Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics

di Emil Prodan (Autore)

Hermann Schulz-Baldes (Autore)

Springer International Publishing AG, 2016

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-trivialinvariants. 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.

• Autore: Emil Prodan, Hermann Schulz-Baldes
• Editore: Springer International Publishing AG
• Collana: Mathematical Physics Studies
• Anno: 2016
• Rilegatura: Hardback
• Pagine: 204 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783319293509

Testo in English