Importance of oxygen octahedra tilts for the electron-phonon coupling in K-doped BaBiO${}_3$

Despite considerable research efforts, a clear understanding of superconductivity in Ba${}_{0.5}$K${}_{0.5}$BiO${}_3$ has been elusive. Recent studies showed that although electron-correlation effects in this compound can significantly increase the electron-phonon coupling, they do not reproduce the measured Eliashberg spectral function (${\alpha }^{2}F$). We show that the oxygen octahedra tilts in Ba${}_{0.5}$K${}_{0.5}$BiO${}_3$ increase ${\alpha }^{2}F$ in the range of frequencies near 30 meV, even on the level of the generalized gradient approximation. This increase in ${\alpha }^{2}F$ changes its shape to provide better agreement with experiment and results in a 50–60% increase of the average electron-phonon coupling strength $\lambda$. We use the Wannier interpolation technique to determine the electron-phonon coupling with high precision.

Figure 1

Hybrid functionals (Ref. [19]) give an overall threefold increase of the VCA spectral function [${\alpha }^{2}F\left(\omega \right)$]. Our work shows that the octahedral rotations, even on the GGA level, transfer spectral weight towards lower frequencies (from $\sim$55 to $\sim$30 meV). The experimental results are taken from Ref. [4].

Figure 2

Three possible arrangements of the dopant atoms (K) in the 20-atom primitive unit cell of Ba${}_{0.5}$K${}_{0.5}$BiO${}_3$. Atomic colors are O: red; K: purple; Ba: green. Bi atoms are inside blue octahedra. All projections are along 110 direction (same as dominant octahedral tilt).

Figure 3

The electron band structure for a parent compound (BaBiO${}_3$) and a doped compound (Ba${}_{0.5}$K${}_{0.5}$BiO${}_3$) with different configurations of dopant atoms (I, II, and III, see Sec. 3a). For comparison we also show the band structure using the virtual crystal approximation (VCA) in the folded Brillouin zone. Total densities of states (black) and the oxygen $2p$ partial density of states (red) are given in the small panel on the right.

Figure 4

The phonon densities of states $F\left(\omega \right)$ (black, upper panel) and the Eliashberg spectral functions ${\alpha }^{2}F\left(\omega \right)$ (blue and red, lower panel). The experimental phonon density of states is from Ref. [4] and corresponds to Ba${}_{1-x}$K${}_x$BiO${}_3$ with $x=0.4$. Two measured Eliashberg spectral functions (red and blue) are from the same Ref. [4] and they correspond to $x=0.375$. We also show calculated $F\left(\omega \right)$ and ${\alpha }^{2}F\left(\omega \right)$ from this work ($x=0.5$) for the configuration of dopant atoms I and II (see Sec. 3a), as well as the calculation using virtual crystal approximation. The $F\left(\omega \right)$ is given in arbitrary units so that area under the curve is the same in each panel.

Figure 5

The Fermi-surface nesting function (Refs. [36] and [37]) (green, above) and the electron-phonon coupling ${\lambda }_{\vec{Q}}$ (black, below) along a path in the phonon Brillouin zone. We show results for Ba${}_{0.5}$K${}_{0.5}$BiO${}_3$ both in the configurations I and II (see Sec. 3a) and for the virtual crystal approximation (VCA). The nesting function is given in arbitrary units. In the plot we impose ${\lambda }_{\vec{Q},\nu }$ to be equal to zero for small $\vec{Q}$ and ${\omega }_{\nu }$.