Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder

Understand

The chiral AIII symmetry class in the periodic table of topological insulators contains topological phases classified by a winding number $\nu$ 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 $\nu$ and, using an explicit 1-dimensional disordered topological model, we show that $\nu$ remains quantized and non-fluctuating when disorder is turned on, even though the bulk energy-spectrum is completely localized.
• Furthermore, $\nu$ remains robust even after the insulating gap is filled with localized states, but when the disorder is increased even further, an abrupt change of $\nu$ to a trivial value is observed.