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Physical Review B

Hybridized mechanism of pairing and the heavy fermion state: Exactly solvable two-band model with strong hybridized interactions

Igor N. Karnaukhov

Published Sep 6, 2005• 1 citation
Publisher

Abstract

The two-band model describing strongly hybridized degenerated electron states in a chain is proposed and solved exactly by means of the Bethe ansatz. The fermions of the subbands interact with each other via one-particle and one-particle correlated on-site hybridized interactions. The chain of electrons is reduced to the model with two noninteracting subbands with a given total number of electrons, in which fermions interact via different effective constants of interactions. In the case of strong hybridized interaction the on-site repulsive interaction is compensated by hybridized interaction, which leads to an effective attractive interaction between particles and the formation of spinless bound states of Cooper type. This electron liquid component determines both heavy fermion- and superconducting-type behavior of electron properties.

DOI
10.1103/physrevb.72.092503

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We present a two band fermion model consisting of a subband of conduction electrons and a subband of local electron pairs interacting via interband interactions. The model is solved in one dimension by means of the Bethe ansatz for an empty subband of local electron pairs. The ground state energy, the chemical potential, the critical exponents, describing the asymptotic behavior of correlation functions at long distances, the effective electron transport mass have been calculated numerically for an arbitrary density of conduction electrons.
Some ground state properties of a fermion system are investigated. An initial Hamiltonian being a generalization of the lattice Anderson model describes this system as a two-band electron-phonon one where both of electron bands are narrow (one is wider than the other). Two bands are hybridized and electrons from both of them are strongly coupled to the same local phonons. After performing the Lang–Firsov type transformation, a new polaron Hamiltonian is obtained. As a result, there appear three effective polaron-polaron interactions in this Hamiltonian and the bandwidths of both of electron bands are reduced. It is assumed that the reduction of the bandwidth of one of the bands is sufficiently strong to make this band dispersionless. Each of the interactions can lead to superconductivity on its own but only one of them is taken into account at this stage; it is the interaction between electrons from the band with a dispersion. The Bogolyubov’s mean field approach is used in order to find the spectrum of the reduced effective Hamiltonian. The effect of the hybridization on the superconducting gap and the relationship between the critical hybridization and the average number of electrons from the wider band per lattice site are investigated.
A modified Anderson lattice is proposed, whose the Hamiltonian accounts for the two-particle hybridization of localized and itinerant electrons instead of one-particle hybridization which takes into account in the original Anderson model. The 1D version of this model can be solved using the Bethe ansazt. It has been shown that hybridization between itinerant and frozen localized electrons results in an effective on-site interaction between itinerant electrons. The magnitude and sign of this interaction depend on the position of the level relative to the Fermi energy (the energy of this level corresponds to the two-particle state of localized electrons at a site). It is shown that when the energy of an localized electron in the two-particle state lies above the Fermi energy, the effective on-site interaction between itinerant electrons is attractive. A repulsive interaction between itinerant electrons occurs when this energy lies below the Fermi energy. Thus, two-part hybridization between localized and itinerant electrons can lead to effective attraction between itinerant electrons, which is unique in itself and may underlie the nature of high-temperature superconductivity.
Two-band hopping model is treated on a two-dimensional square lattice. The atoms are located at the corners and the middles of the edges of the squares. In addition to the strongly overlapping orbitals of the atoms, there are extra orbitals at the corners, which are weakly hybridized. The assumption is made that the Fermi level is inside the broad band and is very near to the narrow band formed by the extra orbitals. The Hamiltonian is Hubbard type, but the off-diagonal part of the two-site interaction is kept also where one creation or annihilation operator acts on the extra orbital and the others on one of its neighbors. The weak coupling is enhanced by the on-site Coulomb repulsion at the corners, which enhancement is a power function of the ratio of the broad band width and the narrow band position measured from the Fermi level. That enhancement is obtained by summation of logarithmic Kondo-type corrections of orbital origin, which reflects the formation of a ground state of new type with strong orbital and spin correlations. Interaction between the particles of the broad band is generated by processes with one heavy and one light particle in the intermediate state. That interaction strongly depends on the momenta of the particles. The generated interaction can result in attractive interaction, but particular parity of the different orbitals are required in the given approximation. The model clearly demonstrates that repulsive interaction can result in superconductivity.