2013/11/30 by Ian Mondragon-Shem, Juntao Song, Taylor L. Hughes +1 · 2 citations
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.113.046802
published as Phys. Rev. Lett. 113, 046802 (2014) · 5 pages 2 figures + 5 pages, 1 figure supplementary information
arxiv created 2013/12/07 · arxiv updated 2014/07/29
The chiral AIII symmetry class in the periodic table of topological insulators contains topological phases classified by a winding number ν for each odd space-dimension. An open problem for this class is the characterization of the phases and phase-boundaries in the presence of strong disorder. In this work, we derive a covariant real-space formula for ν and, using an explicit 1-dimensional disordered topological model, we show that ν remains quantized and non-fluctuating when disorder is turned on, even though the bulk energy-spectrum is completely localized. Furthermore, ν remains robust even after the insulating gap is filled with localized states, but when the disorder is increased even further, an abrupt change of ν to a trivial value is observed. Using exact analytic calculations, we show that this marks a critical point where the localization length diverges. As such, in the presence of disorder, the AIII class displays a markedly different physics from everything known to date, with robust invariants being carried entirely by localized states and bulk extended states emerging from an absolutely localized spectrum. Detailed maps and a clear physical description of the phases and phase boundaries are presented based on numerical and exact analytic calculations.