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Topologically Protected States In One Dimensional Systems
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Book Synopsis Topologically Protected States in One-Dimensional Systems by : Charles Fefferman
Download or read book Topologically Protected States in One-Dimensional Systems written by Charles Fefferman and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They then show that the introduction of an ``edge'', via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized ``edge states''. These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
Book Synopsis Topologically Protected States in One-dimensional Systems by : Charles Fefferman
Download or read book Topologically Protected States in One-dimensional Systems written by Charles Fefferman and published by . This book was released on 2017 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "mDirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized "edge states". These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. Our model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states we construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
Book Synopsis A Short Course on Topological Insulators by : János K. Asbóth
Download or read book A Short Course on Topological Insulators written by János K. Asbóth and published by Springer. This book was released on 2016-02-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topology - Recent Advances and Applications by : Paul Bracken
Download or read book Topology - Recent Advances and Applications written by Paul Bracken and published by BoD – Books on Demand. This book was released on 2023-08-02 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology remains an active and fundamental area of research that plays a foundational role in many branches of mathematics and science, such as analysis, differential geometry, physics and even biology. It is hoped the papers in this book will contribute to stimulating research in this basic area of mathematics.
Book Synopsis Nanoscale Device Physics by : Sandip Tiwari
Download or read book Nanoscale Device Physics written by Sandip Tiwari and published by Oxford University Press. This book was released on 2017 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary advanced textbook for the teaching of science and engineering of nanoscale devices as used in the semiconductor, electronics, magnetics, optics and electromechanics industry.
Book Synopsis Metamaterial Analysis and Design by : Habib Ammari
Download or read book Metamaterial Analysis and Design written by Habib Ammari and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-11-06 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metamaterials are advanced composite materials which have exotic and powerful properties. Their complicated microstructures make metamaterials challenging to model, requiring the use of sophisticated mathematical techniques. This book uses a from-first-principles approach (based on boundary integral methods and asymptotic analysis) to study a class of high-contrast metamaterials. These mathematical techniques are applied to the problem of designing graded metamaterials that replicate the function of the cochlea.
Book Synopsis Topological Aspects of Condensed Matter Physics by : Claudio Chamon
Download or read book Topological Aspects of Condensed Matter Physics written by Claudio Chamon and published by Oxford University Press. This book was released on 2017-02-16 with total page 705 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic. This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics.
Book Synopsis Semiconductor Spintronics by : Thomas Schäpers
Download or read book Semiconductor Spintronics written by Thomas Schäpers and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-05-10 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and expanded edition of the first comprehensive introduction to the rapidly-evolving field of spintronics covers ferromagnetism in nano-electrodes, spin injection, spin manipulation, and the practical use of these effects in next-generation electronics. Moreover, the book now also includes spin-based optics, topological materials and insulators, and the quantum spin Hall effect.
Book Synopsis Tying Light in Knots by : David S Simon
Download or read book Tying Light in Knots written by David S Simon and published by Morgan & Claypool Publishers. This book was released on 2018-11-06 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology is the study of properties of geometrical objects that remain invariant as the object is bent, twisted, or otherwise continuously deformed. It has been an indispensable tool in particle physics and solid state physics for decades, but in recent years it has become increasingly relevant in classical and quantum optics as well. It makes appearances through such diverse phenomena as Pancharatnam-Berry phases, optical vortices and solitons, and optical simulations of solid-state topological phenomena. This book concisely provides the necessary mathematical background needed to understand these developments and to give a rapid survey of some of the optical applications where topological issues arise.
