Disorder-driven phase transitions in chiral-symmetric topological insulators

Chiral-symmetric topological insulators exhibit properties, such as polarization, that are robust to translation-symmetric perturbations provided the perturbations do not close the energy gap. However, it's unclear to what extent these topologically protected properties are robust to disorder, as disorder breaks the translation symmetry. Here we study a collection of 2D chiral-symmetric models with disorder using a covariant real space formula for the topological invariant. Generically, we find that the topological invariants remain precisely quantized until a critical value of disorder, at which point it smoothly decreases to zero. Furthurmore, we find that the critical disorder occurs exactly when states at the Fermi energy become delocalized. We therefore demonstrate that the topological characteristics are robust, and that in the presence of disorder the topology is protected by a mobility gap in place of an energy gap.