Attractive On-site Interaction Research Articles

Superconducting fluctuations in the Hubbard model with an attractive on-site interaction in one dimension

The low-temperature thermodynamics of the one-dimensional Hubbard model with attractive on-site interaction of the electrons is discussed within the framework of the Bethe ansatz for the wave function. At low T the dominant states consist of spin-paired electrons (Cooper-pair-like) and excitations of such pairs (without breaking up the singlet bound states). A critical field Hc (energy required to depair a Cooper pair) is obtained at T=0 (note that the superconducting Tc =0), which disappears for T≠0. There is no magnetic response at T=0 for H<Hc . The one-electron correlation function falls off exponentially with distance, while the singlet pair–singlet pair correlation decreases with a power law. The specific heat is linear in temperature, which is possibly a consequence of the dimension. The elementary excitations of the system are discussed. The excitation spectrum shows some analogies to that of resonant valence bonds in two dimensions.

Superconductivity with On- and Inter-Site Attractions in a Two-Dimensional Square Lattice

We investigate superconductivity in a two-dimensional square lattice characterized by both an on-site attractive interaction (- V 1 ) of the BCS type and an inter-site attractive interaction (- V 2 ). We evaluate the phase diagram in the ( V 1 , V 2 , T ) space, which shows that there appear three kinds of superconducting states, i.e. a pure s -state, a pure d -state and a mixed state, depending on the values of V 1 , V 2 and T . For some appropriate values of V 1 and V 2 , two types of transitions take place on the reduction of temperature; from a normal state to a pure state and then from a pure state to a mixed state. We calculate several physical quantities in order to study their behaviors at these transition points. Implication of the present theory is discussed in relation with high- T c superconductivity.

Thermodynamic Bethe-ansatz equations for the Hubbard chain with an attractive interaction.

The thermodynamic Bethe-ansatz equations for the one-dimensional Hubbard model are derived for an attractive on-site interaction of the electrons, extending in this way Takahashi's result for the repulsive Hubbard chain. The results are discussed in several special limits, e.g., interaction much larger than the hopping, U\ensuremath{\rightarrow}0 case, and the high- and low-temperature limits. The dominating states at low temperatures consist of spin-paired electrons (resembling Cooper pairs) and bound states of such pairs. The excitation spectrum and its properties are discussed in the context of superconductivity and resonant valence bonds.

On the Phonon-Mediated Pairing Interaction in the High-TcOxide Superconductors

We study the effective pairing interaction mediated by the vibration of the O-ions in the insulating layers in the high- T c oxide superconductors, and find that the on-site attractive interaction may become strong enough to dominate the on-site repulsion. Such strong electron-phonon coupling is due to the poor screening effects by the conduction electrons in the CuO 2 -conducting layers. Using this effective pairing interaction together with the realistic values of the parameters, we calculate T c for various types of anisotropic pairing states as functions of the average number of the conduction electrons. The results suggest that the S-like pairing state containing the anisotropic component may be the most favorable. We also study the isotope effect and find that it is appreciably suppressed when the Fermi level stays near the Van Hove singularity.

An extended Hubbard model with inter-site attraction in two dimensions and high-Tcsuperconductivity

The authors study a simple model for superconductivity based on an extended Hubbard model with on-site repulsive and inter-site attractive interaction for arbitrary electron density. The two-dimensional square lattice d-wave pairing is most stable for a nearly half-filled band. p-wave and then extended s-wave pairing become stable upon decreasing band filling. Competition between the various anisotropic pairings and antiferromagnetism as well as the effect of next-nearest-neighbour hopping is discussed. The authors relate the present model to high-Tc superconducting oxides.

Repulsive Interactions Due to Breathing Modes in Ceramic High-Tc Superconductors

What are examined are mutual interactions due to one-phonon exchanges of breathing modes of oxygen octahedrons in recently-discovered ceramic high- T c superconductors. Although mutual interactions due to breathing modes are attractive between the on-site pairs, as expected, they are repulsive between the nearest neighbors. On the basis of an argument that it is difficult for such on-site attractive interactions to overcome strong Coulomb repulsions because of narrow quasi-particle bands, the result obtained here implies that superconductivity should be realized by a certain non-phonon mechanism such as the nearest-neighbor superexchange interaction.

Inherent Spin Density Wave Instability in Heavy-Fermion Superconductors

We have demonstrated an inherent instability of unconventional anisotropic superconducting (SC) states toward the spin density wave (SDW) formation on the reason why these SC states are stabilized. Within a mean field approximation for a simplified model including the on-site repulsive and attractive interactions, we examine the competition between the SDW and various types of the p - and d -pairing states and find that to classify types of the competition, the symmetry property of the SC order parameter under translation of a nesting vector is important in addition to the symmetry of parity. We also discuss relative stability of various pairing states in the presence of the SDW. It is interpreted that the second transition observed in(U 1- x Th x )Be 13 ( x =2∼4 at%) is the SDW transition out of an unconventional pairing state.