Polymorphic and dual topological insulating phases of van der Waals layered materials

We present a study that explores the exotic characteristics of van der Waals (vdW) layered systems, which exhibit both topological insulators and topological crystalline insulators. This intriguing behavior gives rise to the emergence of a dual topological insulator (DTI) within this vdW layered system, characterized by a nontrivial invariant and a nontrivial mirror Chern number . By considering the stacking order of InTe, chosen as an example of vdW layered materials, we discovered the formation of an additional mirror symmetry that enhances the robustness of the surface state against perturbations. These polymorphic variations lead to a triply-protected surface state, combining the newly formed mirror symmetry with the existing mirror symmetry and the time-reversal symmetry. Furthermore, we found that the Dirac states in InTe not only withstand time-reversal symmetry-breaking magnetic fields but also exhibit a displacement away from the time-reversal invariant momentum points, with the direction of movement determined by the spin texture. The dual topological nature induced by vdW stacking offers exciting possibilities for controlling the stability and mobility of Dirac surface states, thus opening avenues for the development of highly versatile and reliable DTI-based devices.