Topological-transition-driven Giant Enhancement of Second-harmonic Generation in Ferroelectric Bismuth Monolayer

The interplay between band topology and light in condensed materials could unlock intriguing nonlinear optical phenomena, enabling modern photonic technologies such as quantum light sources and sub-wavelength topological lasers. Here, we unveil that a buckling-tuned topological transition in ferroelectric bismuth monolayer unleashes a giant second-harmonic generation. Using first-principles calculations, we surprisingly find that ferroelectric bismuth monolayer with a buckling parameter, $\Delta h$, has a large susceptibility $\chi^{(2)}$ on the order of $10^{7}$ $\mathrm{pm}^2/\mathrm{V}$, exceeding monolayer MoS$_2$ by about two orders of magnitude. When $\Delta h$ is engineered to the critical window where Dirac electrons emerge, a low-frequency resonance appears, boosting $\chi^{(2)}$ by an additional order of magnitude. We show that this enhancement is localized on the Dirac cones and dominated by intraband modification contributions. Based on an extended Dirac model, we establish that this enhancement physically originates from the ultralight effective masses $m^{*}$ of Dirac electrons through scaling with the Fermi velocity $v_F$ and band gap $E_g$. Our findings provide a general paradigm for achieving exceptional second-harmonic generation via engineering topological criticality, and could serve as an experimental signature of Dirac electrons in topological materials.