Cooperation and competition of electron-electron interaction and electron-lattice interaction in oxides

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1."Electron correlation and electron-lattice interaction in high Tc cuprates" : Cooperation and competition between electron correlation and electron-lattice interaction in cuprate superconductors are investigated. In particular, the half-breathing mode in the ab plane is focused on. Effects of the electron correlation are taken into account as a vertex correction of the electron-phonon interaction. We reveal that the half-breathing mode of the oxygen ions supports the d-wave superconductivity, and reproduce the anomalous phonon dispersion relation observed in the inelastic neutron scattering.2."Dilution effects in orbital ordered system" : Dilution effects on the long range orbital ordered systems are examined. Recent experimental results show that the orbital ordering temperature rapidly reduces with doping Zn in KCuF_3, in comparison with the diluted magnets. The theoretical model based on the electron-electron interaction and the electron-phonon interaction is investigated by using the Monte-Carlo simulation. We show that the decreasing of the orbital ordering temperature is remarkable in comparison with the prediction of the conventional percolation scenario. This is attributed to the unique interaction between orbitals.3."Electron-electron interaction and electron-lattice interaction in perovskite vanadates" : The perovskite vanadates R_<1-x>A_xVO_3 show the two kinds of spin and orbital ordered patters, i.e. spin-C/orbital-G and spin-G/orbital-C orders. It is revealed experimentally that by doping of a tiny amount of holes, the spin-G/orbital-C phase is rapidly collapsed. We examine the hole motion in the spin and orbital ordered vanadates based on the model where the electron-electron interaction and the electron-lattice interaction are taken into account simultaneously.