Electron-lattice interaction and superconductivity in BaPb _1-xBi_xO₃ and Ba_xK _1-xBiO₃

The electron-lattice interaction of BaPb_1-xBi_xO ₃ (BPB) and Ba_xK_1-xBiO₃ (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 ²F( 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 ²F( 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_BT_c is found to have a value close to that predicted by the Bardeen-Cooper-Schrieffer weak-coupling theory (2 Delta ₀/k_BT_c=3.5). However, the calculated tunnelling differential conductance dI/dV and its derivative d²I/dV² show behaviours that are characteristic to the strong-coupling superconductor.