Multiple Unpinned Dirac Points in Group-Va Single-layers with Phosphorene Structure

TL;DR

This study reveals the emergence of fully unpinned (type-II) Dirac points in group-Va 2D materials with phosphorene structure, including their protection mechanisms and potential to become quantum spin Hall insulators under spin-orbit coupling.

Contribution

It reports the discovery of fully unpinned (type-II) Dirac points in 2D group-Va materials, a novel finding in the electronic structure of these phosphorene-like layers.

Findings

Discovery of two types of Dirac points in group-Va 2D layers.

Identification of fully unpinned (type-II) Dirac points at generic k-points.

Spin-orbit coupling can gap Dirac points, leading to quantum spin Hall phases.

Abstract

Emergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitute one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black phosphorous, has been a subject of intense investigations recently, and it was found that other group-Va elements could also form 2D layers with similar puckered lattice structure. Here, by a close examination of their electronic band structure evolution, we discover two types of Dirac fermion states emerging in the low-energy spectrum. One pair of (type-I) Dirac points is sitting on high-symmetry lines, while two pairs of (type-II) Dirac points are located at generic $k$-points, with different anisotropic dispersions determined by the reduced symmetries at their locations. Such fully-unpinned (type-II) 2D Dirac points are discovered for the first time. In the absence of spin-orbit coupling, we find that each Dirac node is protected by the sublattice symmetry from gap opening, which is in turn ensured by any one of three point group symmetries. The spin-orbit coupling generally gaps the Dirac nodes, and for the type-I case, this drives the system into a quantum spin Hall insulator phase. We suggest possible ways to realize the unpinned Dirac points in strained phosphorene.