| This thesis contains two projects which focus on different aspects of the vortex state of high-temperature superconductors.; In the first project, the relaxation rate of copper nuclear spins due to electron spinflip scattering is calculated within a quantum-mechanical model that assumes that the low-lying excitations of high-temperature superconductors are best described as nodal quasiparticles. The results of these calculations show a nonmonotonic temperature and frequency dependence that differs markedly from semiclassical Doppler-shifted results, and challenges the assertion that experimental observations of the rate of planar Cu and O spin-lattice relaxation in the mixed state of YBa2Cu3O7 point to antiferromagnetic spin fluctuations as a better candidate for the elementary excitations of the superconducting state.; Inspired by recent experimental and theoretical work that suggests the presence of antiferromagnetic ordering in vortex cores, the second project considers the effect of the long-range Coulomb interaction on charge accumulation in antiferromagnetic vortices in high-Tc superconductors. The vortex state is described within a Bogoliubov de Gennes mean-field model which allows for competing antiferromagnetic and d-wave superconducting orders. Antiferromagnetism is found to be associated with an accumulation of charge in the vortex core, even in the presence of the long-range Coulomb interaction. The manifestation of II-triplet pairing in the presence of coexisting d-wave superconductivity and antiferromagnetic order, and the intriguing appearance of one-dimensional stripelike ordering are also discussed. The local density of states in the vortex core is calculated and is found to be in excellent qualitative agreement with experimental data. |
