Characterization of the 2D Su–Schrieffer–Heeger Model with Second-Nearest-Neighbor Interactions

It is known that a 2D-dimerized Su–Schrieffer–Heeger model can produce a nontrivial topological phase. It is a simple nearest-neighbor model with four lattice sites in 2D. The Su–Schrieffer–Heeger model is easy to analyze but neglects important interaction in physical systems. Herein, an extended version of this model is proposed which includes all possible second-nearest-neighbor interactions in order to grant more flexibility when describing realistic systems. The addition of these interactions changes the symmetry of the model and as a result affects the topological properties. In order to characterize the topological changes to the model, a polarization invariant is used. It is further shown that these symmetry breaking interactions can be used to evoke a topological phase transition as well.