Non-commutative odd Chern numbers and topological phases of disordered chiral systems
Prodan E, Schulz-Baldes H (2016)
Publication Type: Journal article
Publication year: 2016
Journal
Publisher: Elsevier
City/Town: to appear in
Book Volume: 271
Pages Range: 1150-1176
Journal Issue: 5
URI: http://de.arxiv.org/abs/1402.5002
DOI: 10.1016/j.jfa.2016.06.001
Abstract
An index theorem for higher Chern characters of odd Fredholm modules over crossed product algebras is proved, together with a local formula for the associated cyclic cocycle. The result generalizes the classic Noether–Gohberg–Krein index theorem, which in its simplest form states that the winding number of a complex-valued function over the circle is equal to the index of the associated Toeplitz operator. When applied to the non-commutative Brillouin zone, this generalization allows to define topological invariants for all condensed matter phases from the chiral unitary (or AIII-symmetry) class in the presence of strong disorder and magnetic fields, whenever the Fermi level lies in a region of Anderson localized spectrum.
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APA:
Prodan, E., & Schulz-Baldes, H. (2016). Non-commutative odd Chern numbers and topological phases of disordered chiral systems. Journal of Functional Analysis, 271(5), 1150-1176. https://dx.doi.org/10.1016/j.jfa.2016.06.001
MLA:
Prodan, Emil, and Hermann Schulz-Baldes. "Non-commutative odd Chern numbers and topological phases of disordered chiral systems." Journal of Functional Analysis 271.5 (2016): 1150-1176.
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