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

摘要

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.