### Abstract

The 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 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 the intermediate mass enhancement, m*/m2-3. 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 nonbonding oxygen orbitals in high-temperature superconductors and different flatbands in the quasi-one-dimensional organic conductors.

Original language | English |
---|---|

Pages (from-to) | 10578-10597 |

Number of pages | 20 |

Journal | Physical Review B |

Volume | 50 |

Issue number | 15 |

DOIs | |

Publication status | Published - 1994 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

**Theory of the orbital Kondo effect with assisted hopping in strongly correlated electron systems : Parquet equations, superconductivity, and mass enhancement.** / Penc, K.; Zawadowski, A.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Theory of the orbital Kondo effect with assisted hopping in strongly correlated electron systems

T2 - Parquet equations, superconductivity, and mass enhancement

AU - Penc, K.

AU - Zawadowski, A.

PY - 1994

Y1 - 1994

N2 - The 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 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 the intermediate mass enhancement, m*/m2-3. 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 nonbonding oxygen orbitals in high-temperature superconductors and different flatbands in the quasi-one-dimensional organic conductors.

AB - The 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 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 the intermediate mass enhancement, m*/m2-3. 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 nonbonding oxygen orbitals in high-temperature superconductors and different flatbands in the quasi-one-dimensional organic conductors.

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U2 - 10.1103/PhysRevB.50.10578

DO - 10.1103/PhysRevB.50.10578

M3 - Article

VL - 50

SP - 10578

EP - 10597

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 15

ER -