Honeycomb lattice with multiorbital structure: Topological and quantum anomalous Hall insulators with large gaps

We construct a minimal four-band model for the two-dimensional (2D) topological insulators and quantum anomalous Hall insulators based on the p(x) -and p(y) -orbital bands in the honeycomb lattice. The multiorbital structure allows the atomic spin-orbit coupling which lifts the degeneracy between two sets of on-site Kramers doublets j(z) = +/- 3/2 and j(z) = +/- 1/2. Because of the orbital angular momentum structure of Bloch-wave states at Gamma and K (K') points, topological gaps are equal to the atomic spin-orbit coupling strengths, which are much larger than those based on the mechanism of the s-p band inversion. In the weak and intermediate regime of spin-orbit coupling strength, topological gaps are the global gap. The energy spectra and eigen wave functions are solved analytically based on Clifford algebra. The competition among spin-orbit coupling lambda, sublattice asymmetrym, and the Neel exchange field n results in band crossings at Gamma and K (K') points, which leads to various topological band structure transitions. The quantum anomalous Hall state is reached under the condition that three gap parameters., m, and n satisfy the triangle inequality. Flat bands also naturally arise which allow a local construction of eigenstates. The above mechanism is related to several classes of solid state semiconducting materials.