SPECIAL TOPIC—Majorana in condensed matter
年轻的意大利理论物理学家马约拉纳在 1937 年研究狄拉克方程时, 发现了一种奇异的粒子,其反粒子即其粒子本身. 这种奇异粒子被后人称为马约拉纳粒子. 在已知的基本粒子世界, 除了中微子, 都不是马约拉纳粒子 (Majorana), 而中微子是否是马约拉纳粒子尚待实验检测. 最近以来, 探索马约拉纳粒子的热点转移到了凝聚态. 凝聚态体系由许多原子或电子、离子组成. 虽然构成体系的粒子本身不是马约拉纳粒子, 但其低能下演生的准粒子可以有全新的性质. 比如在 Kitaev 的一维超导链上, 一个电子可被分拆为束缚在链两端的两个马约拉纳粒子, 称为马约拉纳零能模. 又比如,张首晟和他合作者在理论上阐示的, 在一定条件下量子反常霍尔效应的狄拉克手征边界态可以一分为二, 实现在空间分离的两个手征马约拉纳粒子边界态. 凝聚态中发现马约拉纳粒子将对基础物理有极其重要的意义, 类比于在分数量子霍尔效应发现三分之一的电荷及任意子的统计. 马约拉纳零能模具有非阿贝尔统计, 可以构成拓扑量子比特. 手征马约拉纳粒子可以设计实现电子态的非阿贝尔量子门操作. 它们均可用于组建拓扑量子计算机, 其应用前景十分可观. 由于其在基础物理上的重大意义及在量子计算的可能应用, 马约拉纳粒子已成为凝聚态研究的前沿课题. 在实验方面, 目前在包括超导纳米线、一维原子链, 以及拓扑超导涡旋中都有观察到马约拉纳零能模的诸多证据.编织零能模显示非阿贝尔统计的实验尚待努力. 关于手征马约拉纳粒子的实验, 最初的观察报道至今尚未能重复, 争议较大. 我相信, 理论预的手征马约拉纳粒子会在合适的材料器件上发现. 分数量子霍尔效应中的任意子的分数统计自理论预言至最近的实验证实经历了三十几年, 凝聚态中马约拉纳粒子的研究仅刚刚开始.
应《物理学报》编辑部的邀请, 我和丁洪邀请了部分活跃在研究马约拉纳粒子第一线的中青年科学家, 组织了本期的专题. 胡晓与其合作者详细讨论了拓扑超导机理, 并介绍了各种体系马约拉纳零能模及其新奇性质; 刘雄军与其合作者综述了马约拉纳零能模的统计性质及其在量子计算中的应用; 孔令元和丁洪详细综述了铁基超导涡旋中观察到的马约拉纳零能模及其性质; Yu-ShibaRusinov 态是一维原子链中马约拉纳零能模的基础, 李牮讨论了基于 Yu-Shiba-Rusinov 态的拓扑超导的普遍理论; 王靖详细介绍了他与张首晟等合作者研究的基于量子反常霍尔效应的手征马约拉纳粒子以及设计的量子计算门; 另一位受邀撰文的李耀义和贾金锋综述了在人工拓扑超导体涡旋中寻找马约拉纳零能模 (文章已提前在《物理学报》2019 年第 13 期发表). 他们从不同的角度综述了与凝聚态中马约拉纳粒子有关的理论或实验, 反映了此领域的一些现状, 希望对读者了解此前沿课题有所帮助.
2020, 69 (11): 110301.
doi: 10.7498/aps.69.20200717
Abstract +
During the recent years, the iron-based superconductors with a topological band structure have attracted intensive attention from the science community as a new and promising platform for emerging Majorana zero modes in their vortex core. These topological iron-based superconductors possess all of the desirable properties, i.e. single material, high-Tc superconductivity, strong electron-electron correlation and topological band structure, thus successfully avoiding the difficulties suffered by previous Majorana platforms, such as intrinsic topological superconductors and multiple types of proximitized heterostructures. So far, one has observed pristine vortex Majorana zero modes in several different compounds of iron-based superconductors. The systematic studies performed on those systems show that the vortex Majorana zero modes are quite evident experimentally and very clear theoretically, leading to a bright future in applications. The vortex cores of iron-based superconductors can become one of the major candidates for exploring topological quantum computing in the future. In this review article, we will focus on Fe(Te, Se) single crystal, to introduce the original ideas and research progress of the new emerging “iron home” for Majorana zero modes. Having elabrated the basic band structures and the experimental facts of the observed vortex zero modes in Fe(Te, Se), we will systematically summarize the main observations and fundamental physics of vortex Majorana zero modes in Fe(Te, Se). First of all, with the help of the observed behavior of Majorana wavefunction and quasiparticle poisioning, we will analyze the emerging mechanism of vortex Majorana zero modes in Fe(Te, Se). Then we will elaborate the measurements on Majorana symmetry and topological nature of vortex Majorana zero modes, assisted by several existing Majorana theories. After that, we will switch our view angle from quantum physics to quantum engineering, and comprehensively analyze the fate of vortex Majorana zero modes in a real material under a real environment, which may benefit the potential engineering applications in the future. This review article follows the physical properties of vortex Majorana zero modes, and emphasizes the link between theories and experiments. Our goal is to bridge the gap between the classical Majorana theories and the new emerging Majorana platform in iron-based superconductors, and help the readers to understand the experimental observations of the newly discovered “iron home” for Majoranas.
