Structural phase diagram and electron-phonon interaction in ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_3$

Using the local-density approximation and the full-potential linear muffin-tin-orbital method we have calculated the total energy of ${\mathrm{Ba}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{K}}_{\mathit{x}}$ ${\mathrm{BiO}}_3$ for x=0 and 0.5 as a function of tilting and breathing distortions. For x=0 we find an instability for a combination of both distortions and we correctly reproduce the monoclinic structure. For x=0.5 we correctly find the cubic phase to be stable. The frequencies of the tilting and breathinglike phonons are calculated for x=0 and 0.5. In the cubic structure we calculate the strength ${\lambda }_{\mathit{b}}$ of the electron-phonon coupling for the breathing mode as a function of x using a rigid-band approximation. For 0.37<x<0.5, ${\lambda }_{\mathit{b}}$≊0.3 and follows the trend of ${\mathit{T}}_{\mathit{c}}$. The superconductivity is conceivably mediated by the electron-phonon coupling.