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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 multiorbitalstructure allows the atomic spin-orbit coupling which lifts the degeneracybetween two sets of on-site Kramers doublets $j_z=\pm\frac{3}{2}$ and$j_z=\pm\frac{1}{2}$. Because of the orbital angular momentum structure ofBloch-wave states at $\Gamma$ and $K(K^\prime)$ points, topological gaps areequal to the atomic spin-orbit coupling strengths, which are much larger thanthose based on the mechanism of the $s$-$p$ band inversion. In the weak andintermediate regime of spin-orbit coupling strength, topological gaps are theglobal gap. The energy spectra and eigen wave functions are solved analyticallybased on Clifford algebra. The competition among spin-orbit coupling $\lambda$,sublattice asymmetry $m$ and the N\'eel exchange field $n$ results in bandcrossings at $\Gamma$ and $K (K^\prime)$ points, which leads to varioustopological band structure transitions. The quantum anomalous Hall state isreached under the condition that three gap parameters $\lambda$, $m$, and $n$satisfy the triangle inequality. Flat bands also naturally arise which allow alocal construction of eigenstates. The above mechanism is related to severalclasses of solid state semiconducting materials.

The honeycomb lattice with multi-orbital structure: topological and quantum anomalous Hall insulators with large gaps