Topologically Protected States In One Dimensional Systems
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| Author | : Charles Fefferman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 132 |
| Release | : 2017-04-25 |
| Genre | : Mathematics |
| ISBN | : 1470423235 |
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.
| Author | : Charles Fefferman |
| Publisher | : |
| Total Pages | : 118 |
| Release | : 2017 |
| Genre | : Dirac equation |
| ISBN | : 9781470437077 |
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.
| Author | : János K. Asbóth |
| Publisher | : Springer |
| Total Pages | : 176 |
| Release | : 2016-02-22 |
| Genre | : Science |
| ISBN | : 3319256076 |
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.
| Author | : Paul Bracken |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 218 |
| Release | : 2023-08-02 |
| Genre | : Mathematics |
| ISBN | : 1837695598 |
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.
| Author | : Sandip Tiwari |
| Publisher | : Oxford University Press |
| Total Pages | : 705 |
| Release | : 2017 |
| Genre | : Science |
| ISBN | : 0198759878 |
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.
| Author | : Habib Ammari |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 122 |
| Release | : 2023-11-06 |
| Genre | : Mathematics |
| ISBN | : 3110784963 |
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.
| Author | : Claudio Chamon |
| Publisher | : Oxford University Press |
| Total Pages | : 705 |
| Release | : 2017-02-16 |
| Genre | : Science |
| ISBN | : 019108879X |
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.
| Author | : Thomas Schäpers |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 521 |
| Release | : 2021-05-10 |
| Genre | : Science |
| ISBN | : 3110639327 |
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.
| Author | : David S Simon |
| Publisher | : Morgan & Claypool Publishers |
| Total Pages | : 130 |
| Release | : 2018-11-06 |
| Genre | : Science |
| ISBN | : 1643272349 |
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.
| Author | : Prabhakar Bandaru |
| Publisher | : Springer Nature |
| Total Pages | : 116 |
| Release | : 2022-02-24 |
| Genre | : Technology & Engineering |
| ISBN | : 3030933407 |
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.
