Transport in Z2 invariant in one and two-dimensional topological insulators models

The properties of the electric transport in the neighbourhood of the topological transition is investigated in some topological insulators models such as the Qi-Wu-Zhang model or Chern insulator with aim to verify the behavior of the AC and DC currents employing the Kubo formula of linear response theory. The system describes electrons hopping in one- and two-dimensional chains, in case of one-dimensional model with staggered hopping amplitudes. Our results show a strong effect of the sudden variation of the topological charge Q on conductivity for the two-dimensional Chern insulator case. For the one-dimensional model, we obtain an ideal conductor behavior for the DC current.