An extended multiband Hubbard model of the two-dimensional Cu
O2 planes of high-
Tc superconductors is examined by exact diagonalization of the Hamiltonian for small clusters with periodic boundary conditions. Holes are shown to bind in the limit of large Cu-site and nearest-neighbor Cu-O Coulomb repulsion. A simple explanation of the source of the binding energy is given in this strong-coupling limit. The more realistic case of relatively weak nearest-neighbor repulsion is also examined, and suggestive evidence is presented that the effective attraction will also exist in the thermodynamic limit for this case.
The hole distribution within a
CuO2 plane, a common structural element of high-temperature superconductors, is investigated as a function of doping by holes. The correlated ground state of a three-band Hubbard model is found by making use of a local ansatz which includes local correlations between holes. It is found that doped holes have \ensuremath{\sim}70% oxygen character for the parameters determined from the local-density approximation, in agreement with experimental observations, while hole droplets on oxygen orbitals are formed for large copper-oxygen Coulomb repulsion,
Udp. All our results agree with those obtained from finite-cluster diagonalization.
We calculate the effective interaction
Weff between two holes added to the ground state of the repulsive three-band Hubbard model. To make contact with Cooper theory and with earlier Hubbard model cluster studies, we first use a perturbative canonical transformation, to generate a two-body Hamiltonian. Then, we extend the results to all orders. The approach is exact in principle, and we obtain a close analytic expression including explicitly the effects of all virtual transitions to 4-body intermediate states. Our scheme naturally lends itself to embody off-site, inter-planar, phonon-mediated and other interactions which are not considered in the Hubbard model but may well be important. The result depends qualitatively on the symmetry of the two-hole state:
1B2 and $ ^{1}A_{2}$ pairs are special, because the bare holes do not interact by the on-site repulsion (W=0 pairs). The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid; however
Weff is repulsive for Triplet pairs. Bound two-hole states of the same nature were reported earlier in small cluster calculations by exact diagonalisation methods; only symmetric clusters are good models of the plane. Once
Weff is known, the pair eigenfunction is determined by an integral equation. We present numerical estimates of the binding energy
∣Δ∣ of the pairs, which is in the physically interesting range of tens of meV if unscreened on-site repulsion parameters are used.
We calculate the effective interaction Weff between two holes added to the ground state of the repulsive three-band Hubbard model. To make contact with Cooper theory and with earlier Hubbard model cluster studies, we first use a perturbative canonical transformation, to generate a two-body Hamiltonian. Then, we extend the results to all orders. The approach is exact in principle, and we obtain a close analytic expression including explicitly the effects of all virtual transitions to 4-body intermediate states. Our scheme naturally lends itself to embody off-site, inter-planar, phonon-mediated and other interactions which are not considered in the Hubbard model but may well be important. The result depends qualitatively on the symmetry of the two-hole state: 1 B2 and 1 A2 pairs are special, because the bare holes do not interact by the on-site repulsion (W=0 pairs). The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid; however Weff is repulsive for Triplet pairs. Bound two-hole states of the same nature were reported earlier in small cluster calculations by exact diagonalisation methods; only symmetric clusters are good models of the plane. Once Weff is known, the pair eigenfunction is determined by an integral equation. We present numerical estimates of the binding energy |∆ | of the pairs, which is in the physically interesting range of tens of meV if unscreened on-site repulsion parameters are used. 1 I.
The effective two-band $t\ensuremath{-}J$ Hamiltonian for holes in Cu-O planes of cuprates is obtained from the three-band Hubbard Hamiltonian. In this model a doped oxygen hole together with two neighboring copper holes is treated as a composite spin-
21 three-sites particle. The model is studied by exact diagonalization in a
Cu16O32 square cluster. Both binding energy and hole-hole correlation function indicate that two holes bind together for
J/t>0.11 and are predominantly located on the next-nearest oxygen sites in the same Cu-O chain. Electron-phonon interaction is studied in the adiabatic phonons approximation. Copper (\ensuremath{\pi},0) ``half-breathing'' mode is shown to couple strongly to doped holes and increase the hole-hole correlation as well as the binding energy. These results are compared with experimental data.
The fully symmetric Cu-O clusters with a central Cu have two-hole singlet eigenstates which are not affected by the on-site repulsion. These pairs become bound states if the number of holes in the cluster is appropriate; moreover, the quantization at half-integer values of a magnetic test flux is consistent with a superconducting pattern. To investigate the mechanism of pairing, we study the symmetric clusters with $<~$21 atoms and four holes by exact diagonalization. Further, by the diagrammatic expansion of the ground-state energy and of the scattering amplitude, we obtain the spin-flip diagrams for the effective interaction, which is attractive for singlets and repulsive for triplets. A criterion for pairing in cluster calculations is thereby obtained.