THEORY OF THE ORBITAL KONDO EFFECT WITH ASSISTED HOPPING IN STRONGLY CORRELATED ELECTRON-SYSTEMS - PARQUET EQUATIONS, SUPERCONDUCTIVITY, AND MASS ENHANCEMENT

The orbital Kondo effect is treated in a model where, additional to th e conduction band, there are localized orbitals close to the Fermi ene rgy. If the hopping between the conduction band and the localized heav y orbitals depends on the occupation of the atomic orbitals in the con duction band, then orbital Kondo correlation occurs. The noncommutativ e nature of the coupling required for the Kondo effect is formally due to the form factors associated with the assisted hopping, which in th e momentum representation depends on the momenta of the conduction ele ctrons involved. The leading logarithmic vertex corrections are due to the local Coulomb interaction between the electrons on the heavy orbi tal and in the conduction band. The renormalized vertex functions are obtained as a solution of a closed set of differential equations and t hey show power behavior. The amplitude of large renormalization is det ermined by an infrared cutoff due to finite energy and dispersion of t he heavy particles. The enhanced assisted hopping rate results in mass enhancement and attractive interaction in the conduction band. The su perconductivity transition temperature calculated is largest for the i ntermediate mass enhancement, m/m approximate to 2-3. For larger mass enhancement the small one-particle weight (Z) in the Green's function reduces the transition temperature which may be characteristic for ot her models as well. The theory is developed for different one-dimensio nal and square-lattice models, but the applicability is not Limited to them. In the one-dimensional case charge- and spin-density susceptibi lities are also discussed. Good candidates for the heavy orbital are f bands in the heavy fermionic systems and nonbonding oxygen orbitals i n high temperature superconductors and different flatbands in the quas i-one-dimensional organic conductors.