手征马约拉纳费米子

手征马约拉纳费米子是具有手性的无质量费米子,是其本身的反粒子,只能存在于1+1维(即1维空间+1维时间)或者9+1维.在凝聚态物理中, 1维手征马约拉纳费米子可看成1/2分数化的狄拉克费米子,并作为二维拓扑态的边缘元激发.奇数个手征马约拉纳费米子边缘态的存在也预示着体系中存在满足非阿贝尔量子统计的伊辛任意子.手征马约拉纳费米子也可进行非阿贝尔编织,理论上可用来实现容错量子计算,因此近年来在凝聚态物理研究中引起了广泛的兴趣.本文从二维拓扑态出发,介绍手征拓扑超导态和量子反常霍尔态之间的深刻联系,并由此得出量子反常霍尔平台转变与超导近邻实现手征马约拉纳费米子的方案,最后以单通道手征马约拉纳费米子为例,探讨其实现电子态的非阿贝尓量子门.     

重费米子材料与物理

作为典型的强关联电子体系,重费米子材料表现出丰富的量子基态,如反铁磁序、铁磁序、非常规超导、非费米液体、自旋液体、轨道序和拓扑态等.相比其他强关联电子体系,重费米子体系的特征能量尺度低,可以通过压力、磁场或掺杂等参量对不同量子态进行连续调控,因而是研究量子相变、超导及其相互作用的理想体系.本文简要介绍重费米子研究的发展历史和国内外研究现状,概述几类典型的重费米子材料,并简单阐述重费米子超导、量子相变和强关联拓扑态等前沿科学问题.     

Majorana费米子与拓扑量子计算

1937年,Majorana发现Dirac所提出的相对论性协变的电子波动方程,在另一个表象下所得到解可以描述不带电荷的费米子,具有与Dirac费米子不同的性质。在基本粒子领域,对这种Majorana费米子的寻找至今一直在进行中;而在凝聚态物理领域,对拓扑超导体和分数量子霍尔态的研究,人们已经发现了与Majorana费米子有相同行为的准粒子。特别是在二维拓扑超导体系中出现的涡旋元激发包含了零能量的Majorana准粒子,它们在交换操作下表现出非阿贝尔的统计性质,因而有望借以实现拓扑量子计算。文章系统地介绍了凝聚态物质系统中获得Majorana费米子的理论模型和物理实现,并进一步介绍了与之相关的拓扑量子计算的实现方法。     

周期场驱动下量子材料的非平衡物态

量子材料的拓扑物态的研究是当前凝聚态物理的重要前沿.区别于局域对称性破缺对物质状态进行分类的传统方式,量子物态可以用微观体系波函数的拓扑结构进行分类.这些全新的拓扑物态有望颠覆传统的微电子学并进而推动拓扑电子学的迅猛发展.当前大部分理论和实验研究集中于研究量子材料的平衡态性质.周期性光场驱动下量子材料远离平衡态、而达到非平衡态时的拓扑物态近年来受到人们的广泛关注.本文首先回顾周期场驱动下非平衡态的弗洛凯(Floquet)理论方法,分别介绍无质量(如石墨烯)、有质量(如MoS_2)等狄拉克费米子材料体系在远离平衡态下的拓扑物态,利用光场与量子物态的相干耦合实现对量子材料非平衡物态的调控;从原子制造角度出发,光场诱导的相干声子态直接改变了量子材料中电子跃迁的大小,进而调控量子材料的非平衡拓扑物态.量子材料中丰富的声子态为非平衡拓扑物态的调控提供了更多的可能性.最后,文章展望了量子材料非平衡拓扑物态在超快相变以及瞬态物态调节等未来可能发展方向的应用.     

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.     

具有全局对称性的强关联拓扑物态的规范场论

在有对称性保护的条件下,拓扑能带绝缘体等自由费米子体系的拓扑不变量可以在能带结构计算中得到.但是,为了得到强关联拓扑物质态的拓扑不变量,我们需要全新的理论思路.最典型的例子就是分数量子霍尔效应:其低能有效物理一般可以用Chern-Simons拓扑规范场论来计算得到;霍尔电导的量子化平台蕴含着十分丰富的强关联物理.本文将讨论存在于玻色和自旋模型中的三大类强关联拓扑物质态:本征拓扑序、对称保护拓扑态和对称富化拓扑态.第一类无需考虑对称性,后两者需要考虑对称性.理论上,规范场论是一种非常有效的研究方法.本文将简要回顾用规范场论来研究强关联拓扑物质态的一些研究进展.具体内容集中在"投影构造理论"、"低能有效理论"、"拓扑响应理论"三个方面.     

