a three-dimensional topological insulator on breaking either time-reversal or inversion symmetries, we propose that a topological quantum phase transition to a Weyl semimetal phase occurs under the off-resonant circularly polarized light, in a three-dimensional topological insulator, when the intensity of the incident light exceeds a critical value. The circularly polarized light effectively generates a Zeeman exchange field and a renormalized Dirac mass, which are highly controllable. The phase transition can be exactly characterized by the first Chern number. A tunable anomalous Hall conductivity emerges, which is fully determined by the location of the Weyl nodes in momentum space, even in the doping regime. Our predictions are experimentally realizable through pump-probe angle-resolved photoemission spectroscopy and raise a new way for realizing Weyl semimetals and quantum anomalous Hall effects.     

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...     

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.     

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...     

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.     

拓扑半金属材料的单晶生长研究进展

拓扑半金属已经成为凝聚态物理研究的一个热点领域,这类材料的单晶生长是研究其物理性质的基础.目前,对于拓扑材料的研究已经形成了以理论计算为指引,对潜在的拓扑材料进行单晶制备,并结合物性测量对理论预言加以验证的科研合作方式.在这种科研团队合作中,单晶生长起衔接作用.本文介绍了近年来拓扑半金属材料单晶生长方法,涵盖了拓扑Dirac半金属、Weyl半金属、Node-Line半金属以及其他打破常规分类的拓扑绝缘体及拓扑半金属材料等,并针对各个材料,详细总结了其生长方法.     

Theory of magnetic oscillations in Weyl semimetals

Weyl semimetals are a new class of Dirac material that possesses bulk energy nodes in three dimensions, in contrast to two dimensional graphene. In this paper, we study a Weyl semimetal subject to an applied magnetic field. We find distinct behavior that can be used to identify materials containing three dimensional Dirac fermions. We derive expressions for the density of states, electronic specific heat, and the magnetization. We focus our attention on the quantum oscillations in the magnetization. We find phase shifts in the quantum oscillations that distinguish the Weyl semimetal from conventional three dimensional Schrödinger fermions, as well as from two dimensional Dirac fermions. The density of states as a function of energy displays a sawtooth pattern which has its origin in the dispersion of the three dimensional Landau levels. At the same time, the spacing in energy of the sawtooth spike goes like the square root of the applied magnetic field which reflects the Dirac nature of the fermions. These features are reflected in the specific heat and magnetization. Finally, we apply a simple model for disorder and show that this tends to damp out the magnetic oscillations in the magnetization at small fields.     

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 nodal line semimetals

We review the recent,mainly theoretical,progress in the study of topological nodal line semimetals in three dimensions.In these semimetals,the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone,and any perturbation that preserves a certain symmetry group(generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands.The nodal line(s) is hence topologically protected by the symmetry group,and can be associated with a topological invariant.In this review,(ⅰ) we enumerate the symmetry groups that may protect a topological nodal line;(ⅱ) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface,establishing a topological classification;(ⅲ) for certain classes,we review the proposals for the realization of these semimetals in real materials;(ⅳ) we discuss different scenarios that when the protecting symmetry is broken,how a topological nodal line semimetal becomes Weyl semimetals,Dirac semimetals,and other topological phases;and(ⅴ) we discuss the possible physical effects accessible to experimental probes in these materials.     

Lifshitz transitions via the type-II dirac and type-II Weyl points

The type-II Weyl and type-II Dirac points emerge in semimetals and in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. In one case, the type-II Weyl point connects the Fermi pockets, and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case, the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition, the Weyl point is released from both Fermi surfaces. They loose their Berry flux, which guarantees the global stability, and without the topological support, the inner surface disappears after shrinking to a point at the second Lifshitz transition. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds.     

Topological transport in Dirac electronic systems:A concise review

Various novel physical properties have emerged in Dirac electronic systems, especially the topological characters protected by symmetry. Current studies on these systems have been greatly promoted by the intuitive concepts of Berry phase and Berry curvature, which provide precise definitions of the topological phases. In this topical review, transport properties of topological insulator(Bi2Se3), topological Dirac semimetal(Cd3As2), and topological insulator-graphene heterojunction are presented and discussed. Perspectives about transport properties of two-dimensional topological nontrivial systems,including topological edge transport, topological valley transport, and topological Weyl semimetals, are provided.     

