Multiorbital edge and corner states in black phosphorene

Abstract

We theoretically study emergent edge- and corner-localized states in monolayer black phosphorene. Using the tight-binding model based on the density functional theory, we find that the multiorbital band structure due to the nonplanar puckered geometry plays an essential role in the formation of the boundary localized modes. In particular, we demonstrate that edge states emerge at a boundary along an arbitrary crystallographic direction, and it can be understood from the fact that the Wannier orbitals associated with $3{p}_{x},3{p}_{y},3{p}_{z}$ orbitals occupy all the bond centers of phosphorene. At a corner where two edges intersect, we show that multiple corner-localized states appear due to hybridization of higher-order topological corner state and the edge states nearby. These characteristic properties of the edge and corner states can be intuitively explained by a simple topologically equivalent model where all the bond angles are deformed to ${90}^{\ensuremath{\circ}}$.