Abstract:
The development of a microscopic model which successfully describes cuprate superconductors, particularly underdoped ones, has remained an elusive goal. The t-J model has been widely used as a starting point for the development of such a model; it describes a single band of electrons hopping on a lattice and experiencing an exchange interaction, subject to the constraint that at most one electron can occupy any site. In some circumstances the t-J model exhibits spin-charge separation, in which electrons remain localized but particles carrying only charge (holons) and only spin (spinons) delocalize separately. In this dissertation, we study a recently-developed model Hamiltonian which is derived from the t-J model by renormalization of high-energy holon hopping processes which break spin singlets. This renormalization introduces a holon pair hopping term which provides a basis for the development of superconductivity. The renormalized model is constrained by continuity with the well-understood behavior of the t-J model at half-filling (when there is exactly one electron per site); it matches the symmetry of the known spin states. Here we analyze the renormalized model by mean-field theory and by studying pair fluctuations self-consistently. We reproduce the basic features of the cuprate phase diagram at low hole doping, including the d_x^2 _-y^2 symmetry of the superconducting gap and the two-dimensionality of the pseudogap phase. Importantly, we find a separation of temperature scales between the formation of charged pairs and their condensation. We qualitatively reproduce experimental signatures of paring at temperatures above the superconducting transition by studying the specific heat and diamagnetic response.
