Influence of Electron–Phonon Interaction on Transition Temperature and Isotope Effect of Ba0.6K0.4BiO3

Abstract

We employ a three-square-well model for the three interactions namely, electron-acoustic phonon, electron-optical phonon, and Coulomb in the calculation of superconducting transition temperature (Tc) and isotope effect coefficient (α) for cubic perovskite Ba0.6K0.4BiO3. The analytical solutions for the energy gap equation allow us to understand the relative interplay of these interactions. To correlate the Tc with various coupling strengths as electron-acoustic phonon (λac), electron-optical phonon (λop) and Coulomb (μ*), we present curves of Tc with them. The values of the coupling strength and of the Coulomb interaction parameter indicate that the superconductor is in the intermediate coupling regime. The superconducting transition temperature of optimally doped Ba—K—BiO is estimated as 29 K for λac of ≈0.3, λop of ≈0.2, and μ* of ≈0.12. The present approach also explains the reported oxygen isotope effect in the test material. We suggest from these results that both the acoustic and optical phonons within the framework of a three-square-well scheme consistently explains the effective electron–electron interaction leading to superconductivity in doped cubic perovskites.