© 2016

Bulk and Boundary Invariants for Complex Topological Insulators

From K-Theory to Physics

  • 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


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


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.


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

  1. 1.Yeshiva UniversityPhysics DepartmentNew YorkUSA
  2. 2.Department MathematikFAU Erlangen-NürnbergErlangenGermany

About the authors

Hermann Schulz-Baldes has been professor at the Department of Mathematics of the University of Erlangen since 2004. Before this he received his PhD from the University of Toulouse under the supervision of Jean Bellissard, and he held several positions at TU Berlin and University of California at Irvine. His research focuses on the quantum Hall effect, quantum transport, and topological insulators.

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
  • Series Abbreviated Title Mathematical Physics Stud.
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy Physics and Astronomy (R0)
  • Hardcover ISBN 978-3-319-29350-9
  • Softcover ISBN 978-3-319-80550-4
  • eBook ISBN 978-3-319-29351-6
  • Series ISSN 0921-3767
  • Series E-ISSN 2352-3905
  • Edition Number 1
  • Number of Pages XXII, 204
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics Mathematical Methods in Physics
    Mathematical Physics
    Solid State Physics
  • Buy this book on publisher's site
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