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Phenomena in unconventional superconductivity : d-wave quasiparticles, pseudogap, QED₃ theory and Andreev edge states

This thesis is composed of four research projects on phenomena in unconventional superconductivity. The first three projects are concerned with high T c superconductivity (HTSC) in cuprates and the fourth discusses the newly discovered superconductivity in the cobaltate system. The first project presents a calculation of various correlation functions in the pseudogap (PSG) phase of the cuprates in the frame work of the Q E D 3 theory. The low energy behaviour of many of the quantities is similar to that of the superconducting state. In contrast, the staggered spin susceptibility has an anomalous dimension, leading to a divergent susceptibility as the system approaches half filling, indicating an instability towards antiferromagnetism. The second project demonstrates the possibility of coexistence of antiferromagnetism and superconductivity in the Q E D 3 model. The gauge fluctuations, encoding the quantum fluctuations of vortices dynamically generate a fermionic mass that corresponds to antiferromagnetic ordering. This phenomenon, known as chiral symmetry breaking, is found even when the gauge fluctuations are gapped by a small gauge field mass. This result is in agreement with experimental detection of magnetic order below T c . The third project in this thesis is a proposal for a test of the origin of the pseudogap phenomenon. It distinguishes between a scenario of competing orders and phase fluctuations. Our work discusses the fundamental difference between charged excitations in a superconducting medium and excitations in the presence of some other order parameter in the particle-hole channel. We find that quasiparticle interference due to scattering by an impurity can display this fundamental difference and can be seen in scanning tunneling microscopy measurements of the local density of states (LDOS). The last project in this thesis is a solution for a BCS-like model on a semiinfinite triangular lattice, motivated by the discovery of superconductivity in N a x C o 0 2 • 2/H2O. The work is a development of a new analytic and exact method of finding Andreev bound states on the edges of a superconductor.