Topological bands in two-dimensional orbital-active bipartite lattices

The search for large gap quantum spin Hall (QSH) and anomalous (QAH) insulators is important both fundamental practical interests. degenerate multi-orbitals $p_x,p_y$ in honeycomb lattice provides a paradigm QSH state with boosted topological of the first order atomic spin-orbit coupling. By using elementary band representation, we explore feasibility this mechanism general two-dimensional lattices, find that biparticle lattices $C_{3v}$ or $C_{4v}$ symmetry could work. We further provide concrete tight-binding models on honeycomb, kagome square to demonstrate desired physics. introducing ferromagnetism into state, extend QAH gap. states can be achieved when Fermi level at integer filling only lattice, but certain fractional other lattices. conclude brief discussion possible material venues such mechanism.