Interplay between long-range hopping and disorder in topological systems

We extend the standard Su-Schrieffer-Heeger (SSH) model to include long-range hopping amplitudes and disorder, and analyze how the electronic and topological properties are affected. We show that long-range hopping can change the symmetry class and the topological invariant, while diagonal and off-diagonal disorder lead to Anderson localization. Interestingly, we find that the Lyapunov exponent gamma (E) can be linked in two ways to the topological properties in the presence of disorder-either due to the different response of midgap states to increasing disorder or due to an extra contribution to gamma due to the presence of edge modes. Finally, we discuss its implications in realistic transport measurements.