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We explore the oxidation of a single layer of black phosphorous using abinitio density functional theory calculation. We search for the equilibriumstructures of phosphorene oxides, PO$_x$ with various oxygen concentrations $x$($0{\le}x{\le}1$). By evaluating the formation energies with diverseconfigurations and their vibrational properties for each of various $x$ values,we identify a series of stable oxidized structures with $x$ and confirm thatthe oxidation occurs naturally. We also find that oxidation makes some modesfrom the P-O bonds P-P bonds IR-active implying that the infrared spectra canbe used to determine the degree of oxidation of phosphorene. Our electronicstructure calculation reveals that the fully oxidized phosphorene (PO) has adirect band gap of 0.83 eV similar to the pristine phosphorene. Intriguingly,the PO possesses two nonsymmorphic symmetries with the inversion symmetrybroken, guaranteeing a symmetry-protected band structures including the banddegeneracy and four-fold degenerate Dirac points. Our results may provide asignificant insight into the intriguing relations between symmetry of latticeand band topology of electrons.

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