Topological semimetals are quantum materials that are not only extremely interesting from a theoretical point of view but also have a great potential for technological applications in which superconducting, semiconducting and other semimetal behaviors are involved. Keywords: Quantum Materials, Macroscopic Quantum Phenomena, Topological Semimetals, Dirac Semimetals, Weyl Semimetals, Nodal-Line Semimetals, Antimony and Antimonides, Antimonene, Arsenides, Bismuthides, Boron, Borides, Borophene, Carbon and Carbides, Chalcogenides, Nitrides, Phosphorus, Phosphides, Silicides, Topological Metals, Topological States of Matter.
This thesis describes two topological phases of matter, the Weyl semimetal and the line node semimetal, that are related to but distinct from topological insulator phases. These new topological phases are semimetallic, having electronic energy bands that touch at discrete points or along a continuous curve in momentum space. These states are achieved by breaking time-reversal symmetry near a transition between an ordinary insulator and a topological insulator, using a model based on alternating layers of topological and ordinary insulators, which can be tuned close to the transition by choosing the thicknesses of the layers. The semimetallic phases are topologically protected, with corresponding topological surface states, but the protection is due to separation of the band-touching points in momentum space and discrete symmetries, rather than being protected by an energy gap as in topological insulators. The chiral surface states of the Weyl semimetal give it a non-zero Hall conductivity, while the surface states of the line node semimetal have a flat energy dispersion in the region bounded by the line node. Some transport properties are derived, with a particular emphasis on the behaviour of the conductivity as a function of the impurity concentrations and the temperature.
Spintronic 2D Materials: Fundamentals and Applications provides an overview of the fundamental theory of 2D electronic systems that includes a selection of the most intensively investigated 2D materials. The book tells the story of 2D spintronics in a systematic and comprehensive way, providing the growing community of spintronics researchers with a key reference. Part One addresses the fundamental theoretical aspects of 2D materials and spin transport, while Parts Two through Four explore 2D material systems, including graphene, topological insulators, and transition metal dichalcogenides. Each section discusses properties, key issues and recent developments. In addition, the material growth method (from lab to mass production), device fabrication and characterization techniques are included throughout the book. Discusses the fundamentals and applications of spintronics of 2D materials, such as graphene, topological insulators and transition metal dichalcogenides Includes an in-depth look at each materials system, from material growth, device fabrication and characterization techniques Presents the latest solutions on key challenges, such as the spin lifetime of 2D materials, spin-injection efficiency, the potential proximity effects, and much more
This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.
This book provides an introduction to topological matter with a focus on insulating bulk systems. A number of prerequisite concepts and tools are first laid out, including the notion of symmetry transformations, the band theory of semiconductors and aspects of electronic transport. The main part of the book discusses realistic models for both time-reversal-preserving and -violating topological insulators, as well as their characteristic responses to external perturbations. Special emphasis is given to the study of the anomalous electric, thermal, and thermoelectric transport properties, the theory of orbital magnetisation, and the polar Kerr effect. The topological models studied throughout this book become unified and generalised by means of the tenfold topological-classification framework and the respective systematic construction of topological invariants. This approach is further extended to topological superconductors and topological semimetals. This book covers a wide range of topics and aims at the transparent presentation of the technical aspects involved. For this purpose, homework problems are also provided in dedicated Hands-on sections. Given its structure and the required background level of the reader, this book is particularly recommended for graduate students or researchers who are new to the field.
This book covers basic and advanced aspects in the field of Topological Matter. The chapters are based on the lectures presented during the Topological Matter School 2017. It provides graduate level content introducing the basic concepts of the field, including an introductory session on group theory and topological classification of matter. Different topological phases such as Weyls semi-metals, Majoranas fermions and topological superconductivity are also covered. A review chapter on the major experimental achievements in the field is also provided. The book is suitable not only for master, graduate and young postdoctoral researchers, but also to senior scientists who want to acquaint themselves with the subject.
