Overview
- Offers a complete and detailed description of the state of the
- art in the field from a mathematics point of view
- Contains many original contributions such as the generalized Streda formula, the ranges of the pairings of K-theory, the definition of boundary invariants for chiral systems
- Includes self-contained chapters that can be read independently of each other
- Written by leading experts in the field
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Physics Studies (MPST)
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Table of contents (7 chapters)
-
Front Matter
-
Back Matter
Keywords
- quantum spin-Hall insulator
- bulk-boundary correspondence
- topological solid state systems
- topological invariants
- index theorem
- Streda formula
- chiral unitary class
- Landau gauge
- six-term exact sequence
- Pimsner-Voiculescu sequence
- Bott map
- Volovik-Essin-Gurarie invariants
- Fredholm modules
- Chern numbers
- cyclic cohomology
About this book
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-trivialinvariants. 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.
Authors and Affiliations
About the authors
Emil Prodan is full professor of physics at the Yeshiva University. Before this he received his PhD from the Rice University under the supervision of Peter Nordlander, and he has held several positions at University of California Santa Barbara and Princeton University. His research combines rigorous mathematical and computer simulations to study the physics of the condensed matter. He received the NSF CAREER award to support research on topological insulator.
Bibliographic Information
Book Title: Bulk and Boundary Invariants for Complex Topological Insulators
Book Subtitle: From K-Theory to Physics
Authors: Emil Prodan, Hermann Schulz-Baldes
Series Title: Mathematical Physics Studies
DOI: https://doi.org/10.1007/978-3-319-29351-6
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-29350-9Published: 16 February 2016
Softcover ISBN: 978-3-319-80550-4Published: 30 March 2018
eBook ISBN: 978-3-319-29351-6Published: 05 February 2016
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 1
Number of Pages: XXII, 204
Number of Illustrations: 1 b/w illustrations
Topics: Mathematical Methods in Physics, K-Theory, Mathematical Physics, Solid State Physics