## Abstract

The electron-lattice interaction of BaPb_{1-x}Bi_{x}O _{3} (BPB) and Ba_{x}K_{1-x}BiO_{3} (BKB) is studied microscopically by using the realistic electronic bands of BaBiO _{3} reproduced by the tight-binding model. It is found that the electron-lattice coupling coefficients have strong wavevector and mode dependences. The electron-lattice interaction causes a remarkable renormalization of the longitudinal oxygen stretching and/or breathing mode vibration. Superconductivity is discussed in the framework of the strong-coupling theory of the phonon mechanism. The spectral function alpha ^{2}F( omega ) has some prominent structures in the frequency range of the oxygen stretching/breathing mode. As x increases, some of the main peaks in alpha ^{2}F( omega ) shift to the lower-frequency side, reflecting the phonon frequency renormalisation. The transition temperature T_{c} and the energy gap function Delta ( epsilon ) at T=0 K have been evaluated by solving the Eliashberg equations. The calculated T_{c} increases rapidly with increasing x, and reaches about 30 K for x=0.7. The oxygen isotope shift of T_{c} in BKB is calculated and the characteristic exponent alpha defined by T_{c} varies as M_{O}^{alpha} (M_{O} is oxygen atomic mass) is evaluated to be 0.35-0.45. The superconducting energy gap Delta _{0} is evaluated to be 4.8 meV for x=0.7. The ratio 2 Delta _{0}/k_{B}T_{c} is found to have a value close to that predicted by the Bardeen-Cooper-Schrieffer weak-coupling theory (2 Delta _{0}/k_{B}T_{c}=3.5). However, the calculated tunnelling differential conductance dI/dV and its derivative d^{2}I/dV^{2} show behaviours that are characteristic to the strong-coupling superconductor.

Original language | English |
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Article number | 012 |

Pages (from-to) | 3553-3566 |

Number of pages | 14 |

Journal | Journal of Physics Condensed Matter |

Volume | 2 |

Issue number | 15 |

DOIs | |

Publication status | Published - 1990 |

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