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Bulk and boundary invariants for com...

Prodan, Emil.

Bulk and boundary invariants for complex topological insulatorsfrom K-Theory to physics /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Bulk and boundary invariants for complex topological insulatorsby Emil Prodan, Hermann Schulz-Baldes.
Reminder of title:	from K-Theory to physics /
Author:	Prodan, Emil.
other author:	Schulz-Baldes, Hermann.
Published:	Cham :Springer International Publishing :2016.
Description:	xxii, 204 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	K-theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-29351-6
ISBN:	9783319293516$q(electronic bk.)

Bulk and boundary invariants for complex topological insulatorsfrom K-Theory to physics /
Prodan, Emil.

Bulk and boundary invariants for complex topological insulatorsfrom K-Theory to physics /[electronic resource] :by Emil Prodan, Hermann Schulz-Baldes. - Cham :Springer International Publishing :2016. - xxii, 204 p. :ill., digital ;24 cm. - Mathematical physics studies,0921-3767. - Mathematical physics studies..

Illustration 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.

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.

ISBN: 9783319293516$q(electronic bk.)

Standard No.: 10.1007/978-3-319-29351-6doiSubjects--Topical Terms:

190877
K-theory.

LC Class. No.: QA612.33 / .P76 2016

Dewey Class. No.: 514.23

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520 $a 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.
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