铁基超导涡旋演生马约拉纳零能模

作为马约拉纳零能模(MZM)的一种全新载体,具有拓扑能带结构的铁基超导块材——拓扑铁基超导体——近年来引起了学术界的广泛关注.由于同时具备单一材料、高温超导、强电子关联、拓扑能带等特质,拓扑铁基超导体成功规避了本征拓扑超导体和近邻异质结体系在实现MZM上的困难,为马约拉纳物理开辟了自赋性拓扑超导的新方向.时至今日,人们已经在多种拓扑铁基超导体的磁通涡旋中测量到了纯净的MZM.实验发现,铁基超导体系中演生的涡旋MZM信号明确、物理清晰,具有很好的应用前景.拓扑铁基超导体有望成长为研究马约拉纳物理和制备拓扑量子比特最重要的材料体系之一.本文以Fe(Te,Se)为主要对象详细介绍了铁基超导马约拉纳载体的思想起源和研究进展.在阐明Fe(Te,Se)拓扑能带结构和零能涡旋束缚态基本实验事实的基础上,本文将逻辑清晰地系统总结铁基超导涡旋演生MZM的主要实验观测和基本物理行为;借助波函数、准粒子中毒等实验,解析Fe(Te,Se)单晶中的涡旋MZM演生机制;结合现有马约拉纳理论,深入探讨铁基超导体中的马约拉纳对称性和准粒子拓扑本质的实验测量.最后,本文采用"从量子物理到量子工程"的视角,综合分析涡旋MZM在真实材料和实际实验中的鲁棒性,为未来潜在的工程应用提供有益指导.本文以物理原理为线,注重理论与实验结合,旨在搭建经典马约拉纳理论与新兴拓扑铁基超导体系之间的桥梁,帮助读者理解铁基超导涡旋中演生的MZM.     

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.     

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.     

封面故事

铁基超导体与拓扑绝缘体是当前凝聚态物理研究的热点。铁基超导体是非常规超导体,不同于传统的电声耦合机制的BCS超导体,其超导配对机制的解释仍然是凝聚态物理理论的一个难点。在拓扑绝缘体这类材料中,由于能带的反转,体态仍然保持绝缘态,但是在表面或者边界上存在着导电的金属态。超导体与拓扑绝缘体的结合被认为是实现拓扑超导体和Majorana费米子的一个非常有希望     

基于Yu-Shiba-Rusinov态的拓扑超导理论

Yu-Shiba-Rusinov态是由磁性杂质原子在超导体中诱导出的超导能隙内的束缚态.它们可以作为构造拓扑超导态的基本单元.本文阐述了基于Yu-Shiba-Rusinov态的不同维度拓扑超导的统一理论框架,并通过简单的特例加以解释.这里的理论是理解多个相关实验的基础.     

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。     

拓扑超导Majorana束缚态的探索

Majorana束缚态具有非阿贝尔量子统计特性,是极具潜力的拓扑量子计算方案的核心.近期有多项实验研究提供了Majorana束缚态在某些超导体系中的存在证据,使其成为近期凝聚态物理以及量子计算领域的前沿焦点之一.本文介绍拓扑超导的机理、Majorana束缚态的新奇物理特性、实验观测和操作的方法以及相关量子器件的设计,最后展望该研究方向的发展前景.     

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.     

从高质量半导体/超导体纳米线到马约拉纳零能模

作为马约拉纳费米子的“凝聚态版本”,马约拉纳零能模是当前凝聚态物理领域的研究热点.马约拉纳零能模满足非阿贝尔统计,可以构建受拓扑保护的量子比特.这种由空间上分离的马约拉纳零能模构建的拓扑量子比特不易受局域噪声的干扰,具有长的退相干时间,在容错量子计算中具有重要的应用前景.半导体/超导体纳米线是研究马约拉纳零能模和拓扑量子计算的理想实验平台.本文综述了高质量半导体纳米线外延生长、半导体/超导体异质结制备以及相应的马约拉纳零能模研究方面的进展,并对半导体/超导体纳米线在量子计算中的应用前景进行了展望.     

铁基超导中拓扑量子态研究进展

铁基超导体和拓扑量子材料是近年来凝聚态物理两个重要的前沿研究方向.铁基超导体中是否能衍生出非平庸的拓扑现象是一个非常有意义的问题.本文从晶体对称性、布里渊区高对称点附近的有效模型以及自旋轨道耦合相互作用三个方面具体分析了铁基超导的电子结构的基本特点.在此基础上,重点阐述铁基超导的正常态、临近超导的长程有序态以及超导态中非平庸的拓扑量子态是如何衍生的;具体介绍了相关的理论模型以及结果,回顾了相关的实验进展,展望了该领域的发展前景.     

Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor(Li_(0.84)Fe_(0.16))OHFeSe

The Major ana zero mode(MZM), which manifests as an exotic neutral excitation in superconductors, is the building block of topological quantum computing. It has recently been found in the vortices of several iron-based superconductors as a zero-bias conductance peak in tunneling spectroscopy. In particular, a clean and robust MZM has been observed in the cores of free vortices in(Li_(0.84)Fe_(0.16))OHFeSe. Here using scanning tunneling spectroscopy, we demonstrate that Major ana-induced resonant Andreev reflection occurs between the STM tip and this zero-bias bound state,and consequently, the conductance at zero bias is quantized as 2e~2/h. Our results present a hallmark signature of the MZM in the vortex of an intrinsic topological superconductor, together with its intriguing behavior.     

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.     

Observing Majorana bound states in p-wave superconductors using noise measurements in tunneling experiments

The zero-energy bound states at the edges or vortex cores of chiral p-wave superconductors should behave like Majorana fermions. We introduce a model Hamiltonian that describes the tunneling process when electrons are injected into such states. Using a nonequilibrium Green function formalism, we find exact analytic expressions for the tunneling current and noise and identify experimental signatures of the Majorana nature of the bound states to be found in the shot noise. We discuss the results in the context of different candidate materials that support triplet superconductivity. Experimental verification of the Majorana character of midgap states would have important implications for the prospects of topological quantum computation.     

Quantum computation using vortices and majorana zero modes of a px + ipy superfluid of fermionic cold atoms

We propose to use the recently predicted two-dimensional "weak-pairing" px + ipy superfluid state of fermionic cold atoms as a platform for topological quantum computation. In the core of a vortex, this state supports a zero-energy Majorana mode, which moves to finite energy in the corresponding topologically trivial "strong-pairing" state. By braiding vortices in the "weak-pairing" state, unitary quantum gates can be applied to the Hilbert space of Majorana zero modes. For readout of the topological qubits, we propose realistic schemes suitable for atomic superfluids.     

FeSe基超导体的探索与物性研究

自从2008年铁基超导体发现以来,人们探索并发现了一系列的铁基高温超导材料,其中FeSe基超导体因其具有的独特性质而引起了人们的广泛关注.本文主要介绍了两类新的铁基超导体,即水热合成法合成的（Li,Fe）OHFeSe及电化学插层方法合成的（CTA）_xFeSe的晶体结构及超导性质;对近年发展起来的利用电双层场效应晶体管技术以及固态离子导体调控FeSe的电子态性质的研究做了简要介绍.     

Majorana modes at the ends of superconductor vortices in doped topological insulators

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.     

Probability distribution of Majorana end-state energies in disordered wires

One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy ε(0) that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of ε(0) is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level ε(1) has an algebraic tail at small ε(1). Our findings have implications for the speed at which a topological quantum computer can be operated.     

FeSe基超导单晶与薄膜研究新进展:自旋向列序、电子相分离及高临界参数

FeSe基超导体的超导临界温度可大范围调控,物理现象丰富,是非常规超导机理研究的热点.由于较高的超导临界参数及易于加工等特点,FeSe基超导体在超导应用开发方面也日益受到重视.大尺寸高质量的单晶和薄膜形态的FeSe基超导材料,对于相关基础科学研究和应用开发都极为重要.作者近年来先后开发和发明了水热离子交换（ion-exchange）、离子脱插（ion-deintercalation）、基底辅助水热外延生长方法,成功解决了二元FeSe和插层（Li,Fe）OHFeSe超导体高质量单晶和薄膜的生长和物性调控难题.进而在相关物理问题的研究中取得新进展,包括发现二元FeSe中自旋向列序与超导电性密切相关,观测到（Li,Fe）OHFeSe中的电子相分离现象.此外,（Li,Fe）OHFeSe超导薄膜呈现很高的超导临界电流密度和上临界磁场,其应用前景值得关注.     

A brief review on Majorana bound states in topological superconductors

Topological superconductivity has drawn much attention recently, and most interests are focused on the Majorana bound states existing at the edges of one-dimensional topological superconductors. These Majorana bound states are ideal platform for studying non-Abelian statistics. Meanwhile, they are proposed to be useful in quantum computation. In this review, we introduce the basic concepts and models in this area. We begin from the Kitaev model, which is the most concise model for one-dimensional topological superconductivity. Then, we discuss how to realize this model with spin-orbit coupling in realistic materials. Finally, we show some simple methods to detect the Majorana bound states and study their novel properties with the help of adjacent quantum dots.     

Evolution of edge states and critical phenomena in the Rashba superconductor with magnetization

We study Andreev bound states (ABS) and the resulting charge transport of a Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures are sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode in the topological phase (TP). We clarify two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether or not ABS exists at QCP. In the former type, ABS has an energy gap and does not cross at zero energy in the nontopological phase. These complex properties can be detected by tunneling conductance between normal metal-RSC junctions.