Multiorbital edge and corner states in black phosphorene

TL;DR

This paper theoretically investigates multiorbital edge and corner localized states in monolayer black phosphorene, revealing their topological origins and dependence on the material's puckered structure.

Contribution

It introduces a multi-orbital tight-binding model to explain boundary localized modes and demonstrates the emergence of edge and corner states in black phosphorene.

Findings

Edge states appear along arbitrary crystallographic boundaries.

Multiple corner states emerge at intersections of edges.

Boundary states are explained by a simplified topological model.

Abstract

We theoretically study emergent edge/corner localized states in monolayer black phosphorene. Using the tight-binding model based on the density functional theory, we find that the multi-orbital band structure due to the non-planar 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 $3p_x$, $3p_y$, $3p_z$ 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 $90^{\circ}$.