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.

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• Kane-Mele model
• Quantum anomalous Hall effect
• Quantum spin Hall effect
• Topological insulators
• Topological phases of matter