Magnetic field modulation of corner states in a quantum spin hall insulator

The discovery of higher-order topological phases has brought the exploration of higher-order topological materials to the forefront of topological matter research. In this work, we employ Wannier function center calculations to identify the quantum spin Hall effect in a modified Kane-Mele model that incorporates next-nearest-neighbor Rashba spin-orbit coupling, effectively capturing the essential physics of two-dimensional group IVA materials, such as graphene and silicene. By integrating rigorous theoretical modeling with high-precision numerical calculations, we systematically compute the band structures and spatial weight distributions of particle states, thereby obtaining distinct types of corner states under two axial magnetization configurations. The ability to modulate these corner states by controlling magnetization orientation opens up new opportunities for potential device applications, especially in topological electronics and spintronic systems.