Topological insulators with second and third-neighbor couplings

The energy band of a topological insulator is calculated taken into account second and third neighbors. A tight-binding model based on the Bernevig-Hughes-Zhang (BHZ) approach for quantum wells is used to calculate the energies. The BHZ model is characterized by the mass term M(q)=Δ−Bq2. In the microscopic theory used here, the mass term is E−(q)=Δ−B(sin2⁡qxa/2+sin2⁡qya/2). That is modified when second and/or third neighbors are included in the model. As a consequence, depending on the parameters used the range where the material is an insulator is changed.