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