This new edition presents a unified description of these insulators from one to three dimensions based on the modified Dirac equation. It derives a series of solutions of the bound states near the boundary, and describes the current status of these solutions. Readers are introduced to topological invariants and their applications to a variety of systems from one-dimensional polyacetylene, to two-dimensional quantum spin Hall effect and p-wave superconductors, three-dimensional topological insulators and superconductors or superfluids, and topological Weyl semimetals, helping them to better understand this fascinating field. To reflect research advances in topological insulators, several parts of the book have been updated for the second edition, including: Spin-Triplet Superconductors, Superconductivity in Doped Topological Insulators, Detection of Majorana Fermions and so on. In particular, the book features a new chapter on Weyl semimetals, a topic that has attracted considerable attention and has already become a new hotpot of research in the community.
In this work we explore superconductivity and surface states in topological semimetals. We start from general overview of basic properties of topological semimetals. We review general concepts of Chern insulators, their surface states, and use it as a building block for construction of Weyl metals. We also construct double Weyl metals, which are protected both by topology and discrete rotational symmetry. In addition, we study Luttinger model of semimetals - it the simplest case, it is non-topological, but it can acquire topological Weyl points in the presence of non-zero Zeeman field. We present study of its surface states, and also consider its possible critical points. Next, we turn to the problem of superconductivity in Weyl metals. We demonstrate that Weyl metals are natural candidates for hosting unconventional superconductivity. Specifically, we consider two possible superconducting instabilities: unconventional finite momentum FFLO pairing, and zero momentum BCS pairing, which is also unconventional due to spin-momentum locking in Weyl metals. We demonstrate that its BCS phase is more favorable. In addition, we compute its anomalous Hall conductivity, and demonstrate that it is universal, i.e. not affected by the presence of superconductivity. Finally, we consider Dirac metals, which are protected solely by rotational symmetry. We point out, that mirror symmetry along its Dirac points plays special role. We demonstrate, that by breaking the rotational symmetry, it is possible to convert Dirac metal into a topological crystalline insulator, and Dirac metal itself can be viewed as a critical point between its different topological phases. We explore surface states spectrum in the resulting picture, and demonstrate, that this mechanism can be used to show that surface states in Dirac metal always terminate at Dirac points despite being not topologically protected.
We give a pedagogical introduction to theory of topological insulators. Following an introduction to the role of topology in band theory, we discuss several examples in detail. These include theories of the electric polarization in one dimension, the integer quantum Hall effect in two dimensions and topological insulators in two and three dimensions. We close with a brief discussion of topological crystalline insulators, nodal semimetals, topological superconductivity and topological defects.
This book presents both experimental and theoretical aspects of topology in magnetism. It first discusses how the topology in real space is relevant for a variety of magnetic spin structures, including domain walls, vortices, skyrmions, and dynamic excitations, and then focuses on the phenomena that are driven by distinct topology in reciprocal momentum space, such as anomalous and spin Hall effects, topological insulators, and Weyl semimetals. Lastly, it examines how topology influences dynamic phenomena and excitations (such as spin waves, magnons, localized dynamic solitons, and Majorana fermions). The book also shows how these developments promise to lead the transformative revolution of information technology.
This book is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for researchers and graduate students preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with the fundamental description on the topological phases of matter such as one, two- and three-dimensional topological insulators, and methods and tools for topological material's investigations, topological insulators for advanced optoelectronic devices, topological superconductors, saturable absorber and in plasmonic devices. Advanced Topological Insulators provides researchers and graduate students with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.
The monograph reviews various aspects of electronic properties of Dirac and Weyl semimetals. After a brief discussion of 2D Dirac semimetals, a comprehensive review of 3D materials is given. The description starts from an overview of the topological properties and symmetries of Dirac and Weyl semimetals. In addition, several low-energy models of Dirac and Weyl quasiparticles are presented. The key ab initio approaches and material realizations are given. The monograph includes detailed discussions of the surface Fermi arcs, anomalous transport properties, and collective modes of Dirac and Weyl semimetals. Superconductivity in these materials is briefly addressed.