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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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,