Long range piezoelectricity effects in van der Waals heterobilayer systems beyond 1000 atoms

Twist angle is a relevant design and control component for the piezoelectric coefficients of van der Waals (vdW) heterostructures. This theoretical work assesses in high detail the impact of the twist angle on the piezoelectricity of two-dimensional (2D) heterobilayer systems. We expand the density-functional based tight-binding method to predict the piezoelectric coefficients of twisted and corrugated 2D heterobilayer structures with more than 1000 atoms. We showcase the method on hexagonal III-V/transition metal dichalcogenide vdW heterosystems. Our calculations yield a periodic relationship between the in-plane piezoelectric coefficients and the corresponding twist angles, indicating the tunability of the in-plane piezoelectricity. In contrast, the out-of-plane piezoelectricity is not twist angle dependent, but nonlinearly changes with the average interlayer distance.