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A Computational Non-commutative Geometry Program for Disordered Topological InsulatorsDisordered Topological Insulators: A Brief Introduction

A Computational Non-commutative Geometry Program for Disordered Topological Insulators:... [Our main goal for this Chapter is to introduce the periodic table of topological insulators and superconductors (see Table 1.1). Since the physical principles behind this table involve the robustness of certain physical properties against disorder, we will take a short detour and introduce first the class of homogeneous materials and then the sub-class of homogeneous disordered crystals. Our brief exposition introduces the main physical characteristics of these materials and puts forward a possible physical definition of the class of homogeneous materials. In parallel, it introduces general concepts from the mathematical program pioneered by Jean Bellissard and his collaborators (Bellissard, Lect. Notes Phys. 257, 99–156, 1986, [4], Bellissard, Geometric and Topological Methods for Quantum Field Theory, 2003, [7], Bellissard et al., Directions in Mathematical Quasicrystals, 2000, [5]), which will become central to our exposition.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Computational Non-commutative Geometry Program for Disordered Topological InsulatorsDisordered Topological Insulators: A Brief Introduction

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Publisher
Springer International Publishing
Copyright
© The Author(s) 2017
ISBN
978-3-319-55022-0
Pages
1 –9
DOI
10.1007/978-3-319-55023-7_1
Publisher site
See Chapter on Publisher Site

Abstract

[Our main goal for this Chapter is to introduce the periodic table of topological insulators and superconductors (see Table 1.1). Since the physical principles behind this table involve the robustness of certain physical properties against disorder, we will take a short detour and introduce first the class of homogeneous materials and then the sub-class of homogeneous disordered crystals. Our brief exposition introduces the main physical characteristics of these materials and puts forward a possible physical definition of the class of homogeneous materials. In parallel, it introduces general concepts from the mathematical program pioneered by Jean Bellissard and his collaborators (Bellissard, Lect. Notes Phys. 257, 99–156, 1986, [4], Bellissard, Geometric and Topological Methods for Quantum Field Theory, 2003, [7], Bellissard et al., Directions in Mathematical Quasicrystals, 2000, [5]), which will become central to our exposition.]

Published: Mar 18, 2017

Keywords: Homogeneous Material; Gibbs Measure; Topological Index; Topological Insulator; Atomic Configuration

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