Topological edge and corner states and fractional corner charges in blue phosphorene

We theoretically study emergent edge and corner states in monolayer blue phosphorus (blue phosphorene) using the first-principles calculation tight-binding model. show that existence of Wannier orbitals at every bond center yields both zigzag armchair nanoribbons. The properties can be well described by a simple effective Hamiltonian for uncoupled orbitals, where structural relaxation near boundary significantly affects band structure. For states, we examine two types structures consisting edges, find multiple emerge bulk gap as consequence hybridization orbitals. In corner, particular, demonstrate appear right Fermi energy, which leads to emergence fractional charge due filling anomaly. Finally, discuss relationship between phosphorene black phosphorene, systems share equivalent orbital positions similar edge/corner state even though their atomic are totally different.