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 photonic states in artificial microstructures[Invited]

Topological photonics provides a new opportunity for the examination of novel topological properties of matter, in which the energy band theory and ideas in topology are utilized to manipulate the propagation of photons. Since the discovery of topological insulators in condensed matter, researchers have studied similar topological effects in photonics.Topological photonics can lead to materials that support the robust unidirectional propagation of light without back reflections. This ideal transport property is unprecedented in traditional optics and may lead to radical changes in integrated optical devices. In this review, we present the exciting developments of topological photonics and focus on several prominent milestones of topological phases in photonics, such as topological insulators, topological semimetals, and higher-order topological phases. We conclude with the prospect of novel topological effects and their applications in topological photonics.     

Atomic-Ordering-Induced Quantum Phase Transition between Topological Crystalline Insulator and Z_2 Topological Insulator

Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, and the transition may also occur between different classes of topological Dirac phases.It is a fundamental challenge to realize quantum transition between Z_2 nontrivial topological insulator(TI) and topological crystalline insulator(TCI) in one material because Z_2 TI and TCI have different requirements on the number of band inversions. The Z_2 TIs must have an odd number of band inversions over all the time-reversal invariant momenta, whereas the newly discovered TCIs, as a distinct class of the topological Dirac materials protected by the underlying crystalline symmetry, owns an even number of band inversions. Taking PbSnTe_2 alloy as an example, here we demonstrate that the atomic-ordering is an effective way to tune the symmetry of the alloy so that we can electrically switch between TCI phase and Z_2 TI phase in a single material. Our results suggest that the atomic-ordering provides a new platform towards the realization of reversibly switching between different topological phases to explore novel applications.     

Topology of triple-point metals

We discuss and illustrate the appearance of topological fermions and bosons in triple-point metals where a band crossing of three electronic bands occurs close to the Fermi level.Topological bosons appear in the phonon spectrum of certain triple-point metals, depending on the mass of atoms that form the binary triple-point metal.We first provide a classification of possible triple-point electronic topological phases possible in crystalline compounds and discuss the consequences of these topological phases, seen in Fermi arcs, topological Lifshitz transitions, and transport anomalies.Then we show how the topological phase of phonon modes can be extracted and proven for relevant compounds.Finally,we show how the interplay of electronic and phononic topologies in triple-point metals puts these metallic materials into the list of the most efficient metallic thermoelectrics known to date.     

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.     

Layer construction of topological crystalline insulator LaSbTe

Topological crystalline insulator(TCI) is one of the symmetry-protected topological states. Any TCI can be deformed into a simple product state of several decoupled two-dimensional(2 D) topologically nontrivial layers in its lattice respecting its crystalline symmetries called the layer construction(LC) limit. In this work, based on first-principles calculations we have revealed that both tetragonal LaSbTe(t-LaSbTe) and orthorhombic LaSbTe(o-LaSbTe) can be interpreted as stacking of 2 D topological insulators in each lattice space. The structural phase transition from t-LaSbTe to o-LaSbTe due to soft phonon modes demonstrates how the real space change can lead to the modification of topological states. Their symmetry-based indicators and topological invariants have been analyzed based on LC. We propose that LaSbTe is an ideal example demonstrating the LC paradigm, which bridges the crystal structures in real space to the band topology in momentum space.     

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.     

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 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.     

Accuracy of topological analysis of gridded electron densities

Topological analysis of electron densities sampled on 3D grids have been performed on two different crystalline compounds—ammonium dihydrogen phosphate and urea—using the software package InteGriTy and the results are compared to that of analytical derivation from the software Newprop and TOPOND. Both critical points and integrated quantities are considered with emphasis put on bond critical points and atomic charges.     

Experimental preparation of topologically ordered states via adiabatic evolution

Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological orders can arise in two-dimensional spin-lattice models. In this paper, we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution. The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators. Each sector is highly entangled, as shown from the completely reconstructed density matrices. This paves the way towards exploring the properties of topological orders and the application of topological orders in topological quantum memory.     

Transport properties of doped Bi_2Se_3 and Bi_2Te_3 topological insulators and heterostructures

In this review article, the recent experimental and theoretical research progress in Bi_2Se_3-and Bi_2Te_3-based topological insulators is presented, with a focus on the transport properties and modulation of the transport properties by doping with nonmagnetic and magnetic elements. The electrical transport properties are discussed for a few different types of topological insulator heterostructures, such as heterostructures formed by Bi_2Se_3-and Bi_2Te_3-based binary/ternary/quaternary compounds and superconductors, nonmagnetic and magnetic metals, or semiconductors.     

