ROLES OF PHONON-INDUCED POTENTIALS FOR A BIPOLARON IN A SUPERCONDUCTOR

The bipolaronic system model of an infinite quantum well, in which two electrons or holes are weakly or intermediately coupled with both lon gitudinal optical (LO) and surface optical (SO) phonons, may be applie d to layer-type high-T-c superconductivity. A double unitary transform ation of the Hamiltonian is carried out. The numerical results show th at when the thickness of the polar slab increases the LO phonon contri bution to the binding energy increases but that from the SO phonon dec reases. On taking the Coulombic repulsion into account, the binding en ergy of the bipolaron is found to depend on the distance between the t wo electrons or holes. It is shown that the potential energy of the ef fective interaction of the two holes that form the stable bipolaron in a relatively thin polar slab of YBCO has a distinct equilibrium posit ion at its minimum. The magnitude of the binding energy of these two h oles becomes larger as the bipolaron size, taken as the equilibrium di stance between the holes, becomes smaller.