Book Synopsis Topological States for New Modes of Information Storage and Transfer by : Prabhakar Bandaru
Download or read book Topological States for New Modes of Information Storage and Transfer written by Prabhakar Bandaru and published by Springer Nature. This book was released on 2022-02-24 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews evidence for the existence of information storing states present in specific materials systems called Topological Materials. It discusses how quantum computation, a possible technology for the future, demands unique paradigms where the information storing states are just not disturbed by classical forces. They are protected from environmental disturbance, suggesting that whatever information is stored in such states would could be safe forever. The authors explain how the topological aspect arises from the configuration or the shape of energy space. He further explains that the existence of related topological states has not been conclusively established in spite of significant experimental effort over the past decade. And The book as such illustrates the necessity for such investigations as well as application of the topological states for new computational technologies. The scope of coverage includes all the necessary mathematical and physics preliminaries (starting at the undergraduate level) enabling researchers to quickly understand the state of the art literature.
Book Synopsis Topological Insulators by : Shun-Qing Shen
Download or read book Topological Insulators written by Shun-Qing Shen and published by Springer. This book was released on 2017-08-18 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Topological Quantum Matter & Quantum Computation by : Tudor D. Stanescu
Download or read book Introduction to Topological Quantum Matter & Quantum Computation written by Tudor D. Stanescu and published by CRC Press. This book was released on 2024-07-02 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid-state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture and emphasizing two major new paradigms in condensed matter physics – quantum topology and quantum information – this book is ideal for graduate students and researchers entering this field, as it allows for the fruitful transfer of ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and unveils the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the toric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Topological quantum computation is also presented using a broad perspective, which includes elements of classical and quantum information theory, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and key ideas underlying quantum computation with anyons. This new edition has been updated throughout, with exciting new discussions on crystalline topological phases, including higher-order topological insulators; gapless topological phases, including Weyl semimetals; periodically-driven topological insulators; and a discussion of axion electrodynamics in topological materials. Key Features: · Provides an accessible introduction to this exciting, cross-disciplinary area of research. · Fully updated throughout with new content on the latest result from the field. · Authored by an authority on the subject. Tudor Stanescu is a professor of Condensed Matter Theory at West Virginia University, USA. He received a B.S. in Physics from the University of Bucharest, Romania, in 1994 and a Ph.D. in Theoretical Physics from the University of Illinois at Urbana Champaign in 2002. He was a Postdoctoral Fellow at Rutgers University and at the University of Maryland from 2003 to 2009. He joined the Department of Physics and Astronomy at West Virginia University in Fall 2009. Prof. Stanescu’s research interests encompass a variety of topics in theoretical condensed matter physics including topological insulators and superconductors, topological quantum computation, ultra-cold atom systems in optical lattices, and strongly correlated materials, such as, for example, cuprate high-temperature superconductors. His research uses a combination of analytical and numerical tools and focuses on understanding the emergence of exotic states of matter in solid state and cold atom structures, for example, topological superconducting phases that host Majorana zero modes, and on investigating the possibilities of exploiting these states as physical platforms for quantum computation.
Book Synopsis Topological Insulators and Topological Superconductors by : B. Andrei Bernevig
Download or read book Topological Insulators and Topological Superconductors written by B. Andrei Bernevig and published by Princeton University Press. This book was released on 2013-04-07 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topological Insulators by : Inamuddin
Download or read book Topological Insulators written by Inamuddin and published by Materials Research Forum LLC. This book was released on 2024-01-15 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 50 Years Of Anderson Localization by : Elihu Abrahams
