Bulk and Boundary Invariants for Complex Topological Insulators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bulk and Boundary Invariants for Complex Topological Insulators write by Emil Prodan. This book was released on 2016-02-05. Bulk and Boundary Invariants for Complex Topological Insulators available in PDF, EPUB and Kindle. 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
A Short Course on Topological Insulators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Short Course on Topological Insulators write by János K. Asbóth. This book was released on 2016-02-22. A Short Course on Topological Insulators available in PDF, EPUB and Kindle. 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 Insulators and Topological Superconductors
Topological Insulators and Topological Superconductors - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topological Insulators and Topological Superconductors write by B. Andrei Bernevig. This book was released on 2013-04-07. Topological Insulators and Topological Superconductors available in PDF, EPUB and Kindle. 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
Topology in Condensed Matter - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topology in Condensed Matter write by Michael I. Monastyrsky. This book was released on 2006-02-04. Topology in Condensed Matter available in PDF, EPUB and Kindle. 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.
Topological Insulators
Topological Insulators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topological Insulators write by Shun-Qing Shen. This book was released on 2013-01-11. Topological Insulators available in PDF, EPUB and Kindle. 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.
