Two-dimensional Dirac fermions on oxidized black phosphorus

Abstract

We explore the oxidation of a single layer of black phosphorus using ab initio density functional theory calculations. We search for the equilibrium structures of phosphorene oxides, PO_x with various oxygen concentrations x (0 ≤ x ≤ 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 and P–P bonds IR-active implying that the infrared spectra can be used to determine the degree of oxidation of phosphorene. Our electronic structure calculations reveal 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 symmetry-protected band structures including the band degeneracy and four-fold degenerate Dirac points. Our results provide an important guide in the search for the rare example of a Dirac semimetal with a higher level of degeneracy, giving significant insight into the relations between the symmetry of the lattice and band topology of electrons.