Topological phases of generalized Su-Schrieffer-Heeger models

We study the extended Su-Schrieffer-Heeger model with both nearest-neighbor and next-nearest-neighbor hopping strengths cyclically modulated and find the family of the model system exhibiting topologically nontrivial phases, which can be characterized by a nonzero Chern number defined in a two-dimensional space spanned by the momentum and a modulation parameter. It is interesting that the model has a similar phase diagram to that of the well-known Haldane model. We propose to use photonic crystal systems as the ideal systems to fabricate our model systems and probe their topological properties. Some other models with modulated on-site potentials are also found to exhibit similar phase diagrams, and their connection to the Haldane model is revealed.