Magnetic second-order topological insulators and semimetals

We propose magnetic second-order topological insulators (SOTIs). First, we study a three-dimensional model. It is pointed out that the previously proposed topological hinge insulator has actually surface states along the [001] direction in addition to hinge states. We gap out these surface states by introducing magnetization, obtaining a SOTI only with hinge states. The bulk topological number is the $Z_2$ index protected by the combined symmetry of the four-fold rotation and the inversion symmetry. We next study two dimensional magnetic SOTIs, where the corner states are robust also in the presence of the magnetization. Finally, we construct a magnetic second-order topological semimetals by layering the two-dimensional magnetic SOTIs, where hinge-arc states are robust also in the presence of the magnetization.