V. Mechanism of Superconductivity

Abstract

A possibility of phonon-mediated interaction as a mechanism of high- T c superconductivity is discussed. Because of different spatial distribution of Bloch wave function for up-spin particle and down-spin particle in the present model, the effective pair interaction which is derived from electron–phonon interaction is shown to have significant momentum- transfer dependence that is quite different from ordinary phonon-mediated interaction. This characteristic of pair interaction together with the geometric feature of Fermi-surface derived in a previous paper III leads to a dx2-y2 symmetric gap state which is consistent with experimental results. Since d-wave state has much smaller Coulomb repulsion term than s-wave state, strong electron-phonon coupling in the present model is expected to cause the occurrence of high-temperature superconductivity. However, in the present model, it is shown that a factor that reduces superconducting transition temperature appear as a result of a fluctuation effect of antiferromagnetic (AF) order of localized Cu spins. The factor λs which should be proportional to AF correlation length λ AF , determines the time scale τs which eliminates the contribution from the retarded effective pair interaction of time argument larger than τs. Existence of length scale λs explains why T c goes to zero as increasing hole carrier to some extent, and why non-magnetic impurity such as Pb reduces T c strongly. λs also explains the finite density of zero-gap states observed in overdoped regime or samples with non-magnetic impurities.