A Multipolar Approach to Understanding Sliding Ferroelectricity

Despite studies which separately address the symmetry changes and the local electron density distortions that accompany the sliding ferroelectric transition, theoretical approaches toward understanding what drives the transition have yet to fully unite these two pictures. Here, we develop an approach for doing so by relating distortions of the electron density to symmetry-adapted combinations of local basis functions. Our methodology utilizes a rigorous combination of group theory and ab-initio density functional theory to identify which symmetry-adapted components of the microscopic electron density are responsible for inducing sliding ferroelectricity via their distortions. In this way, we find for honeycomb bilayer systems that combinations of dipole-like and quadrupole-like distortions of lone pair electrons mainly control the transition. We expect that this approach can be generalized to any semiconducting sliding ferroelectric to inform future functional materials design.