Microscopic theory of electron-phonon interaction and superconductivity of BaPb_1-xBi_xO₃

Electron-phonon coupling coefficients in BaPb_1-xBi_xO₃ are calculated microscopically on the basis of the tight-binding band model which utilizes energy band structures obtained with the use of the self-consistent LAPW method by Mattheiss and Hamann. Assuming the rigid-band model we calculate, as a function of Bi concentration x, the dimension-l less electron-phonon coupling constant λ in McMillan's strong-coupling theory of superconductor. We obtain large values of λ such as λ>1 for x>0.1. The origin of this large electron-phonon coupling is ascribed to: (i) the hybridization between 2pσ orbitals of 0 atoms and 6s orbitals of Pb or Bi atoms is large in the conduction band, (ii) this σ-bonding is strongly affected by a vibrational motion of 0 atoms in the direction connecting the 0 and Pb (Bi) atoms, and (iii) the mass of 0 atoms is light. We also evaluate superconducting transition temperature T_c as a function of x on the basis of the McMillan-Allen-Dynes equation. The results explain semi-quantitatively the observed x-dependence of T_c.