Calculations of the electronic structure and superconducting properties of ${\mathrm{BaPb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Sb}}_{\mathit{x}}$${\mathrm{O}}_3$

We have performed a band-structure calculation of the cubic perovskite compound ${\mathrm{BaSbO}}_3$ by the augmented-plane-wave method. Using these results we have constructed an accurate tight-binding Hamiltonian which we used to calculate the density of states of the alloy ${\mathrm{BaPb}}_{0.75}$ ${\mathrm{Sb}}_{0.25}$ ${\mathrm{O}}_3$ by the coherent-potential approximation. We have also calculated the electron-phonon coupling and found that such coupling can explain the low transition temperature ${\mathit{T}}_{\mathit{c}}$ of this alloy system and the higher ${\mathit{T}}_{\mathit{c}}$ for the Bi-doped alloy. A prediction is made for a much higher transition temperature for Sb- or Bi-rich alloys.