Topics in the Theory of High-Temperature Superconductors

One important clue to understanding the origin of superconductivity in the hightemperature cuprate superconductors lies in the intriguing properties of the global phase diagram of the cuprate materials. In particular, strongly underdoped cuprates exhibit antiferromagnetic order, whereas moderately underdoped cuprate superconductors exhibit a pseudogap in the excitation spectrum above the superconducting transition temperature. It is likely that an understanding of the relationship between antiferromagnetism and superconductivity as well as an understanding of the nature of the pseudogap will be essential to the development of a theory for the cuprate superconductors. In this Thesis we propose experimental tests aimed at assessing the validity of two particular scenarios for the cuprate superconductors. The first scenario which we examine is the phase-fluctuation model of the pseudogap phenomena, which posits that the pseudogap is due to the existence of local phase-incoherent superconducting correlations. We propose and theoretically explore experiments designed to directly probe these correlations. The second scenario which we examine is the SO(5) theory of superconductivity, which attempts to unify the antiferromagnetic and superconducting regions of the phase diagram. We propose and theoretically explore experiments designed to test the SO(5) scenario.U of I OnlyThesi