The Spin Fluctuation, Superconducting Pairing In Kagome Lattice And Pseudogap In Unconventional Superconductors

Based on the two-dimensional Hubbard model, fluctuation exchange approxima-tion and cluster perturbation theory, we study the spin susceptibility and the pairing symmetry mediated by spin fluctuations on the metallic Kagome lattice. We also inves-tigate the pseudogap phenomenon in organic and high-Tc superconductors. This thesis is organized as follows:1.We first investigate the spin susceptibility and the pairing symmetry mediated by spin fluctuations on the metallic Kagome lattice based on the three-band Hubbard model and the FLEX approximation. We find that the spin susceptibility is caused by the nesting of the renormalized FS arising from the Coulomb interaction. We point out that superconductivity would be more easily realized in the hole doped case at a doping level of 25%, which corresponds to 8% electron doping relative to the Dirac point. For low dopings, the most favorable pairing state has a d-wave-like symmetry described by the E2g representation of the group D6h. For a large hole doping, the pairing symmetry is described by the A2g representation.2.We have performed numerical calculations of the anisotropic two-dimensional t - t' - U Hubbard model on the anisotropic triangular lattice by use of the cluster perturbation theory. We choose 0.4< t'/t< 0.8 and find that when we fix t'/t and increase U from non-interaction to large interaction, the Fermi liquid phase, the pseu-dogap and the Mott insulator phase will occur one by one. The pseudogap here has a dx2_y2-like form which is consistent with the scanning tunneling microscope and ther-mal conductivity tensor experiments. The pseudogap and Fermi arc are shown to be the precursor preceding the Mott insulator.3.We study the properties of the Fermi surface in high-Tc superconductors using the cluster perturbation theory with the two-dimensional t-t'-U Hubbard model. We find the coexistence of Fermi arc and Fermi pocket at 1/6 hole doping. We think this coexistence comes from the band renormalization and the Fermi pocket is shown hole-like. When doping is above 1/6 hole doping, Fermi pocket will disappear and the Fermi arc is nearly as large as the original Fermi surface. When doping is below 1/6 hole doping, the Fermi arc keep its length in spite of the change of doping. Our results agree with recent experiment. As far as the pseudogap is concerned, the Hubbard model may capture the essential physics.