在人工拓扑超导体磁通涡旋中寻找Majorana零能模

寻找具有拓扑序的新物质态是目前一个非常活跃和令人激动的研究领域.与拓扑绝缘体类似,在超导体中也存在着拓扑非平庸的超导态,它与传统的超导体在拓扑性上是不等价的,这种具有非平庸拓扑序的超导体被称为拓扑超导体.拓扑超导体在体内具有非零的超导能隙,而在表面有无能隙的表面态.理论预言在拓扑超导体中能够实现具有非Abelian统计特性的Majorana费米子. Majorana费米子可以用来构建拓扑量子比特,在拓扑量子计算方面有重大的科研和应用前景.拓扑绝缘体的出现催生出了许多人工拓扑超导体材料.本专题将主要介绍在拓扑绝缘体/超导体异质结中探测Majorana费米子的一系列实验工作.通过对拓扑超导体的研究,人们对超导电性有了全新的认识,有可能找到实现Majorana费米子新奇量子物理性质的方法.     

人工带隙材料的拓扑性质

近年来,人工带隙材料(如声子晶体和光子晶体)由于其优异的性能,已成为新一代智能材料的研究焦点.另一方面,材料拓扑学由凝聚态物理领域逐渐延伸到其他粒子或准粒子系统,而研究人工带隙材料的拓扑性质更是受到人们的广泛关注,其特有的鲁棒边界态,具有缺陷免疫、背散射抑制和自旋轨道锁定的传输等特性,潜在应用前景巨大.本文简要介绍拓扑材料特有的鲁棒边界态的物理图像及其物理意义,并列举诸如光/声量子霍尔效应、量子自旋霍尔效应、Floquet拓扑绝缘体等相关工作;利用Dirac方程,从原理上分析光/声拓扑性质的由来;最后对相关领域的发展方向和应用前景进行了相应的讨论.     

拓扑半金属-超导体异质结的约瑟夫森效应

拓扑半金属是一类受对称性保护的无能隙量子材料.因其相对论性能带色散关系,拓扑半金属中涌现出丰富的量子态和量子效应,例如费米弧表面态和手征反常.近年来,因在拓扑量子计算的潜在应用,拓扑与超导的耦合体系受到广泛关注.本文从两方面回顾拓扑半金属-超导体异质结体系近年来的实验进展:1)超导电流对拓扑量子态的模式过滤; 2)拓扑超导和Majorana零能模的探测与调控.对于前者,利用约瑟夫森电流对电磁场的响应,拓扑半金属中费米弧表面态的弹道输运被揭示,高阶拓扑半金属相被证实,有限动量配对及超导二极管效应被实现.对于后者,通过交流约瑟夫森效应,狄拉克半金属中4π周期的拓扑超导态被发现,纯电学栅压调控的拓扑相变被实现.本文最后展望了拓扑半金属-超导体异质结体系的发展前景和在Majorana零能模编织和拓扑量子计算上的潜在应用.     

磁光光子晶体中拓扑光子态研究进展

拓扑光子态是具有单向传输特性的新型波导态,展示出抗背向散射、障碍物及缺陷免疫等独特而神奇的物理性质。拓扑光子态因其独特性在拓扑激光器、量子信息、混合集成光路、非线性光学等领域具有广泛的潜在应用。磁光光子晶体为实现拓扑光子态、探索拓扑光子态新物性提供了重要平台。本文聚焦磁光光子晶体中拓扑光子态的研究进展,首先回顾有序、无序晶格中的拓扑光子态,揭示拓扑光子态的微观物理图像。接着讨论时间和空间反演对称性双破缺体系中的拓扑光子态,简述反手性拓扑光子态的产生。然后介绍宽带拓扑光子态及拓扑慢光态研究,展示新颖的拓扑光学现象及器件设计。最后针对磁光光子晶体中拓扑光子态研究面临的关键问题、未来发展趋势进行分析和展望。     

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 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.     

