Moiré Topology in Twisted Structures with Noncollinear Spin-Orbit Coupling

Moiré superlattices provide a powerful platform for flat bands and correlated topological phases, yet most established examples rely on valley-contrasting Berry curvature in hexagonal lattices. Here, we propose a different route to achieve topological moiré minibands based on noncollinear spin-orbit coupling (SOC) in centrosymmetric type-II SOC bilayers. Interlayer hybridization opens local pseudogaps and produces sharply localized Berry curvature, which twisting reconstructs into isolated topological minibands without requiring valley degrees of freedom or hexagonal symmetry. We demonstrate this mechanism in tetragonal Dresselhaus-SOC HgI2, where a Lieb-like moiré potential yields topological flat bands. To improve miniband isolation, we develop a physics-informed machine-learning surrogate that identifies stronger SOC as a key design principle and guides the replacement of Hg by Pb. The resulting PbI2 minibands are narrower and better isolated, supporting correlation-driven magnetism and tunable quantum spin Hall and Chern insulating phases, thereby providing an optimized material realization for experimental exploration.