Valence skipping, internal doping, and site-selective Mott transition in ${\mathrm{PbCoO}}_3$ under pressure

We present a computational study of ${\mathrm{PbCoO}}_3$ at ambient and elevated pressure. We employ the static and dynamic treatment of local correlation in the form of density functional theory $+$ $U$ $(\mathrm{DFT}+U)$ and $+$ dynamical mean-field theory $(\mathrm{DFT}+\mathrm{DMFT})$. Our results capture the experimentally observed crystal structures and identify the unsaturated Pb $6s–\mathrm{O}$ $2p$ bonds as the driving force beyond the complex physics of ${\mathrm{PbCoO}}_3$. We provide a geometrical analysis of the structural distortions and we discuss their implications, in particular the internal doping, which triggers a transition between phases with and without local moments and a site-selective Mott transition in the low-pressure phase.

Figure 1

(a) Energy vs volume curves for various structures obtained with $\mathrm{DFT}+U$ of $U_{\mathrm{eff}}=5.9$ eV. The bottom of the $c$-phase is set to zero energy. (b) Volume vs pressure curves with $P_c=30$ GPa, obtained by common tangent construction from (a).

Figure 2

Orbital-resolved densities of states of simple perovskite structure obtained with $\mathrm{DFT}+U$ of $U_{\mathrm{eff}}=5.9$ eV. The orbitals are defined as atomic sphere projections of given angular symmetry.

Figure 3

(a) O-displacements due to tilting of the ${\mathrm{CoO}}_6$ octahedron. (Red dots mark the O ions, Pb ions sit in the corners of the cube.) Diagonal (b) and parallel (c) displacements of O ions in the PbO layer. (Pb ions sit in the vertices, O ions in the square centers.) The $c$ (d) and $t$ (e) structures with O sites (red) and Pb sites (gold). The green plaquettes and cuboids belong to Pb sites with a saturated Pb 6s–O 2p bond.

Figure 4

Dispersion of isolated Pb $6s$ antibonding state in (a) simple perovskite, (b) $c^{*}$-phase, and (c) $t$-phase. All bands are unfolded into the Brillouin zone of the simple perovskite [51]. The right panels show the densities of states projected on inequivalent Pb sites. Note that $E=0$ does not mean Fermi energy in this construction.

Figure 5

Left: $\mathrm{DFT}+\mathrm{DMFT}$ orbital-resolved densities of states in the $c$ structure (low-pressure structure) on (a) Co LB site, (b) Co SB site, and (c) Pb lone and plaquette, and O sites. (The orbitals correspond to the Wannier basis.) The imaginary parts of the DMFT self-energies $\mathrm{\Sigma }\left(\omega \right)$ of the Co $3d$ orbitals are shown in the insets of panels (a) and (b). Right: $\mathrm{DFT}+\mathrm{DMFT}$ orbital-resolved projected density of states in the $t$ structure (high-pressure structure) on (d) Co site, (e) Pb lone, plaquette, and cuboid. The element resolved spectra are shown in panel (f). The inset in panel (e) shows the low-energy region.

Figure 6

Weights of dominant atomic states in $d^6$ (green), $d^7$ (red), and $d^8$ (blue) occupation sectors at (a) Co LB site and (b) Co SB site calculated by the $\mathrm{DFT}+\mathrm{DMFT}$ method. The spin-correlation function ${\chi }_{\mathrm{spin}}\left(\tau \right)$ calculated at the Co LB and the Co SB site is shown in the inset of panel (a) and (b), respectively.