Large in-plane negative piezoelectricity and giant nonlinear optical susceptibility in elementary ferroelectric monolayers

Negative piezoelectrics contract in the direction of applied electric field, which are opposite to normal piezoelectrics and rare in dielectric materials. The raising of low dimensional ferroelectrics, with unconventional mechanisms of polarity, opens a fertile branch for candidates with prominent negative piezoelectricity. Here, the distorted $\alpha$-Bi monolayer, a newly-identified elementary ferroelectric with puckered black phosphorous-like structure [J. Guo, {\it et al}. Nature \textbf{617}, 67 (2023)], is computationally studied, which manifests a large negative in-plane piezoelectricity (with $d_{33}\sim-26$ pC/N). Its negative piezoelectricity originates from its unique buckling ferroelectric mechanism, namely the inter-column sliding. Consequently, a moderate tensile strain can significantly reduce its ferroelectric switching energy barrier, while the compressive strain can significantly enhance its prominent nonlinear optical response. The physical mechanism of in-plane negative piezoelectricity also applies to other elementary ferroeletric monolayers.