Bulk and Boundary Invariants for Complex Topological Insulators

From K-Theory to Physics

  • Emil Prodan
  • Hermann Schulz-Baldes

Part of the Mathematical Physics Studies book series (MPST)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Emil Prodan, Hermann Schulz-Baldes
    Pages 1-18
  3. Emil Prodan, Hermann Schulz-Baldes
    Pages 19-53
  4. Emil Prodan, Hermann Schulz-Baldes
    Pages 55-83
  5. Emil Prodan, Hermann Schulz-Baldes
    Pages 85-111
  6. Emil Prodan, Hermann Schulz-Baldes
    Pages 113-143
  7. Emil Prodan, Hermann Schulz-Baldes
    Pages 145-172
  8. Emil Prodan, Hermann Schulz-Baldes
    Pages 173-191
  9. Back Matter
    Pages 193-204

About this book

Introduction

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.

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

Authors and affiliations

  • Emil Prodan
    • 1
  • Hermann Schulz-Baldes
    • 2
  1. 1.Yeshiva UniversityPhysics DepartmentNew YorkUSA
  2. 2.Department MathematikFAU Erlangen-NürnbergErlangenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-29351-6
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-29350-9
  • Online ISBN 978-3-319-29351-6
  • Series Print ISSN 0921-3767
  • Series Online ISSN 2352-3905
  • About this book
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