Widespread Negative Longitudinal Piezoelectric Responses in Ferroelectric Crystals with Layered Structures

In this study, we investigate the underlying mechanisms of universal negative piezoelectricity in low-dimensional layered materials by carrying out first-principles calculations. Two-dimensional ferroelectric $\mathrm{CuIn}{\mathrm{P}}_{2}{\mathrm{S}}_{6}$ is analyzed detail as a typical example, but theory can be applied to any other piezoelectrics. Consistent with proposed [Phys. Rev. Lett. 119, 207601 (2017), anomalous ${\mathrm{CuIn}\mathrm{P}}_{2}{\mathrm{S}}_{6}$ also results from its clamped-ion term, which cannot compensated positive internal-strain part. Here, focus on more general rule proposing that having term should among piezoelectric materials, attributed ``lag Wannier center'' effect. The change polarization due structural relaxation response strain, mostly determined spatial structure and chemical bonding material. material such ${\mathrm{CuIn}\mathrm{P}}_{2}{\mathrm{S}}_{6}$, approximately zero. This because internal molecular layers, are bonded weak van der Waals interaction, responds little strain. As result, magnitude dipole, depends strongly dimension layer, has small respect An equation bridging strain responses three-dimensional piezoelectrics derived analytically express point. work aims deepen our understanding about effect, especially provide strategies for discovering novel electromechanical properties.