Electron-phonon coupling and properties of doped ${\mathrm{BaBiO}}_3$

We report density-functional calculations based on the local-density approximation (LDA) of the properties of doped barium bismuthates. Using the linear-response approach developed in the framework of the linear muffin-tin-orbital method the phonon spectrum of the ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{BiO}}_3$ system is calculated and is compared with the results of the neutron-diffraction measurements. The effect of doping in the calculation is modeled by the virtual crystal and mass approximations. The electron-phonon coupling constant $\lambda$ is then evaluated for a grid of phonon wave vectors using the change in the potential due to phonon distortion found self-consistently. A large coupling of the electrons to the bond-stretching oxygen vibrations and especially to the breathinglike vibrations is established. Also, a strongly anharmonic potential well is found for the tiltinglike motions of the oxygen octahedra. This mode is not coupled to the electrons to linear order in the displacements; therefore an anharmonic contribution to $\lambda$ is estimated using the frozen-phonon method. Our total (harmonic plus anharmonic) $\lambda$ is found to be 0.34. This is too small to explain high-temperature superconductivity in ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{BiO}}_3$ within the standard mechanism. Finally, based on standard LDA and LDA+$U$ like calculations, a number of properties of pure ${\mathrm{BaBiO}}_3$ such as tilting of the octahedra, breathing distortion, charge disproportionation, and semiconducting energy gap value is evaluated and discussed in connection with the negative-$U$ extended Hubbard model frequently applied to this compound.