Non-Commutative Tools for Topological Insulators

Details Non-Commutative Tools for Topological Insulators Non-Commutative Tools for Topological Insulators

2009-11-14

arxiv.org/abs/0911.2816v4

New J. Phys. 12, 065003 (2010)

Physics

Condensed Matter

Statistical Mechanics

Final version (some arguments were corrected)

Scientific paper

10.1088/1367-2630/12/6/065003

This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have non-trivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.

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