Prodan E., Schulz-Baldes H. Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics

Springer International Publishing Switzerland, 2016. – 204 p. – ISBN10: 3319293508.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.
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
Topics
Mathematical Methods in Physics
K-Theory
Mathematical Physics
Solid State PhysicsIllustration 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