Bulk and Boundary Invariants for Complex Topological Insulators

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

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

Number of Illustrations and Tables
1 illustrations in colour
Topics
Mathematical Methods in Physics
K-Theory
Mathematical Physics
Solid State Physics

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