Unconventional Piezoelectricity of Two-Dimensional Materials Driven by the Hall Effect

Piezoelectricity has been widely explored for nanoelectromechanical applications, yet its working modes are mainly limited in polar directions. Here we discover the intrinsic electro-mechanical response in crystal materials that is transverse to the conventional polarized direction, which is named unconventional piezoelectricity. A Hall-like mechanism is proposed to interpret unconventional piezoelectricity as charge polarization driven by a built-in electric field for systems with asymmetric Berry curvature distributions. Density functional theory simulations and statistical analyses justify such a mechanism and confirm that unconventional piezoelectricity is a general property for various two-dimensional materials with spin splitting or valley splitting. An empirical formula is derived to connect the conventional and unconventional piezoelectricity. The extended understanding of the piezoelectric tensor in quantum materials opens an opportunity for applications in multidirectional energy conversion, broadband operation, and multifunctional sensing.