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arXiv · 1607.04013

Topological insulators from the perspective of non-commutative geometry and index theory

Hermann Schulz-Baldes
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Abstract

Topological insulators are solid state systems of independent electrons for which the Fermi level lies in a mobility gap, but the Fermi projection is nevertheless topologically non-trivial, namely it cannot be deformed into that of a normal insulator. This non-trivial topology is encoded in adequately defined invariants and implies the existence of surface states that are not susceptible to Anderson localization. This non-technical review reports on recent progress in the understanding of the underlying mathematical structures, with a particular focus on index theory.

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Hermann Schulz-Baldes. 2016-07-14. Topological insulators from the perspective of non-commutative geometry and index theory. https://arxiv.org/abs/1607.04013

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