Bulk and boundary invariants for complex topological insulators [electronic resource] : from K-Theory to physics / Emil Prodan, Hermann Schulz-Baldes.
2016
QA612.33
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Title
Bulk and boundary invariants for complex topological insulators [electronic resource] : from K-Theory to physics / Emil Prodan, Hermann Schulz-Baldes.
Author
Prodan, Emil, author.
ISBN
9783319293516 (electronic book)
3319293516 (electronic book)
9783319293509
3319293516 (electronic book)
9783319293509
Published
[Switzerland] : Springer, 2016.
Language
English
Description
1 online resource (xxii, 204 pages) : color illustrations.
Item Number
10.1007/978-3-319-29351-6 doi
Call Number
QA612.33
Dewey Decimal Classification
514/.23
Summary
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 use analysis 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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed February 16, 2016).
Added Author
Schulz-Baldes, Hermann, author.
Series
Mathematical physics studies.
Available in Other Form
Bulk and Boundary Invariants for Complex Topological Insulators : From K-Theory to Physics
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Table of Contents
Illustration of key concepts in dimension d = 1
Topological solid state systems: conjectures, experiments and models
Observables algebras for solid state systems
K-theory for topological solid state systems
The topological invariants and their interrelations
Index theorems for solid state systems
Invariants as measurable quantities.
Topological solid state systems: conjectures, experiments and models
Observables algebras for solid state systems
K-theory for topological solid state systems
The topological invariants and their interrelations
Index theorems for solid state systems
Invariants as measurable quantities.