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Topological Semimetals

Author: David J. Fisher

Publisher: Materials Research Forum LLC

Published: 2019-04-20

Total Pages: 163

ISBN-13: 1644900149

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.

Linear Electrodynamic Response of Topological Semimetals

Author: Artem V. Pronin

Publisher: Springer Nature

Published: 2023-08-17

Total Pages: 141

ISBN-13: 3031356373

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This book provides a model description for the electromagnetic response of topological nodal semimetals and summarizes recent experimental findings in these systems. Specifically, it discusses various types of topological semimetals – Dirac, Weyl, nodal-line, triple-point, and multifold semimetals – and provides description for the characteristic features of the linear electrodynamic response for all these types of materials. Topological semimetals possess peculiar bulk electronic band structure, which leads to unusual electrodynamic response. For example, the low-energy inter-band optical conductivity of nodal semimetals is supposed to demonstrate power-law frequency dependence and the intra- and inter-band contributions to the conductivity are often mixed. Further, the magneto-optical response is also unusual, because of the non-equidistant spacing between the Landau levels. Finally, in semimetals with chiral electronic bands, e.g. in Weyl semimetals, the simultaneous application of parallel magnetic and electric fields leads to the chiral anomaly, i.e. to a misbalance between the electrons with diffident chiralities. This misbalance affects the electrodynamics properties of the material and can be detected optically. All these points are addressed here in detail. The book is written for a wide audience of physicists, working in the field of topological condensed matter physics. It gives a pedagogical introduction enabling graduate students and non-experts to familiarize themselves with the subject.

Topological Insulators and Topological Superconductors

Author: B. Andrei Bernevig

Publisher: Princeton University Press

Published: 2013-04-07

Total Pages: 264

ISBN-13: 1400846730

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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.

Topological Insulators

Author: Shun-Qing Shen

Publisher: Springer Science & Business Media

Published: 2013-01-11

Total Pages: 234

ISBN-13: 364232858X

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Topological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological insulators and related areas. Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.

Electronic Properties Of Dirac And Weyl Semimetals

Author: Eduard V Gorbar

Publisher: World Scientific

Published: 2021-01-04

Total Pages: 535

ISBN-13: 9811207364

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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.

Geometry, Topology and Physics

Author: Mikio Nakahara

Publisher: Taylor & Francis

Published: 2018-10-03

Total Pages: 596

ISBN-13: 1420056948

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Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.