Weak Anti-Localization and Quantum Oscillations in Topological Crystalline Insulator PbTe

Topological crystalline insulators(TCIs) have attracted worldwide interest since their theoretical predication and have created exciting opportunities for studying topological quantum physics and for exploring spintronic applications. In this work, we successfully synthesize PbTe nanowires via the chemical vapor deposition method and demonstrate the existence of topological surface states by their 2D weak anti-localization effect and Shubnikov-de Haas oscillations. More importantly,the surface state contributes ~61% of the total conduction,suggesting dominant surface transport in PbTe nanowires at low temperatures. Our work provides an experimental groundwork for researching TCIs and is a step forward for the applications of PbTe nanowires in spintronic devices.     

Topological modes in radiofrequency resonator arrays

Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an experimental and accompanying numerical toolbox to create and analyze topological states in radiofrequency resonator arrays including non-local coupling. These arrays are very easily constructed, offer a variety of geometric configurations, and their eigenfunctions and eigenvalues are amenable to detailed analysis. They offer well defined analogs to coupled oscillator systems in general in that they are characterized by resonances whose frequency spectra depend on the individual resonators, their interactions, and boundary conditions. A comparison of a small one-dimensional experimental system with theory by means of easy to measure S-parameters shows excellent agreement. The numerical toolbox allows for simulations of arbitrarily large systems, revealing an astonishing richness of band structures under systematic parameter variation.     

Structure and magnetic properties of layers formed by laser fusing of powders on nonmagnetic substrates

Studies of the structure and magnetic properties of layers formed on nonmagnetic substrates by laser powder fusing (LPF) showed that crystalline phases are separated from initial powders of bronze, inconel (IN 625), and PGSR-4with the transformation of nonmagnetic materials to soft ferromagnets. The fused bronze powder layer exhibits soft ferromagnetic properties with two types of magnetic domains with the Curie temperatures of 80 and 300 K and a coercivity to 90 Oe at 300 K; in layers based on In625 and PGSR-4, only one type of magnetic domains with the Curie temperatures of 260–270 K is formed, which provides soft ferromagnetic properties at 4 К and the paramagnetic transition at 300 K.     

XAuBi (X=Eu, Ba)拓扑nodal chain半金属的第一性原理研究

由于在磁性材料体系中缺失时间反演对称性,导致nodal chain被破坏,所以nodal chain通常存在于非磁材料中。但是,磁性材料EuAuBi是与常规磁性材料不同。本工作以第一性原理计算为研究方法,预言了在不考虑自旋轨道相互作用时,磁性材料EuAuBi体系为新型拓扑nodal chain半金属;当考虑自旋轨道耦合时,EuAuBi会退化为外尔半金属。对于非磁材料BaAuBi来说,在不考虑自旋轨道相互作用时,它同样是一种拓扑nodal chain半金属;当考虑自旋轨道相互作用时,由于C3旋转对称性的存在,BaAuBi会退化为狄拉克半金属。在XAuBi (X=Eu, Ba)中发现nodal chain半金属,会促进对六角材料的拓扑性质研究以及开拓其新实际应用领域。     

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.     

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.     

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。     

拓扑绝缘体/超导体异质结中的近邻效应

拓扑超导体自身具有对量子退相干天然的免疫性以及可编织性,这使得它在现代量子计算领域中受到了越来越多的重视,并且成为了下一代计算技术中最有希望的候选者之一。由于拓扑超导态在固有拓扑超导体中相当罕见,因此,当前大部分实验上的工作主要集中在由 s 波超导体与拓扑绝缘体之间通过近邻效应所诱导的拓扑超导体上。本论文中,我们回顾了基于拓扑绝缘体/超导体异质结的拓扑超导体的研究进展。在理论上,Fu 和 Kane 提出,通过近邻效应将 s 波超导体的能隙引入到拓扑绝缘体,可以诱导出拓扑超导电性。在实验上,我们也回顾了一些不同体系中的拓扑超导近邻效应的研究进展。文章的第一部分,我们介绍了一些异质结,包括：三维拓扑绝缘体 Bi2Se3和 Bi2Se3 与 s 波超导体NbSe2 以及 d 波超导体 Bi2Sr2CaCu2O8+δ 的异质结,拓扑绝缘体 Sn1−xPbxTe 与 Pb 的异质结,二维拓扑绝缘体 WTe2 与NbSe2 的异质结。此外,还介绍了 TiBiSe2 在 Pb 上的拓扑绝缘近邻效应。另一部分中,我们对基于拓扑绝缘体的约瑟夫森结进行了回顾,包括著名的基于 Fu-Kane 体系的拓扑绝缘体约瑟夫森结,以及基于约瑟夫森结的超导量子干涉器件。