This thesis is devoted to an in-depth examination of the various effects of disorder in the cuprate high-temperature superconductors. Disorder is ubiquitous in these materials and is central to... Show moreThis thesis is devoted to an in-depth examination of the various effects of disorder in the cuprate high-temperature superconductors. Disorder is ubiquitous in these materials and is central to a number of phenomena observed in various phases. We revisit several phenomena in the cuprates in light of what is now known about the nature of disorder present in these materials. First, the phenomenon of quasiparticle scattering interference is revisited using a number of different realistic models of distributed disorder which go beyond the single-impurity paradigms used in much of the literature. Next, we study the manner in which a finite DOS at the Fermi energy, seen in a large number of experiments, is generated by various models of disorder, and consider the possibility that smooth disorder from off-plane dopants explains this phenomenon. In addition the localization properties of the superconducting quasiparticles in the presence of various types of disorder are studied. Finally, we show how a number of nontrivial interaction effects in the superconducting and normal states of the cuprates could be visualized by scanning tunneling spectroscopy experiments. Show less
The phenomenon of high temperature (high-Tc) superconductivity, although discovered 20 years ago, still remains mysterious. In conventional superconductors, the supercurrent is carried by a gas of... Show moreThe phenomenon of high temperature (high-Tc) superconductivity, although discovered 20 years ago, still remains mysterious. In conventional superconductors, the supercurrent is carried by a gas of weakly interacting pairs of electrons (Cooper pairs). Experiments suggest that the electron in high-Tc superconductors are at the verge of solidifying into a stripe-crystal, invalidating the conventional `gaseous' picture. Inspired by this problem, the work in this thesis offers an opposite paradigm for high-Tc superconductivity, based on the notion of the `almost ordered' superconductor. Formulating the problem in the field theoretical language of quantum elasticity and utilizing the duality transformation, quantum phases of matter are constructed which are as close as possible to a solid, which can be considered as quantum version of liquid crystals. We find that these ``dual shear superconductors'' are also genuine electromagnetic superconductors with properties which are however subtly different from conventional superconductors and invoke rather unconventional experiments: quantum-liquid crystalline orders, oscillations of magnetic screening currents, overscreening of Coulomb force, and especially a new collective mode found in the dynamical electromagnetic response. Show less