Download or read book 50 Years Of Anderson Localization written by Elihu Abrahams and published by World Scientific. This book was released on 2010-06-25 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his groundbreaking paper “Absence of diffusion in certain random lattices (1958)”, Philip W Anderson originated, described and developed the physical principles underlying the phenomenon of the localization of quantum objects due to disorder. Anderson's 1977 Nobel Prize citation featured that paper, which was fundamental for many subsequent developments in condensed matter physics and technical applications. After more than a half century, the subject continues to be of fundamental importance. In particular, in the last 25 years, the phenomenon of localization has proved to be crucial for the understanding of the quantum Hall effect, mesoscopic fluctuations in small conductors, some aspects of quantum chaotic behavior, and the localization and collective modes of electromagnetic and matter waves.This unique and invaluable volume celebrates the five decades of the impact of Anderson localization on modern physics. In addition to the historical perspective on its origin, the volume provides a comprehensive description of the experimental and theoretical aspects of Anderson localization, together with its application in various areas, which include disordered metals and the metal-insulator transition, mesoscopic physics, classical systems and light, strongly-correlated systems, and mathematical models.The volume is edited by E Abrahams, who has been a contributor in the field of localization. A distinguished group of experts, each of whom has left his mark on the developments of this fascinating theory, contribute their personal insights in this volume. They are: A Amir (Weizmann Institute of Science), P W Anderson (Princeton University), G Bergmann (University of Southern California), M Büttiker (University of Geneva), K Byczuk (University of Warsaw & University of Augsburg), J Cardy (University of Oxford), S Chakravarty (University of California, Los Angeles), V Dobrosavljević (Florida State University), R C Dynes (University of California, San Diego), K B Efetov (Ruhr University Bochum), F Evers (Karlsruhe Institute of Technology), A M Finkel'stein (Weizmann Institute of Science & Texas A&M University), A Genack (Queens College, CUNY), N Giordano (Purdue University), I V Gornyi (Karlsruhe Institute of Technology), W Hofstetter (Goethe University Frankfurt), Y Imry (Weizmann Institute of Science), B Kramer (Jacobs University Bremen), S V Kravchenko (Northeastern University), A MacKinnon (Imperial College London), A D Mirlin (Karlsruhe Institute of Technology), M Moskalets (NTU “Kharkiv Polytechnic Institute”), T Ohtsuki (Sophia University), P M Ostrovsky (Karlsruhe Institute of Technology), A M M Pruisken (University of Amsterdam), T V Ramakrishnan (Indian Institute of Science), M P Sarachik (City College, CUNY), K Slevin (Osaka University), T Spencer (Institute for Advanced Study, Princeton), D J Thouless (University of Washington), D Vollhardt (University of Augsburg), J Wang (Queens College, CUNY), F J Wegner (Ruprecht-Karls-University) and P Wölfle (Karlsruhe Institute of Technology).
Book Synopsis Topology In Condensed Matter: An Introduction by : Miguel A N Araujo
Download or read book Topology In Condensed Matter: An Introduction written by Miguel A N Araujo and published by World Scientific. This book was released on 2021-05-19 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text serves as a pedagogical introduction to the theoretical concepts on application of topology in condensed matter systems. It covers an introduction to basic concepts of topology, emphasizes the relation of geometric concepts such as the Berry phase to topology, having in mind applications in condensed matter. In addition to describing two basic systems such as topological insulators and topological superconductors, it also reviews topological spin systems and photonic systems. It also describes the use of quantum information concepts in the context of topological phases and phase transitions, and the effect of non-equilibrium perturbations on topological systems.This book provides a comprehensive introduction to topological insulators, topological superconductors and topological semimetals. It includes all the mathematical background required for the subject. There are very few books with such a coverage in the market.
Book Synopsis Quantum Hybrid Electronics and Materials by : Yoshiro Hirayama
Download or read book Quantum Hybrid Electronics and Materials written by Yoshiro Hirayama and published by Springer Nature. This book was released on 2022-05-03 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights recent advances in quantum control technologies with regard to hybrid quantum systems. It addresses the following topics: phonon engineering based on phononic crystals, carbon-based nano materials like graphene and nanotubes, Terahertz light technology for single-molecule and quantum dots, nuclear-spin-based metrology for semiconductor quantum systems, quantum anomalous Hall effect in magnetic topological insulators, chiral three-dimensional photonic crystals, and bio-inspired magnonic systems. Each topic, as a component in the framework of hybrid quantum systems, is concisely presented by experts at the forefront of the field. Accordingly, the book offers a valuable asset, and will help readers find advanced technologies and materials suitable for their purposes.
