| Disordered systems have been of continuing interest to condensed matter physicists. Disorder is associated with a wide range of interesting phenomena such as glassiness and localization. Superconductivity, the phase of matter in which materials conduct without dissipation, has similarly fascinated condensed matter physicists, as it is an outstanding example of the macroscopic effects of quantum mechanics. In this thesis, the interplay of superconductivity and disorder is discussed. The particular focus of this thesis is how a BCS d-wave superconductor in the quantum superconductor to metal transition can develop a global s-wave phase due to the existence of rare regions. The critical assumption of this work is that the metal is highly conducting. Though the calculations done in this thesis are all in the weak coupling framework, it is possible that this phase might be observed in the overdoped cuprates.;Additionally, this thesis contains a discussion of the effect of critical nematic fluctuations on relativistic nodal quasiparticles. In this work, it is found that the nematic order increases the anisotropy in the velocity of the nodal quasiparticles and broadens the quasiparticle peaks except for a narrow wedge in momentum space near the Fermi surface where the quasiparticles remain sharp. The implications for the cuprates are discussed. |
