Spin separation and filtering assisted by topological corner states in the Kekulé lattice

Higher-order topological corner states have been realized in a two-dimensional Kekul\'e lattice, which can be further coupled with spin polarization through the implementation of local magnetization. In this paper, we numerically investigate the spin-dependent transport properties assisted by topological corner states in the Kekul\'e lattice. By applying local magnetization and an electric potential, the topological corner states are spin polarized with opposite spins localized at different corners, thereby demonstrating a spin-corner state locking mechanism. Transport characteristics, including transmission, local density of states, and local current density, are calculated for a two-terminal setup consisting of a diamond-shaped Kekul\'e lattice connected to two leads. When opposite local magnetization is applied to the corners, spin-up and spin-down electrons are perfectly separated, forming two spin-polarized conducting channels and leading to spin spatial separation. In the presence of identical local magnetization on both corners and an electric potential at one corner, the spin-polarized corner states can facilitate selective filtering of different spins and generate spin-polarized currents by tuning the energy. Furthermore, spin-resolved transmission diagrams as functions of both the Fermi energy and electric potential are presented, illustrating the global distribution of spin filtering through topological corner states.