Non-Commutative Tools for Topological Insulators
Statistical Mechanics
2010-06-22 v4 Disordered Systems and Neural Networks
Abstract
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.
Cite
@article{arxiv.0911.2816,
title = {Non-Commutative Tools for Topological Insulators},
author = {Emil Prodan},
journal= {arXiv preprint arXiv:0911.2816},
year = {2010}
}
Comments
Final version (some arguments were corrected)