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Mathematical Physics Studies

Bulk and Boundary Invariants for Complex Topological Insulators

From K-Theory to Physics

Authors: Prodan, Emil, Schulz-Baldes, Hermann

  • 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
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Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-319-29351-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-3-319-29350-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-3-319-80550-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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-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.

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.

Table of contents (7 chapters)

  • Illustration of Key Concepts in Dimension $$d=1$$ d = 1

    Prodan, Emil (et al.)

    Pages 1-18

  • Topological Solid State Systems: Conjectures, Experiments and Models

    Prodan, Emil (et al.)

    Pages 19-53

  • Observables Algebras for Solid State Systems

    Prodan, Emil (et al.)

    Pages 55-83

  • K-Theory for Topological Solid State Systems

    Prodan, Emil (et al.)

    Pages 85-111

  • The Topological Invariants and Their Interrelations

    Prodan, Emil (et al.)

    Pages 113-143

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-3-319-29351-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-3-319-29350-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA in USD
  • ISBN 978-3-319-80550-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bulk and Boundary Invariants for Complex Topological Insulators
Book Subtitle
From K-Theory to Physics
Authors
Series Title
Mathematical Physics Studies
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29351-6
DOI
10.1007/978-3-319-29351-6
Hardcover ISBN
978-3-319-29350-9
Softcover ISBN
978-3-319-80550-4
Series ISSN
0921-3767
Edition Number
1
Number of Pages
XXII, 204
Number of Illustrations
1 b/w illustrations
Topics