Download or read book Boundary Physics and Bulk Boundary Correspondence in Topological Phases of Matter written by Abhijeet Alase and published by Springer Nature. This book was released on 2019-11-20 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis extends our understanding of systems of independent electrons by developing a generalization of Bloch’s Theorem which is applicable whenever translational symmetry is broken solely due to arbitrary boundary conditions. The thesis begins with a historical overview of topological condensed matter physics, placing the work in context, before introducing the generalized form of Bloch's Theorem. A cornerstone of electronic band structure and transport theory in crystalline matter, Bloch's Theorem is generalized via a reformulation of the diagonalization problem in terms of corner-modified block-Toeplitz matrices and, physically, by allowing the crystal momentum to take complex values. This formulation provides exact expressions for all the energy eigenvalues and eigenstates of the single-particle Hamiltonian. By precisely capturing the interplay between bulk and boundary properties, this affords an exact analysis of several prototypical models relevant to symmetry-protected topological phases of matter, including a characterization of zero-energy localized boundary excitations in both topological insulators and superconductors. Notably, in combination with suitable matrix factorization techniques, the generalized Bloch Hamiltonian is also shown to provide a natural starting point for a unified derivation of bulk-boundary correspondence for all symmetry classes in one dimension.

Download or read book Bulk and Boundary Invariants for Complex Topological Insulators written by Emil Prodan and published by Springer. This book was released on 2016-02-05 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

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.

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.

Download or read book The Role of Topology in Materials written by Sanju Gupta and published by Springer. This book was released on 2018-04-21 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure–property–function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.

Download or read book Mechanics and Physics of Structured Media written by Igor Andrianov and published by Academic Press. This book was released on 2022-01-20 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics and Physics of Structured Media: Asymptotic and Integral Methods of Leonid Filshtinsky provides unique information on the macroscopic properties of various composite materials and the mathematical techniques key to understanding their physical behaviors. The book is centered around the arguably monumental work of Leonid Filshtinsky. His last works provide insight on fracture in electromagnetic-elastic systems alongside approaches for solving problems in mechanics of solid materials. Asymptotic methods, the method of complex potentials, wave mechanics, viscosity of suspensions, conductivity, vibration and buckling of functionally graded plates, and critical phenomena in various random systems are all covered at length. Other sections cover boundary value problems in fracture mechanics, two-phase model methods for heterogeneous nanomaterials, and the propagation of acoustic, electromagnetic, and elastic waves in a one-dimensional periodic two-component material. Covers key issues around the mechanics of structured media, including modeling techniques, fracture mechanics in various composite materials, the fundamentals of integral equations, wave mechanics, and more Discusses boundary value problems of materials, techniques for predicting elasticity of composites, and heterogeneous nanomaterials and their statistical description Includes insights on asymptotic methods, wave mechanics, the mechanics of piezo-materials, and more Applies homogenization concepts to various physical systems

Download or read book Memorial Volume For Shoucheng Zhang written by Xiaoliang Qi and published by World Scientific. This book was released on 2021-08-24 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book honors the remarkable science and life of Shoucheng Zhang, a condensed matter theorist known for his work on topological insulators, the quantum Hall effect, spintronics, superconductivity, and other fields. It contains the contributions displayed at the Shoucheng Zhang Memorial Workshop held on May 2-4, 2019 at Stanford University.

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.

Download or read book Topology in Condensed Matter written by Michael I. Monastyrsky and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

Download or read book Berry Phases in Electronic Structure Theory written by David Vanderbilt and published by Cambridge University Press. This book was released on 2018-11 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the role of Berry phases in our modern understanding of the physics of electrons in solids.

Download or read book Analysis Applications and Computations written by Uwe Kähler and published by Springer Nature. This book was released on 2023-12-01 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Download or read book Glide Symmetric Z2 Magnetic Topological Crystalline Insulators written by Heejae Kim and published by Springer Nature. This book was released on 2022-01-25 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive theory on glide-symmetric topological crystalline insulators. Beginning with developing a theory of topological phase transitions between a topological and trivial phase, it derives a formula for topological invariance in a glide-symmetric topological phase when inversion symmetry is added into a system. It also shows that the addition of inversion symmetry drastically simplifies the formula, providing insights into this topological phase, and proposes potential implementations. Lastly, based on the above results, the author establishes a way to design topological photonic crystals. Allowing readers to gain a comprehensive understanding of the glide-symmetric topological crystalline insulators, the book offers a way to produce such a topological phase in various physical systems, such as electronic and photonic systems, in the future.

Download or read book Topological Phases in Condensed Matter Physics written by Saurabh Basu and published by Springer Nature. This book was released on 2023-10-16 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is mainly designed for post-graduate students to learn modern-day condensed matter physics. While emphasizing an experiment called the ‘Quantum Hall effect’, it introduces the subject of 'Topology' and how the topological invariants are related to the quantization of the Hall plateaus. Thus, the content tries to deliver an account of the topological aspects of materials that have shaped the study of condensed matter physics in recent times. The subject is often quite involved for a student to grasp the fundamentals and relate them to physical phenomena. Further, these topics are mostly left out of the undergraduate curriculum, although they often require a simplistic view of the concepts involved to be presented pedagogically. The book contains examples, worked-out concepts, important derivations, diagrams for illustration, etc. to aid the understanding of the students. The book also emphasizes the experimental discoveries that put the subject in its perspective and elaborate on the applications which are likely to be of interest to scientists and engineers.

Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2023-09-14 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the success of prior editions, this graduate text provides a comprehensive introduction to core concepts and methods of quantum field theory in condensed matter. It covers modern advances, from condensation phenomena and superfluidity to gauge theory, non-equilibrium phenomena and topological quantum matter.

Download or read book The Geometric Phase in Quantum Systems written by Arno Bohm and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "...useful for experts in mathematical physics...this is a very interesting book, which deserves to be found in any physical library." (OPTICS & PHOTONICS NEWS, July/August 2005).

Download or read book Excursions in Ill Condensed Quantum Matter written by Adhip Agarwala and published by Springer. This book was released on 2019-06-13 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Impurities, disorder or amorphous systems – ill-condensed matter – are mostly considered inconveniences in the study of materials, which is otherwise heavily based on idealized perfect crystals. The Kondo effect and the scaling theory of localization are among the fundamental and early discoveries which revealed the novelty hidden in impure or disordered systems. Recent advances in condensed matter physics have emphasized the role of topology, spin-orbit coupling, and certain discrete symmetries such as time reversal in many physical phenomena. These have irreversibly transformed the essential ideas and purview of condensed matter physics, both in theoretical and experimental directions. However, many of these recent developments and their implications are limited to, or by, ideas that pertain to clean systems. This thesis deals with various aspects of these new developments, but in the case of unclean systems. The author introduces new ideas such as amorphous topological insulators, fractalized metals and fractionalized spins.