Quantum Spin Hall (QSH) insulators with a large topologically nontrivial bulk gap are crucial for future applications of the QSH effect. Among these, group III-V monolayers and their halides with chair structure (regular hexagonal framework, RHF) were widely studied. Using first-principles calculations, we propose a new structure model for the functionalized group III-V monolayers, which consist of rectangular GaBi-X2 (X=I, Br, Cl) monolayers with a distorted hexagonal framework (DHF). These structures have a much lower energy than the GaBi-X2 monolayers with chair structure. Remarkably, the DHF GaBi-X2 monolayers are all QSH insulators, which exhibit sizeable nontrivial band gaps ranging from 0.17 eV to 0.39 eV. Those band gaps can be widely tuned by applying different spin-orbit coupling (SOC) strengths, resulting in a distorted Dirac cone.
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