Magnetization-induced higher-order topological effects in quantum spin Hall insulators

Higher-order topological phases offer a promising platform for low-dissipation electronic and spintronic devices, motivating the search for experimentally accessible control schemes. Here we investigate higher-order topological states in a rhombic geometry of two-dimensional group-IV A materials subjected to external magnetic fields, described by a modified Kane-Mele model with next-nearest-neighbor Rashba spin-orbit coupling. We identify two distinct types of corner modes governed by different physical mechanisms: under out-of-plane magnetization, corner states emerge at the acute angles due to boundary hybridization induced by spin-orbit coupling, whereas under in-plane magnetization, corner modes appear at the obtuse angles as topologically protected Jackiw-Rebbi solitons arising at the domain wall between boundaries with different topological invariants. Using first-principles-based parameters for realistic materials including silicene, germanene, and stanene, we show that the obtuse-angle corner states are robust and enhanced in systems with stronger spin-orbit coupling. Our results establish a feasible route for magnetically creating and controlling higher-order topological states, enabling reconfigurable corner-mode-based topological devices.