Superconductivity Due to the Softening of the Breathing Mode in Ba_1−xK_xBiO₃Compounds

Abstract

Recent experiments^1–3seem to indicate that the superconductivity in Ba_1−xK_xBiO₃compounds occurs in samples with stoichiometry close to the transition from metallic to charge density wave (CDW) state as the value of x decreases. The isotope effect has been measured for Ba_0.625K_0.375BiO₃and was found to be large (α=0.41), indicating that the pairing interaction is predominantly phonon -mediated⁴. Although a later measurement⁵indicates a smaller isotope effect (α=0.2). Evidence of phonon softening has also been observed very recently by neutron scattering in this type of material⁶. The crystal structure of Ba_1−xK_xBiO₃is similar to that of BaPb_xBi_1−xO ⁷₃ except the dopant K atom replaces Ba atom and leave the BiO₃octahedral network intact. The BiO based compound has perovskite-type structure with one Bi-atom surrounded by six nearest neighboring oxygen atoms in three dimension. The lattice formed by the Bi atoms in the metallic phase is simple cubic. In this article we assume that local breathing mode due to the oxygen atoms around a Bi-atom is responsible for both CDW and superconducting states and study the enhancement of the superconducting transition temperature T_Cdue to the softening of this mode from the metallic side near the CDW instability as a function of carrier doping. In the next section, we shall adopt the band structure from the tight binding theory to describe the motion of charged carriers on Bi atoms and discuss how the phonon spectrum can be renormalized and softened. in section III, the phonon softening is demonstrated numerically and the superconducting transition temperature T_Cis calculated as a function of the doping parameter x. The obtained result yields the essential feature of the experimental measurements³. A summary and discussion weill be given by Section IV.