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 pₓ- and py-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 jz=±3/2 and jz=±1/2. Because of the orbital angular momentum structure of Bloch-wave states at Γ and K4pt0ex(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 λ, sublattice asymmetry m, and the N\'eel exchange field n results in band crossings at Γ and K4pt0ex(K^') points, which leads to various topological band structure transitions. The quantum anomalous Hall state is reached under the condition that three gap parameters λ, 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.