Symmetry-Protected Degeneracies in the Electronic Band Structure of Oxidized Black Phosphorous

Abstract

We explore the oxidation of a single layer of black phosphorous using ab initio density functional theory calculation. We search for the equilibrium structures of phosphorene oxides, PO${}_x$ with various oxygen concentrations $x$ ($0\le x\le 1$). By evaluating the formation energies with diverse configurations and their vibrational properties for each of various $x$ values, we identify a series of stable oxidized structures with $x$ and confirm that the oxidation occurs naturally. We also find that oxidation makes some modes from the P-O bonds P-P bonds IR-active implying that the infrared spectra can be used to determine the degree of oxidation of phosphorene. Our electronic structure calculation reveals that the fully oxidized phosphorene (PO) has a direct band gap of 0.83 eV similar to the pristine phosphorene. Intriguingly, the PO possesses two nonsymmorphic symmetries with the inversion symmetry broken, guaranteeing a symmetry-protected band structures including the band degeneracy and four-fold degenerate Dirac points. Our results may provide a significant insight into the intriguing relations between symmetry of lattice and band topology of electrons.

arXiv comment15 pages, 4 figures

References in corpus (15)

• Phonons and related properties of extended systems from density-functional perturbation theory
• Black phosphorus field-effect transistors
• Phosphorene: A New 2D Material with High Carrier Mobility
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Isolation and characterization of few-layer black phosphorus
• Electric field effect in ultrathin black phosphorus
• Semiconducting layered blue phosphorus: A computational study
• Environmental instability of few-layer black phosphorus
• Dirac Semimetals in Two Dimensions
• Oxygen defects in phosphorene
• Phosphorene oxides: bandgap engineering of phosphorene by oxidation
• Phosphorene Oxide: Stability and electronic properties of a novel 2D material
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Spin-Orbit Semimetals in the Layer Groups
• Hidden antiunitary symmetry behind "accidental" degeneracy and its protection of degeneracy

Cited by in corpus (1)

• Simple linear response model for predicting energy band alignment of two-dimensional vertical heterostructure