Remote control of spin polarization of topological corner states

In two-dimensional higher-order topological insulators, the corner states are separated by a non-negligible distance. The crystalline symmetries protect the robustness of their corner states with long-range entanglement, which are robust against time-reversal-breaking perturbations. Here, we demonstrate the possibility of direct control of the topological corner states by introducing the spin degree of freedom in a rhombus-shaped Kekule nanostructure with local magnetization and local electric potential. By applying a local magnetization on one corner, the other corner can also be strongly spin polarized. By further applying a local electric potential at the same corner, the sign of the spin polarization can be reversed at both corners. We also prove the robustness of the control of the spin polarization under the disorder. Moreover, we demonstrate the material realization in a gamma-graphyne nanostructure with Mn adsorption and Si replacement at one corner by using first-principles calculations. Other higher-order lattices and the shape of the nanostructure are also discussed. Our studies give a showcase of the remote correlation of quantum states in higher-order topological materials for spintronic and quantum applications.