Robustness of topological edge states in amorphous systems

Since their discovery in crystalline materials, topological insulators have also been realized in amorphous solids, where non-trivial topology is captured by the real space version of the Chern number. Unlike the periodic lattice, disorder in amorphous structure induces Anderson localization of the bulk modes. Working with a model of an amorphous topological insulator with geometric disorder that preserves local coordination number, we study how the interplay of localization and nonlinearity improves the stability of edge states. The analytical investigation is based on the extracted finite-size scaling of the localization of the bulk modes. We also simulate time-domain evolution numerically, verifying suppressed dissipation in edge state propagation for the amorphous lattice compared with its periodic counterpart.