Quasiparticles and vortices in the high temperature cuprate superconductors

In this thesis I present a study of the interplay of vortices and the fermionic quasi-particle states in a quasi 2-dimensional d-wave superconductors, such as high temperature cuprate superconductors. In the first part, I start by analyzing the quasiparticle states in the presence of the magnetic field induced vortex lattice. Unlike in the s-wave superconductor, there are no vortex bound states, rather all the quasiparticle states are extended. By using general arguments based on symmetry principles and by direct (numerical) computation, I show that these extended quasiparticle states are gapped. In addition, they are characterized by a topological invariant with regard to their spin Hall conduction. Finally, I relate the spin Hall conductivity tensor $sspinxy$ to the thermal Hall conductivity κ_xy by deriving the appropriate “Wiedemann-Franz” law. In the second part, I analyze the fluctuations around an ordered d-wave super-conductor (in the absence of the external magnetic field), focusing on the interaction between the low energy nodal fermions and the vortex-antivortex phase excitations. It is shown that the corresponding low energy effective theory for the nodal fermions in the normal (non-superconducting) state is QED₃ or quantum electrodynamics in 2+1 space time dimensions. The massless U(1) gauge field encodes the topological interaction between the quasiparticles and the hc/2e vortices at long wavelengths. I analyze the symmetries, correlations and stability of this state. In particular, I study the role of Dirac cone anisotropy and residual interactions in QED₃ as well as the physical meaning of the chiral symmetry breaking. Remarkably, the spin density wave corresponds to an instability of a phase fluctuating d-wave superconductor.