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Titlebook: Bulk and Boundary Invariants for Complex Topological Insulators; From K-Theory to Phy Emil Prodan,Hermann Schulz-Baldes Book 2016 Springer

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期刊全稱Bulk and Boundary Invariants for Complex Topological Insulators
期刊簡(jiǎn)稱From K-Theory to Phy
影響因子2023Emil Prodan,Hermann Schulz-Baldes
視頻videohttp://file.papertrans.cn/192/191919/191919.mp4
發(fā)行地址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
學(xué)科分類Mathematical Physics Studies
圖書封面Titlebook: Bulk and Boundary Invariants for Complex Topological Insulators; From K-Theory to Phy Emil Prodan,Hermann Schulz-Baldes Book 2016 Springer
影響因子.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 advan
Pindex Book 2016
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Illustration of Key Concepts in Dimension ,, model [205] of a conducting polymer. This model has a chiral symmetry and non-trivial topology, given by a non-commutative winding number which is remarkably stable against perturbations like a random potential [139]. Hence this is a relatively simple example of a topological insulator. Here the fo
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Observables Algebras for Solid State Systems, physical models for topological insulators presented in Chap.?.. Then the exact sequence connecting these algebras is discussed. In particular, it is shown to be isomorphic to the Pimsner-Voiculescu exact sequence. This chapter also introduces the non-commutative analysis tools and the smooth sub-a
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The Topological Invariants and Their Interrelations,iants. The discussion is then specialized to the algebras of physical observables. The strong and the weak topological invariants, for both bulk and boundary, are defined as pairings of specific cyclic cocycles with the elements of the .-groups encoding the topology of the solid state systems. The d
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Index Theorems for Solid State Systems,ke integer values in general. In this chapter index theorems are proved for these strong invariants which allow to extend this integrality to the regime with mobility gap. For this purpose it is first shown how cyclic cocycles obtained from Fredholm modules pair integrally with .-theory. When co
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Invariants as Measurable Quantities,ants are connected to linear and nonlinear transport coefficients and the expected physical effects are discussed in depth for class A and class AIII of topological insulators, in several space dimensions. Then we follow with an in depth analysis of orbital polarization and magneto-electric effects,
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