Index pairings in presence of symmetries with applications to topological insulators
type: Item
instance of: scholarly article
title: Index pairings in presence of symmetries with applications to topological insulators
zbMATH Open document ID: 1348.82083
author: Julian Großmann
author: Hermann Schulz-Baldes
published in: Communications in Mathematical Physics
publication date: 2016-05-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1503.04834
review text: The authors consider the index pairings of the complex classes which are known for arbitrary even dimensions [\textit{E. Prodan} et al., J. Phys. A, Math. Theor. 46, No. 48, Article ID 485202, 20 p. (2013; Zbl 1290.82016)] and arbitrary odd dimensions [\textit{E. Prodan} and \textit{H. Schulz-Baldes}, J. Funct. Anal. 271, No. 5, 1150--1176 (2016; Zbl 1344.82055)], and to implement the symmetries of the Fermi projection in order to deduce \(Z\)-, \(Z_2\)- and \(2Z\)-valued index pairings. These general results are applied to prove index theorems for the strong invariants of disordered topological insulators.
reviewed by: Nasir N. Ganikhodjaev
Mathematics Subject Classification ID: 82D20
Mathematics Subject Classification ID: 82D30
zbMATH DE Number: 6579794
zbMATH Keywords: index pairings
zbMATH Keywords: topological insulators
zbMATH Keywords: Fermi projection
MaRDI profile type: Publication
OpenAlex ID: W3104602445
arXiv ID: 1503.04834
cites work: Clifford modules
cites work: Index theory for skew-adjoint Fredholm operators
cites work: Topological invariants of edge states for periodic two-dimensional models
cites work: The index of a pair of projections
cites work: Q3752945
cites work: The noncommutative geometry of the quantum Hall effect
cites work: \(K\)-theory for real \(C^*\)-algebras via unitary elements with symmetries
cites work: A non-commutative framework for topological insulators
cites work: Noncommutative geometry and reality
cites work: Classification of ``real'' Bloch-bundles: topological quantum systems of type AI
cites work: Spectral flows associated to flux tubes
cites work: Twisted equivariant matter
cites work: Q4956073
cites work: Bulk-edge correspondence for two-dimensional topological insulators
cites work: Topological insulators and \(C^{*}\)-algebras: theory and numerical practice
cites work: Q4160083
cites work: THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
cites work: On the \(C^*\)-algebraic approach to topological phases for insulators
cites work: EDGE CURRENT CHANNELS AND CHERN NUMBERS IN THE INTEGER QUANTUM HALL EFFECT
cites work: Bott periodicity for \(\mathbb Z_2\) symmetric ground states of gapped free-fermion systems
cites work: Periodic table for topological insulators and superconductors
cites work: Q3995493
cites work: \(K\)-theory and pseudospectra for topological insulators
cites work: Q4853983
cites work: The non-commutative \(n\)th-Chern number \((n\geq 1)\)
cites work: Non-commutative odd Chern numbers and topological phases of disordered chiral systems
cites work: Q4520088
cites work: Q3142515
cites work: \(\mathbb Z_{2}\)-indices and factorization properties of odd symmetric Fredholm operators
cites work: Symmetries, dimensions and topological insulators: the mechanism behind the face of the Bott clock
cites work: On the \(K\)-theoretic classification of topological phases of matter
cites work: K-THEORY FOR GRADED BANACH ALGEBRAS I
DOI: 10.1007/S00220-015-2530-6
description: scientific article; zbMATH DE number 6579794