Sliding Ferroelectricity Engineered Coupling between Spin Hall Effect and Layertronics in 2D Lattice

Coupling the spin Hall effect with novel degrees of freedom of electrons is central to the rich phenomena observed in condensed-matter physics. Here, using symmetry analysis and a low-energy k·p model, we report the sliding ferroelectricity engineered coupling between spin Hall effect and emerging layertronics, thereby generating the layer spin Hall effect (LSHE), in a 2D lattice. The physics is rooted in a pair of T-symmetry connected valleys, which experience spin splitting accompanied by large Berry curvature under spin-orbit coupling. The interaction between the out-of-plane ferroelectricity and electronic properties gives rise to the layer-locked Berry curvature and thus layer-polarized spin Hall effect (LP-SHE) in the bilayers. Such LP-SHE is strongly coupled with sliding ferroelectricity, enabling it to be ferroelectrically reversible. Using first-principles calculations, the mechanism is further demonstrated in a series of real bilayer systems, including MoS₂, MoTe₂, WSe₂, MoSi₂P₄, and MoSi₂As₄. These phenomena and insights open a new direction for spin Hall effect.