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
This thesis describes a study from both a theoreticaL and an experimental point of view. I deveLop a new ru•deL for electron transport through networks of interconnected narnzparticLes In the... Show moreThis thesis describes a study from both a theoreticaL and an experimental point of view. I deveLop a new ru•deL for electron transport through networks of interconnected narnzparticLes In the Coulomb blockade regime and compare this ru•del tc experimental data. The main conclusion from this study is that cotunneLing does not give any significant contribution tc electron transport. Instead, transport is governed by perccIatLng paths thrcugh the netwcrk. Here, disorder In the array (in the form of variation of the Coulomb chargLng energy of the nanzparticLes) is the domLnating factor. Morecver, usLng Low—energy electron potentiometry, I visualise the f Low cf electrcns through the network. We find here that the contact resistance is negligibLe, and Chat the electi•zn flow 13 not impeded by small irregularities such as small and grain boundaries . Show less
Topological superconductors are a novel type of superconductors that carry Majorana particles at their boundary. These surface states are equal superpositions of electrons and holes, and hence are... Show moreTopological superconductors are a novel type of superconductors that carry Majorana particles at their boundary. These surface states are equal superpositions of electrons and holes, and hence are their own anti-particles. There has been a recent surge of theoretical and experimental effort to realize these special particles in the lab. While first observations support the theoretical predictions, fail-safe experimental evidence for Majoranas is still needed. Part of the challenge is that due to their vanishing charge they are not easily detected electrically. The topic of this thesis is the proposal and study of electrical signatures of Majoranas that are present in spite of their charge neutrality. By applying scattering and random matrix theory we first examine their generic properties. With the tool of numerical simulations we then put our predictions to test on realistic systems. Show less
This thesis is devoted to the effects of disorder on two-dimensional systems of Dirac fermions. Disorder localizes the usual electron system governed by the Schroedinger equation. The influence of... Show moreThis thesis is devoted to the effects of disorder on two-dimensional systems of Dirac fermions. Disorder localizes the usual electron system governed by the Schroedinger equation. The influence of disorder on Dirac fermions is qualitevely different. We concentrate on a random mass term in the Dirac equation. We have discovered that Dirac fermions in graphene are localized by a random mass, without any transition into metallic state. The situation is entirely different for Dirac fermions in a p-wave superconductor. There electrostatic disorder appears in the Dirac equation as a random mass, which localizes the excitation, but only if the disorder is relatively weak. For large mass fluctuations a transition into metallic state appears. This qualitatively different response to disorder in graphene and in p-wave superconductors is explained by the appearance of Majorana bound states, which allow for resonant tunneling and metallic state. Electrostatic disorder in a d-wave superconductor represented as random vector potential in the Dirac equation. We look at the transmission of Dirac fermions for electrostatic potential with long- and short-range fluctuations. We study the interplay of electrical and mechanical properties of suspended graphene by calculating the correction to the conductivity due to its deformation by a gate electrode. Show less
