A Short Course On Topological Insulators
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A Short Course On Topological Insulators
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Author : János K. Asbóth
language : en
Publisher: Springer
Release Date : 2016-02-22
A Short Course On Topological Insulators written by János K. Asbóth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-22 with Science categories.
This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.
Topological Phases Of Matter
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Author : Roderich Moessner
language : en
Publisher: Cambridge University Press
Release Date : 2021-04-29
Topological Phases Of Matter written by Roderich Moessner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-29 with Mathematics categories.
This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.
Topological Insulators And Topological Superconductors
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Author : B. Andrei Bernevig
language : en
Publisher: Princeton University Press
Release Date : 2013-04-07
Topological Insulators And Topological Superconductors written by B. Andrei Bernevig and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-07 with Science categories.
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.
Topology In Condensed Matter
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Author : Michael I. Monastyrsky
language : en
Publisher: Springer
Release Date : 2010-02-12
Topology In Condensed Matter written by Michael I. Monastyrsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-12 with Science categories.
This volume is based on the talks and lectures given by the participants of the 3-month seminar program “Topology in Condensed Matter,” which was held in the MPIPKS Dresden, 8 May–31 July 2002 under the scienti?c direction of Professors M. Kleman, S. Novikov, and myself. The aim of this program was to discuss recent applications of topology to several areas in condensed matter physics and related ?elds like biology. The last 30 years of the development of modern physics a?rmed two important ideas. The ?rst is the e?cient applications of topology in physics. One should mention applications in condensed matter, such as classi?cation of defects and textures in liquid crystals and super?uid liquids, the role of entangibility in polymer physics and DNA structures. The second tendency is also very prevalent. Some important discoveries in particle physics and condensed m- ter led to new and unpredictable questions in pure mathematics. We refer to the invention of monopoles and instantons in quantum ?eld theory, q- sicrystals ?uid membranes of high genus, fullerenes (C ,C , etc. ), and so on 60 90 in condensed matter. The number of such applications in the last years has increased substantially. The papers presented in this volume and the next one “Topology in - ology” re?ect the spectrum of topics discussed. Besides original papers, a mini-course in topology for physicists and biologists was organized. These lectures will be published in the second volume.
Topological Insulators
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Author : Shun-Qing Shen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-11
Topological Insulators written by Shun-Qing Shen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Technology & Engineering categories.
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.
Bulk And Boundary Invariants For Complex Topological Insulators
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Author : Emil Prodan
language : en
Publisher: Springer
Release Date : 2016-02-05
Bulk And Boundary Invariants For Complex Topological Insulators written by Emil Prodan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-05 with Science categories.
This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.
Acoustic Metamaterials
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Author : Richard Craster
language : en
Publisher: Springer Nature
Release Date : 2024-11-16
Acoustic Metamaterials written by Richard Craster and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-16 with Science categories.
The revised edition of this book offers an expanded review of acoustic metamaterials; novel materials which can manipulate sound waves, surface Rayleigh waves and water waves, in surprising ways, which include collimation, focusing, negative refraction, passive and active cloaking, sonic screening and extraordinary transmission. It covers both experimental and theoretical aspects of acoustic and elastic waves propagating in structured composites, with a focus on effective properties associated with negative refraction, lensing and cloaking. Updated chapters cover filtering effects, extraordinary transmission, sub-wavelength imaging via tomography or time-reversal techniques, cloaking via transformation acoustics, elastodynamics, and acoustic scattering cancellation. For this revised edition, six new chapters have been introduced to reflect recent developments in experimental acoustics and metasurfaces including acoustic impedance gratings and mirror symmetric metamaterials, phononic subsurfaces, time-modulated and topological crystals. The latter two are illustrated by simple Python program examples. The broad scope gives the reader an overview of the state of the art in acoustic metamaterials research and an indication of future directions and applications. It will serve as a solid introduction to the field for advanced students and researchers in physics, applied mathematics and mechanical engineering, and a valuable reference for those working in metamaterials and related areas.
Topological Insulators
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Author : Inamuddin
language : en
Publisher: Materials Research Forum LLC
Release Date : 2024-01-15
Topological Insulators written by Inamuddin and has been published by Materials Research Forum LLC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-15 with Technology & Engineering categories.
A topological insulator is an area that has yet to be fully explored and developed. The charge-induced bandgap fluctuation in the best-known bismuth-chalcogenide-based topological insulators is approximately 10MeV in magnitude. The major focus has shifted to the investigation of the presence of high-symmetry electronic bands as well as the utilization of easily produced materials. As the subject of topological insulators is still in the nascent stage, there is growing research and knowledge in the emerging field. This book is intended to provide the readers with an understanding of the needs and application of these materials. Keywords: Topological Insulators, Insulators, One-Dimensional Topological Insulators, Graphene, Magnetic Topological Insulator, Antiferromagnetic Phase, Ferromagnetic Phase, Topological Superconductor, Nonlinear Optical Behavior, Saturable Absorber, Quantum, Band Gap, Photonic Topological Insulators.
Reshaping Of Dirac Cones In Topological Insulators And Graphene
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Author : Álvaro Díaz Fernández
language : en
Publisher: Springer Nature
Release Date : 2020-12-09
Reshaping Of Dirac Cones In Topological Insulators And Graphene written by Álvaro Díaz Fernández and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-09 with Science categories.
Dirac cones are ubiquitous to non-trivial quantum matter and are expected to boost and reshape the field of modern electronics. Particularly relevant examples where these cones arise are topological insulators and graphene. From a fundamental perspective, this thesis proposes schemes towards modifying basic properties of these cones in the aforementioned materials. The thesis begins with a brief historical introduction which is followed by an extensive chapter that endows the reader with the basic tools of symmetry and topology needed to understand the remaining text. The subsequent four chapters are devoted to the reshaping of Dirac cones by external fields and delta doping. At all times, the ideas discussed in the second chapter are always a guiding principle to understand the phenomena discussed in those four chapters. As a result, the thesis is cohesive and represents a major advance in our understanding of the physics of Dirac materials.
Berry Phases In Electronic Structure Theory
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Author : David Vanderbilt
language : en
Publisher: Cambridge University Press
Release Date : 2018-11
Berry Phases In Electronic Structure Theory written by David Vanderbilt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11 with Science categories.
An introduction to the role of Berry phases in our modern understanding of the physics of electrons in solids.