Topological bands in two-dimensional orbital-active bipartite lattices

The search for large gap quantum spin Hall (QSH) and quantum anomalous Hall (QAH) insulators is important both for fundamental and practical interests. The degenerate multiorbitals ${p}_x,{p}_y$ in a honeycomb lattice provides a paradigm for the QSH state with a boosted topological gap of the first order in atomic spin-orbit coupling. By using an elementary band representation, we explore the feasibility of this mechanism for QSH in general two-dimensional lattices, and find that the biparticle lattices with ${C}_3v$ or ${C}_4v$ symmetry and degenerate multiorbitals could work. We further provide concrete tight-binding models on honeycomb, kagome, and square lattices to demonstrate the desired topological physics. By introducing ferromagnetism into the QSH state, we extend the mechanism to the QAH state with a boosted gap. The QSH and QAH states can be achieved when the Fermi level is at integer filling only for a honeycomb lattice, but at certain fractional filling for the other lattices. We conclude with a brief discussion on the possible material venues for such a mechanism.