Interlayer Registry Dictates Interfacial 2D Material Ferroelectricity.

We discover that the complex ferroelectric response of layered materials toward interlayer sliding is fully dictated by the interlayer lattice registry. Importantly, the entire sliding polarization landscape of two-dimensional (2D) layered material interfaces is fully described via a simple and intuitive geometric measure, termed the polarization registry index (PRI), that quantifies the degree of interlayer commensurability. Beyond the understanding of the fundamental origin of 2D ferroelectricity, the developed tool also provides highly efficient characterization and rationalization of existing experimental and computational evidence of 2D interfacial ferroelectricity, as well as the prediction of emergent controllable polarization in new noncentrosymmetric layered systems.