Switchable band topology and geometric current in sliding bilayer elemental ferroelectric

We demonstrate that the sliding motion between two layers of the newly discovered ferroelectric and topologically trivial bismuth (Bi) monolayer Nature 617, 67 (2023) can induce a sequence of topological phase transitions, alternating between Z₂ trivial and nontrivial states. The lateral shift, while preserving spatial symmetry, can switch the quantum spin Hall state on and off. The sliding-induced changes in out-of-plane atomic buckling, which are directly coupled to inplane ferroelectricity, are shown to significantly modulate the band gap and drive the topological phase transitions. We map out the topological phase diagram and in-plane ferroelectricty with respect to sliding displacements. With appropriate sliding, the bismuth bilayer can transition into a nontrivial polar metal, exhibiting a pronounced shift current response arising from interband geometric quantities of electronic bands. Moreover, bilayer Bi supports a sliding-tunable nonlinear anomalous Hall response resulting from the geometric Berry curvature dipole. Configurations that are Z₂ nontrivial can generate drastically different transverse currents orthogonal to the external electric field, as both the direction and magnitude of the Berry curvature dipole at the Fermi level are highly sensitive to the sliding displacement. Our results suggest that bilayer bismuth, with its ability to generate multiple types of geometric currents, offers a versatile platform for power-efficient “Berry slidetronics” for multistate memory applications integrating both band topology and ferroelectricity.