2014/02/28 by Juntao Song, Emil Prodan · 2 citations
Physics and Astronomy · #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.89.224203
published as Phys. Rev. B 89, 224203 (2014) · 10 pages and 8 figures; one figure was added and some paragraphs were updated
arxiv created 2014/06/28 · arxiv updated 2014/07/01
Using an explicit 1-dimensional model, we provide direct evidence that the one-dimensional topological phases from the AIII and BDI symmetry classes follow a \mathbb Z-classification, even in the strong disorder regime when the Fermi level is embedded in a dense localized spectrum. The main tool for our analysis is the winding number ν, in the non-commutative formulation introduced in I. Mondragon-Shem, J. Song, T. L. Hughes, and E. Prodan, arXiv:1311.5233. For both classes, by varying the parameters of the model and/or the disorder strength, a cascade of sharp topological transitions ν=0 → ν=1 → ν=2 is generated, in the regime where the insulating gap is completely filled with the localized spectrum. We demonstrate that each topological transition is accompanied by an Anderson localization-delocalization transition. Furthermore, to explicitly rule out a \mathbb Z2 classification, a topological transition between ν=0 and ν=2 is generated. These two phases are also found to be separated by an Anderson localization-delocalization transition, hence proving their distinct identity.