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

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.