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Topological edge states of a graphene zigzag nanoribbon with spontaneous edge magnetism

The topological phases of graphene with spin-orbit coupling, an exchange field, and a staggered-sublattice potential determine the properties of the edge states of the zigzag nanoribbon. In the presence of the Hubbard interaction, the spontaneous magnetization at the zigzag terminations induces sizable magnetic moments at the lattice sites in the bulk region. Thus, the exchange field and staggered-sublattice potential in the bulk region are effectively changed, which in turn change the topological phase. Within a certain parameter regime, quasi-stable excited states of the zigzag nanoribbon exist, which have a different magnetism configuration at the zigzag terminations from the ground state. The quasi-stable excited states could effectively suppress the finite size effect of the topological edge states. The investigation of the topological edge states in the presence of interaction helps the engineering of spintronic nanodevices based on realistic materials.