| This thesis considers various aspects of the interplay between superconductivity and magnetism in strongly correlated electron systems.; Chapter 2 studies the effects of weak translational symmetry breaking on the quasiparticle spectrum of a d-wave superconductor. A general formalism is developed to discuss periodic charge order, as well as quasiparticle scattering off localized defects. I argue that STM experiments on Bi2Sr2CaCu2O8+delta cannot be explained using a simple charge density wave order parameter, but are consistent with the presence of a periodic modulation in the electron hopping or pairing amplitude. I also discuss the effects of randomness and pinning of the charge order and compare it to the impurity scattering of quasiparticles.; Chapter 3 explores the possibility of direct detection of spin nematic order: a state which breaks spin SU(2) symmetry while preserving translational and time reversal symmetries. Spin nematic order can arise naturally from charge fluctuations of a spin stripe state. The nematic is a spin-two operator, and therefore does not couple directly to neutrons. However, I show that neutron scattering and Knight shift experiments can detect the spin anisotropy of electrons moving in a nematic background. I build a nematic wave function starting from a t--J type model, and analyze the mean field phase diagram for the nematic taking into account spin-orbit effects.; Finally, in Chapters 4 and 5, I investigate the competition between antiferromagnetism and triplet superconductivity in quasi one-dimensional Bechgaard salts, unifying the two orders in an SO(4) symmetric framework. I demonstrate the existence of such symmetry in one-dimensional Luttinger liquids, and argue that approximate SO(4) symmetry remains valid even when interchain hopping is strong enough to turn the system into a strongly anisotropic Fermi liquid. SO(4) symmetry, which strongly constrains the phase diagram, can explain coexistence regions between antiferromagnetic, superconducting, and normal phases, as observed in (TMTSF)2PF6. I discuss experimental tests of the SO(4) symmetry, including the prediction of a sharp resonance in neutron scattering experiments on superconducting samples. |