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。     

Electronic states with nontrivial topology in Dirac materials

The theoretical studies of phase states with a linear dispersion of the spectrum of low-energy electron excitations have been reviewed. Some main properties and methods of experimental study of these states in socalled Dirac materials have been discussed in detail. The results of modern studies of symmetry-protected electronic states with nontrivial topology have been reported. Combination of approaches based on geometry with homotopic topology methods and results of condensed matter physics makes it possible to clarify new features of topological insulators, as well as Dirac and Weyl semimetals.     

拓扑材料中的超导

近来,人们在凝聚态体系中发现了由拓扑不变量定义的物相,其中最重要的有拓扑绝缘体、拓扑半金属和拓扑超导体等.这些物相的拓扑性质由非平凡的拓扑数描述,相应的材料被称为拓扑材料,具有诸多新奇的物理特性.其中拓扑超导体由于边界上有满足非阿贝尔统计的Majorana零能模,成为实现拓扑量子计算的主要候选材料.除了探索本征的拓扑超导体外,由于拓扑性质上的相似性,在不超导的拓扑材料中调制出超导自然成为了实现拓扑超导的重要手段.目前,人们发展了栅极调制、掺杂、高压、近邻效应调制和硬针尖点接触等多种技术,已经成功地在许多拓扑绝缘体和半金属中诱导出了超导,并对超导的拓扑性和Majorana零能模进行了研究.本文回顾了本征拓扑超导候选材料,以及拓扑绝缘体和半金属中诱导出超导的代表性工作,评述了不同实验手段的优势和缺陷、分析了其超导拓扑性的证据,并提出展望.     

Competition between weak localization and antilocalization in topological surface states

A magnetoconductivity formula is presented for the surface states of a magnetically doped topological insulator. It reveals a competing effect of weak localization and weak antilocalization in quantum transport when an energy gap is opened at the Dirac point by magnetic doping. It is found that, while random magnetic scattering always drives the system from the symplectic to the unitary class, the gap could induce a crossover from weak antilocalization to weak localization, tunable by the Fermi energy or the gap. This crossover presents a unique feature characterizing the surface states of a topological insulator with the gap opened at the Dirac point in the quantum diffusion regime.     

Electron transport in Dirac and Weyl semimetals

Recently, the Dirac and Weyl semimetals have attracted extensive attention in condensed matter physics due to both the fundamental interest and the potential application of a new generation of electronic devices. Here we review the exotic electrical transport phenomena in Dirac andWeyl semimetals. Section 1 is a brief introduction to the topological semimetals(TSMs). In Section 2 and Section 3, the intriguing transport phenomena in Dirac semimetals(DSMs) andWeyl semimetals(WSMs) are reviewed, respectively. The most widely studied Cd_3A_(s2) and the TaAs family are selected as representatives to show the typical properties of DSMs and WSMs, respectively. Beyond these systems, the advances in other TSM materials,such as ZrTe_5 and the MoTe_2 family, are also introduced. In Section 4, we provide perspectives on the study of TSMs especially on the magnetotransport investigations.     

Transport properties of topological insulators films and nanowires

The last several years have witnessed the rapid developments in the study and understanding of topological insulators. In this review, after a brief summary of the history of topological insulators, we focus on the recent progress made in transport experiments on topological insulator films and nanowires. Some quantum phenomena, including the weak antilocalization, the Aharonov-Bobm effect, and the Shubnikov-de Haas oscillations, observed in these nanostructures are described. In addition, the electronic transport evidence of the superconducting proximity effect as well as an anomalous resistance enhancement in topological insulator/superconductor hybrid structures is included.     

Predication of topological states in the allotropes of group-IV elements

Three-dimensional (3D) topological insulators (TIs) have been studied for approximately fifteen years, but those made from group-IV elements, especially Ge and Sn, seem particularly attractive owing to their nontoxicity, sizable intrinsic spin–orbit coupling (SOC) strength and natural compatibility with the current semiconductor industry. However, group-IV elemental TIs have rarely been reported, except for the low temperature phase of α-Sn under strain. Here, based on first-principles calculations, we propose new allotropes of Ge and Sn, named T5-Ge/Sn, as desirable TIs. These new allotropes are also highly anisotropic Dirac semimetals if the SOC is turned off. To the best of our knowledge, T5-Ge/Sn are the first 3D allotropes of Ge/Sn that possess topological states in their equilibrium states at room temperature. Additionally, their isostructures of C and Si are metastable indirect and direct semiconductors. Our work not only reveals two promising TIs, but more profoundly, we justify the advantages of group-IV elements as topological quantum materials (TQMs) for fundamental research and potential practical applications, and thus reveal a new direction in the search for desirable TQMs.