Non-commutative odd Chern numbers and topological phases of disordered chiral systems
Mathematical Physics
2016-10-27 v2 Disordered Systems and Neural Networks
math.MP
Operator Algebras
Abstract
An odd index theorem for higher odd Chern characters of crossed product algebras is proved. It generalizes the Noether-Gohberg-Krein index theorem. Furthermore, a local formula for the associated cyclic cocycle is provided. When applied to the non-commutative Brillouin zone, this allows to define topological invariants for 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 region of Anderson localization.
Keywords
Cite
@article{arxiv.1402.5002,
title = {Non-commutative odd Chern numbers and topological phases of disordered chiral systems},
author = {Emil Prodan and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:1402.5002},
year = {2016}
}
Comments
Final Version to appear in J. Funct. Anal., several corrections and improvements based on referee reports