Electrodynamics in the superconducting state of the high Tc cuprates

The high-T_c cuprate superconductors form an excitation gap (or “pseudogap”) at a higher temperature scale T* than the superconducting transition temperature T _c. The origin of this pseudogap is presently unknown and is the subject of intense debate. We argue both on experimental and theoretical grounds that the pseudogap, easily observed above T_c, persists into the superconducting state and modifies its properties. The pseudogap necessarily alters the nature of the charged excitations of the superconducting state so that superconductivity is destroyed at T_c while the excitation gap remains. The optical conductivity σ(ω) is a probe of the charged excitations of the superconducting state and should therefore probe the pseudogap mechanism and its relation to superconductivity.; This work primarily focuses on a natural extension of BCS theory in which the attractive coupling between electrons becomes strong, as is associated with the observed short coherence length. This Thesis presents an analysis of the electrodynamic response, specifically σ(ω), in the superconducting state of the theory. Below T_c this theory has both BCS-like gapped quasiparticles as well as soft bosonic excitations where are responsible for the pseudogap. Some puzzling features of σ(ω) seen experimentally in the underdoped region of the cuprate phase diagram are addressed naturally by the contribution of these bosons to the electrodynamic response. Chief among these is the fact that spectral weight over a broad range of frequencies condenses to from the superfluid even though the excitation gap is nearly temperature-independent. We also calculate σ(ω) below T_c in two models which attribute pseudogap formation to other physical mechanisms. We find that the frequency distribution of condensing spectral weight can distinguish sharply between two general classes of pseudogap theories. The experimental data pose serious difficulties for theories in which there are only fermionic quasiparticle excitations out of the superconducting state.