Localization in two-dimensional trivial and Chern insulators

We investigate the localization properties of two-dimensional tight-binding models using transfer matrix methods. In particular, we numerically determine the localization length for cylindrical lattices with single-particle hamiltonians that have nearest-neighbor and next-nearest-neighbor hopping terms, both in the trivial and Chern insulator phases. We consider the role of disorder strength and particle energy on localization, and construct phase diagrams of conductivity properties. In addition, we use these results to guide an exploration of the critical behavior of localization-delocalization transitions in these models.