Electron-lattice interaction and superconductivity in BaPb1-xBixO3and BaxK1-xBiO3

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.