Laser-engineered <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="normal">Γ</mml:mi> </mml:math> -point topology in trigonal bismuthene

The $\mathrm{\ensuremath{\Gamma}}$-point topology represents a significant segment in the family of topological insulators. Here we provide a comprehensive prediction of light-induced $\mathrm{\ensuremath{\Gamma}}$-point-based topological manipulation in trigonal bismuthene and its derivatives. Our findings unveil a two-stage process of topological phase transitions (TPT) as the laser intensity increases. Initially, a quantum-spin-Hall or metallic state transitions to a quantum-anomalous-Hall (QAH) state ($C=\ifmmode\pm\else\textpm\fi{}3$), followed by another TPT that yields a compensated Chern-insulating state ($C=0$). The trigonal warping model accounts for these states, describing the ${C}_{3z}$-rotational band-inversion process, which is determined by $\ifmmode\pm\else\textpm\fi{}1$ orders of replica bands. Notably, this high Chern-number QAH state persists over a broad range of laser parameters. It remains functional beyond room temperature, as indicated by the substantial global energy gaps ($\ensuremath{\ge}60\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$) that are less constrained by other factors, including magnetic transition temperatures and doping effects. Our work provides a comprehensive roadmap towards the designer $\mathrm{\ensuremath{\Gamma}}$-point topology under laser excitation, facilitating applications of artificial topological materials.