2020, 69 (11): 110302.
doi: 10.7498/aps.69.20200812
Abstract +
Since their prediction as fundamental particles in 1937, Majorana fermions have drawn lots of interests in particle physics and dark matter. Their counterparts in condensed matter physics, Majorana zero-Modes (MZMs), have attracted remarkable attention in condensed matter for their potential in building a fault-tolerant quantum computer. Due to the relentless effort, lots of important progress has been made in Majorana physics in the past two decades, as introduced in several excellent review articles. This review focuses on the non-Abelian statistics of MZMs and their application to quantum computation. In the first section of this work, the theoretical progress in searching for MZM is briefly reviewed and the latest experimental progresses are summarized. We next introduce the basic concepts of non-Abelian statistics of MZMs and explain how they can be applied to quantum computation. We then discuss two key experiments to implementing quantum computers in the MZM platform: MZM braiding and MZM qubit readout. In this part, several representative proposals for the Majorana braiding and MZM qubit readout are elaborated. Finally, we introduce a latest concept, the symmetry-protected non-Abelian braiding of Majorana Kramers pairs in time-reversal invariant topological superconductors.
2020, 69 (11): 117302.
doi: 10.7498/aps.69.20200534
Abstract +
The chiral Majorana fermion, is a massless fermionic particle being its own antiparticle, which was predicted to live in (1+1)D (i.e. one-dimensional space plus one-dimensional time) or (9+1)D. In condensed matter physics, one-dimensional (1D) chiral Majorana fermion can be viewed as the 1/2 of the chiral Dirac fermion, which could arise as the quasiparticle edge state of a two-dimensional (2D) topological state of matter. The appearance of an odd number of 1D chiral Majorana fermions on the edge implies that there exist the non-Abelian defects in the bulk. The chiral Majorana fermion edge state can be used to realize the non-Abelian quantum gate operations on electron states. Starting with the topological states in 2D, we illustrate the general and intimate relation between chiral topological superconductor and quantum anomalous Hall insulator, which leads to the theoretical prediction of the chiral Majorana fermion from the quantum anomalous Hall plateau transition in proximity to a conventional s-wave superconductor. We show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes, and may be used for the topological quantum computation.
2020, 69 (11): 117401.
doi: 10.7498/aps.69.20200831
Abstract +
Yu-Shiba-Rusinov states are subgap bound states induced by magnetic impurity atoms in a superconductor. These states can be used as building blocks in constructing an effective topological superconductor. Here we formulate a unified theory of topological superconductivity in different dimensions based on Yu-Shiba-Rusinov states, and demonstrate its application with simple but illustrative examples. Such a theory underlies a number of recent experiments on the related platform.
2020, 69 (11): 117102.
doi: 10.7498/aps.69.20190959
Abstract +
Majorana bound states are considered useful for realizing topological quantum computation since they obey the non-Abelian quantum statistics. Recent experiments have provided evidences for their existence in some superconducting systems, triggering significant interests from scientists in the field of condensed matter physics and related materials science. In this article, we briefly review the basic concepts and recent developments in the study of Majorana bound states. We first discuss about the origin of the nontrivial topology in superconducting systems within the Bogoliubov-de Gennes mean-field scheme. Then we show the construction of Majorana quasiparticle excitations from an electronic state, and the realization of non-Abelian statistics based on position exchanges of the Majorana bound states hosted in superconductivity vortices. Afterwards we talk about specific one-dimensional and two-dimensional topological superconductors, and propose possible experimental methods for detecting Majorana bound states and operating the Majorana qubits. In particular, a quantum device for Majorana braiding without moving vortices is introduced. Finally, perspectives of the study on Majorana bound states are provided.
2019, 68 (13): 137401.
doi: 10.7498/aps.68.20181698
Abstract +
The search for new states that exhibit topological order is currently a very active and exciting area of research. Like a topological insulator, superconducting order can also exhibit topological order, which is different from that of a conventional superconductor. This superconductor is so-called " topological superconductor”, which has a full pairing gap in the bulk and gapless surface state. Majorana Fermions obey non-Abelian fractional statistics, and have been proposed to construct topological qubits, so there is a great prospect of scientific research and application in topological quantum computing. It is very interesting that Majorana Fermions are predicted to exist in topological superconductors. However, natural topological superconductor is very rare. Inspired by the realization of topological insulators, theoretical physicists have proposed that via the fabrication of the s-wave superconductor/topological insulator heterostructure, Majorana Fermions may exist in the superconducting topological insulator induced by proximate effect. Due to various kinds of topological insulators and conventional s-wave superconductors, heterostructures constructed by this method can greatly increase the variety of artificial topological superconductors. In this paper we review the experimental progress in the heterostructure composed of the Bi2Te3-type topological insulator and the conventional s-wave superconductor NbSe2. Using molecular beam epitaxy, atomically flat topological insulator film can be fabricated at the top of superconductor substrate. The spatial distribution of Majorana Fermions on the surface of topological insulator can be directly observed by in situ scanning tunneling microscopy/spectroscopy. In the center of a magnetic vortex, Majorana Fermions will appear as the Majorana zero mode, a zero-energy peak inside the superconducting gap. Although the energy gap between low energy quasiparticle excitation and the Majorana zero mode is very small, the evidences such as zero bias conductance anomaly, Y-shape splitting of zero-bias conductance, spin-selective Andreev reflection are self-consistent and reveal that the Majorana zero mode exists in the center of a magnetic vortex. These experiments have led to a new insight into superconductivity. It may open a door to probing the novel physics of Majorana fermions.
