Topics in cuprate superconductors

In this thesis, we focus on two specific problem in the high temperature cuprate superconductors. One is the tunneling behavior along the c-axis in the normal state. We use two-layer system coupling with fluctuation to study this problem. The other on the crossover behavior from p-wave Cooper pairing to Boson condensation in 2D case as the attractive interaction increases.; First we discuss the tunneling behavior along the c-axis in the case of static impurities on the layers. We found out the symmetric impurities play no role in the damping of the coherent tunneling. However the anti-symmetric impurities gradually destroy the interference of the consecutive tunneling wave function. The tunneling behavior changes from coherent tunneling to incoherently tunneling smoothly as the density of impurities increases.; Later we discuss the three possible sources of dynamic fluctuation in the high temperature cuprate superconductors: the phonons, the plasmons and the spin fluctuation. The explicit form the spectral function of those three fluctuations are obtained. And we reduced them into two-layer system for the purpose of studying c-axis tunneling in the future. We integrate out the q variable to give the spectral function of o variable to investigate the low temperature properties. We also use the single parameter, the fluctuation at the same point and at the same time, to compare the strengths of those three fluctuations.; We also study the p-wave pairing in 2D case. The crossover from Cooper pairing to Boson condensation is a weak transition at the chemical potential mu = 0. If the gap function is angledependent, the energy gap of quasiparticle change from angle dependence to angel independence as the chemical potential mu changes from above zero to below zero.