Theory of the orbital Kondo effect with assisted hopping in strongly correlated electron systems: Parquet equations, superconductivity, and mass enhancement.

Orbital Kondo effect is treated in a model, where additional to the conduction band there are localized orbitals close to the Fermi energy. If the hopping between the conduction band and the localized heavy orbitals depends on the occupation of the atomic orbitals in the conduction band then orbital Kondo correlation occurs. The noncommutative nature of the coupling required for 1 the Kondo effect is formally due to the form factors associated with the assisted hopping which in the momentum representation depends on the momenta of the conduction electrons involved. The leading logarithmic vertex corrections are due to the local Coulomb interaction between the electrons on the heavy orbital and in the conduction band. The renormalized vertex functions are obtained as a solution of a closed set of differential equations and they show power behavior. The amplitude of large renormalization is determined by an infrared cutoff due to finite energy and dispersion of the heavy particles. The enhanced assisted hopping rate results in mass enhancement and attractive interaction in the conduction band. The superconductivity transition temperature calculated is largest for intermediate mass enhancement, m∗/m ≈ 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 other models as well. The theory is developed for different one–dimensional and square lattice models, but the applicability is not limited to them. In the one–dimensional case charge– and spin–density susceptibilities are also discussed. Good candidates for the heavy orbital are f–bands in the heavy fermionic systems and non–bonding oxygen orbitals in high temperature superconductors and different flat bands in the quasi–one dimensional organic conductors. Typeset using REVTEX 2