Boundary Physics And Bulk Boundary Correspondence In Topological Phases Of Matter
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Boundary Physics And Bulk Boundary Correspondence In Topological Phases Of Matter
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Author : Abhijeet Alase
language : en
Publisher: Springer Nature
Release Date : 2019-11-20
Boundary Physics And Bulk Boundary Correspondence In Topological Phases Of Matter written by Abhijeet Alase and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-20 with Science categories.
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.
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.
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 Aspects Of Condensed Matter Physics
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Author : Claudio Chamon
language : en
Publisher: Oxford University Press
Release Date : 2017
Topological Aspects Of Condensed Matter Physics written by Claudio Chamon and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Science categories.
This book contains lecture notes by world experts on topological quantum phenomena, which are being developed at unprecedented rates in novel material systems.
Diffusionics
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Author : Fu-Bao Yang
language : en
Publisher: Springer Nature
Release Date : 2024-03-11
Diffusionics written by Fu-Bao Yang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-11 with Science categories.
This open access book presents a comprehensive exploration of diffusion metamaterials that control energy and mass diffusion. Currently, if from the perspective of governing equations, diffusion metamaterials and wave metamaterials (pioneered by J. B. Pendry in the 1990s) are recognised as the two most prominent branches in the field of metamaterials. These two branches differ in their emphasis on the diffusion equation (as the governing equation) and time-dependent characteristic lengths in diffusion metamaterials, as opposed to the wave equation (as the governing equation) and time-independent characteristic lengths in wave metamaterials. Organized into three distinct parts – 'Thermal Diffusion Metamaterials', 'Particle Diffusion Metamaterials', and 'Plasma Diffusion Metamaterials' – this book offers a rigorous exploration spanning physics, engineering, and materials science, aimed at advancing our understanding of diffusion processes controlled by diffusion metamaterials. Incorporating foundational theory, computational simulations, and laboratory experiments, the book equips researchers and scholars across these disciplines with comprehensive methods, insights, and results pivotal to the advancement of diffusion control. Beyond facilitating interdisciplinary discourse, the book serves as a catalyst for innovative breakthroughs at the crossroads of physics, thermodynamics, and materials science. Essentially, readers will acquire profound insights that empower them to spearhead advancements in diffusion science (diffusionics) and the engineering of metamaterials.
Basic Physics Of Functionalized Graphite
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Author : Pablo D. Esquinazi
language : en
Publisher: Springer
Release Date : 2016-07-12
Basic Physics Of Functionalized Graphite written by Pablo D. Esquinazi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-12 with Technology & Engineering categories.
This book summarizes the basic physics of graphite and newly discovered phenomena in this material. The book contains the knowledge needed to understand novel properties of functionalized graphite demonstrating the occurrence of remarkable phenomena in disordered graphite and graphite-based heterostructures. It also discusses applications of thin graphitic samples in future electronics. Graphite consists of a stack of nearly decoupled two-dimensional graphene planes. Because of the low dimensionality and the presence of Dirac fermions, much of graphite physics resembles that of graphene. On the other hand, the multi-layered nature of the graphite structure together with structural and/or chemical disorder are responsible for phenomena that are not observed yet in graphene, such as ferromagnetic order and superconductivity. Each chapter was written by one or more experts in the field whose contributions were relevant in the (re)discovery of (un)known phenomena in graphite. The book is intended as reference for beginners and experts in the field, introducing them to many aspects of the new physics of graphite, with a fresh overview of recently found phenomena and the theoretical frames to understand them.
Topological Phases In Condensed Matter Physics
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Author : Saurabh Basu
language : en
Publisher: Springer Nature
Release Date : 2023-09-14
Topological Phases In Condensed Matter Physics written by Saurabh Basu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-14 with Science categories.
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.
Chirality Magnetism And Magnetoelectricity
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Author : Eugene Kamenetskii
language : en
Publisher: Springer Nature
Release Date : 2021-03-27
Chirality Magnetism And Magnetoelectricity written by Eugene Kamenetskii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-27 with Science categories.
This book discusses theoretical and experimental advances in metamaterial structures, which are of fundamental importance to many applications in microwave and optical-wave physics and materials science. Metamaterial structures exhibit time-reversal and space-inversion symmetry breaking due to the effects of magnetism and chirality. The book addresses the characteristic properties of various symmetry breaking processes by studying field-matter interaction with use of conventional electromagnetic waves and novel types of engineered fields: twisted-photon fields, toroidal fields, and magnetoelectric fields. In a system with a combined effect of simultaneous breaking of space and time inversion symmetries, one observes the magnetochiral effect. Another similar phenomenon featuring space-time inversion symmetries is related to use of magnetoelectric materials. Cross-coupling of the electric and magnetic components in these material structures, leading to the appearance of new magnetic modes with an electric excitation channel – electromagnons and skyrmions – has resulted in a wealth of strong optical effects such as directional dichroism, magnetochiral dichroism, and rotatory power of the fields. This book contains multifaceted contributions from international leading experts and covers the essential aspects of symmetry-breaking effects, including theory, modeling and design, proven and potential applications in practical devices, fabrication, characterization and measurement. It is ideally suited as an introduction and basic reference work for researchers and graduate students entering this field.
Quantum Theory And Symmetries
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Author : M. B. Paranjape
language : en
Publisher: Springer Nature
Release Date : 2021-03-26
Quantum Theory And Symmetries written by M. B. Paranjape and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-26 with Science categories.
This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montréal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions.
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.