Electronic structure of the bond disproportionated bismuthate ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$

We present a comprehensive study on the silver bismuthate ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$, synthesized under high-pressure, high-temperature conditions, which has been the subject of recent theoretical work on topologically complex electronic states. We present x-ray photoelectron spectroscopy results showing two different bismuth states and x-ray absorption spectroscopy results on the oxygen $K$ edge showing holes in the oxygen bands. These results support a bond disproportionated state with holes on the oxygen atoms for ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$. We estimate a band gap of $\sim 1.25$ eV for ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ from optical conductivity measurements, which matches the band gap in density functional calculations of the electronic band structure in the nonsymmorphic space group $Pnn2$, which supports two inequivalent Bi sites. In our band structure calculations the disproportionated ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ is expected to host Weyl nodal chains, one of which is located $\sim 0.5$ eV below the Fermi level. Furthermore, we highlight similarities between ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ and the well-known disproportionated bismuthate ${\mathrm{BaBiO}}_3$, including breathing phonon modes with similar energy. In both compounds, hybridization of Bi $6s$ and O $2p$ atomic orbitals is important in shaping the band structure, but in contrast to the Ba $5p$ bands in ${\mathrm{BaBiO}}_3$, the Ag $4d$ bands in ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ extend up to the Fermi level.

Figure 1

(a) The powder x-ray diffraction pattern measured at room temperature of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ (top) and the calculated pattern for ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ in the $Pnn2$ phase (middle) and the $Pnna$ phase (bottom). (b) Part of the unit cell of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ in the $Pnn2$ phase with “${\mathrm{Bi}}^{3+}$” (purple) and “${\mathrm{Bi}}^{5+}$” (brown) highlighting the different oxygen metal distances [10]. (c) Unit cell of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ in the $Pnn2$ phase along the $ac$ plane showing the shared edges of the octahedra along the $a$ direction. (d) Unit cell of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ in the $Pnn2$ phase along the $bc$ plane. (e) Unit cell of ${\mathrm{BaBiO}}_3$ showing the corner-sharing octahedra and ${\mathrm{Bi}}^{3+}$ (red) and ${\mathrm{Bi}}^{5+}$ (blue).

Figure 2

X-ray photoelectron spectra of O, Ag, and Bi in ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ are shown in (a), (b), and (c), respectively. In (a) the three peaks A, B, and C are needed to fit the measured spectra for the O $1s$ states. In (b) the splitting between peaks D1 and D2 is consistent with that expected due to spin-orbit coupling (SOC) for Ag $3d$ states. In (c) the splitting between F1 and F2 is consistent with that expected due to SOC for Bi $4f$ states, and the same can be said for the split between G1 and G2. Due to the asymmetry of the measured spectra, four curves are needed to fit the Bi $4f$ states. This leads us to conclude the existence of two different Bi states in ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$, both close in energy to ${\mathrm{Bi}}^{3+}$ [15].

Figure 3

(a) The x-ray absorption spectra at the oxygen $K$ edge of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ and a reference sample of ${\mathrm{BaBiO}}_3$. (b) Optical spectroscopy data on ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ extracted from ellipsometry measurement. (c) Brillouin zone of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ with the high-symmetry points indicated by black dots. The nodal chains are schematically illustrated by the blue and red lines. At the $Z$ and $S$ points (yellow) there are fourfold degeneracies, formed by two Weyl points with opposite chirality. (d) Band structure of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ in the $Pnn2$ phase using DFT calculation with hybrid functionals.

Figure 4

(a) The DFT (LDA) band structures of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ in the $Pnn2$ phase. The contributions from the O $a_{1g}$ molecular orbital of the small (purple) and large (brown) octahedra are represented with fat bands. The colors for octahedra match the ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ unit cell presented in Fig. 1. (b) The band structures of ${\mathrm{BaBiO}}_3$ in the $P{2}_1/n$ phase. The contributions from the O $a_{1g}$ molecular orbital of the small (red) and large (blue) octahedra are represented with fat bands. The colors for octahedra match the ${\mathrm{BaBiO}}_3$ unit cell presented in Fig. 1. (c) Partial density of states (PDOS) of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$, showing the contribution from Ag, Bi, and O. (d) PDOS of ${\mathrm{BaBiO}}_3$, showing the contribution of Ba, Bi, and O.

Figure 5

(a) Raman spectra of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ at different $T$, between 290 and 10 K. (b) The same Raman spectra in (a), emphasizing the peak at 520 ${\mathrm{cm}}^{-1}$, characteristic of the breathing mode in disproportionated bismuthates. (c) Powder XRD of ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ collected at different $T$, between 293 and 203 K. The calculated XRD pattern for ${\mathrm{Ag}}_2{\mathrm{BiO}}_3$ in the $Pnn2$ phase is plotted at the bottom.