Manipulation of Dirac states in polymorphic and dual topological insulating phases of van der Waals systems

Van der Waals (vdW) layered systems provide a versatile platform for exploring dual topological insulator phases, characterized by the coexistence of nontrivial $${{\mathbb{Z}}}₂$$ invariants and mirror Chern numbers $${C}_M$$ . Here, we demonstrate that stacking sequences in vdW materials can introduce additional mirror symmetry, enabling surface states robust against perturbations through multiple symmetry protections. The polymorphic nature of these systems introduces stacking-dependent mirror planes, allowing control over the topology of surface Dirac states. We further show that the spin texture of these surface states determines the direction of Dirac point shifts under time-reversal symmetry breaking. This response reveals the interplay between spin momentum locking and external fields. Additionally, we find that surface responses to magnetic fields vary with termination layers, offering enhanced tunability. These results highlight the potential of vdW systems as robust platforms for realizing and manipulating symmetry-protected topological phases, with promising implications for spintronic and quantum device applications.