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.     

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。     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Tunable topological quantum states in three- and two-dimensional materials

We review our theoretical advances in tunable topological quantum states in three- and twodimensional materials with strong spin–orbital couplings. In three-dimensional systems, we propose a new tunable topological insulator, bismuth-based skutterudites in which topological insulating states can be induced by external strains. The orbitals involved in the topological band-inversion process are the d- and p-orbitals, unlike typical topological insulators such as Bi₂Se₃and BiTeI, where only the p-orbitals are involved in the band-inversion process. Owing to the presence of large d-electronic states, the electronic interaction in our proposed topological insulator is much stronger than that in other conventional topological insulators. In two-dimensional systems, we investigated 3d-transition-metal-doped silicene. Using both an analytical model and first-principles Wannier interpolation, we demonstrate that silicene decorated with certain 3d transition metals such as vanadium can sustain a stable quantum anomalous Hall effect. We also predict that the quantum valley Hall effect and electrically tunable topological states could be realized in certain transition-metal-doped silicenes where the energy band inversion occurs. These findings provide realistic materials in which topological states could be arbitrarily controlled.     

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.     

超构材料中的光学量子自旋霍尔效应

电子的量子自旋霍尔效应的发现推进了当今凝聚态物理学的发展,它是一种电子自旋依赖的具有量子行为的输运效应.近年来,大量的理论和实验研究表明,描述电磁波场运动规律的麦克斯韦方程组内禀了光的量子自旋霍尔效应,存在于界面的倏逝波表现出强烈的自旋与动量关联性.得益于新兴的光学材料:超构材料(metamaterials)的发展,不仅能够任意设定光学参数,同时也能引入很多复杂的自旋-轨道耦合机理,让我们能够更加清晰地了解和验证其中的物理机理.本文对超构材料中量子自旋霍尔效应做了简要的介绍,内容主要包括真空中光的量子自旋霍尔效应的物理本质、电单负和磁单负超构材料能带反转导致的不同拓扑相的界面态、拓扑电路系统中光量子自旋霍尔效应等.     

Quantum anomalous Hall effect in real materials

Under a strong magnetic field,the quantum Hall(QH) effect can be observed in two-dimensional electronic gas systems.If the quantized Hall conductivity is acquired in a system without the need of an external magnetic field,then it will give rise to a new quantum state,the quantum anomalous Hall(QAH) state.The QAH state is a novel quantum state that is insulating in the bulk but exhibits unique conducting edge states topologically protected from backscattering and holds great potential for applications in low-power-consumption electronics.The realization of the QAH effect in real materials is of great significance.In this paper,we systematically review the theoretical proposals that have been brought forward to realize the QAH effect in various real material systems or structures,including magnetically doped topological insulators,graphene-based systems,silicene-based systems,two-dimensional organometallic frameworks,quantum wells,and functionalized Sb(111) monolayers,etc.Our paper can help our readers to quickly grasp the recent developments in this field.     

二维拓扑绝缘体退相干效应研究

拓扑绝缘体是当前凝聚态物理研究的热点.退相干效应对该体系的影响的研究不仅有重要的理论意义,而且也是实现未来量子器件的不可或缺的前期工作.文章作者从理论上研究了退相干对二维拓扑绝缘体特别是量子自旋霍尔效应的影响.研究结果表明,作为量子自旋霍尔效应的标志的量子化纵向电阻平台对不破坏自旋记忆的退相干效应(普通退相干)不敏感,但却对破坏自旋记忆的退相干效应(自旋退相干)非常敏感.因此,该量子化平台只能在尺寸小于自旋退相干长度的介观样品中存在,从而解释了量子自旋霍尔效应实验中所观测到的结果(见Science,2007,318:766).同时,文章作者还定义了一个新的物理量,即自旋霍尔电阻,并发现该自旋霍尔电阻也有量子化平台.特别是该量子化平台对两种类型的退相干都不敏感.这说明在宏观样品中也能观测到自旋霍尔电阻的量子化平台,因此更能全面地反映量子自旋霍尔效应的拓扑特性.