The Non-Commutative Geometry of the Complex Classes of Topological Insulators

• Authors: Emil Prodan
• Languages of publication: EN

Abstracts

EN

Alain Connes’ Non-Commutative Geometry program
[1] has been recently carried out [2, 3] for the entire
A- and AIII-symmetry classes of topological insulators,
in the regime of strong disorder where the insulating
gap is completely filled with dense localized spectrum.
This is a short overview of these results, whose goal is to
highlight the methods of Non-Commutative Geometry involved
in these studies. The exposition proceeds gradually
through the cyclic cohomology, quantized calculus with
Fredholm-modules, local formulas for the odd and even
Chern characters and index theorems for the odd and even
Chern numbers. The characterization of the A- and AIIIsymmetry
classes in the presence of strong disorder and
magnetic fields emerges as a natural application of these
tools.

Keywords

EN

topological insulators; non-commutative geometry; aperiodic crystals; A- and AIII-symmetry classes

• Publisher: De Gruyter Open
• Journal: Topological Quantum Matter
• Year: 2014
• Volume: 1
• Issue: 1

Dates

received

23 - 2 - 2014

online

30 - 6 - 2014

accepted

6 - 6 - 2014

Contributors

author

Emil Prodan

• Department of Physics,
  Yeshiva University, 245 Lexington Av, 10016 New York, USA

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Identifiers

DOI

10.2478/topor-2014-0001