The simplest model for superconductor electrodynamics are the London equations, which treats the impact of electromagnetic fields on the current density as a localized phenomenon. However, the charge carriers of superconductivity are quantum mechanical objects, and their wavefunctions are delocalized within the superconductor, leading to non-local effects. The Pippard equation is the generalization of London electrodynamics which incorporates this intrinsic non-locality through the introduction of a new superconducting characteristic length, \xi_0, called the Pippard coherence length. When building nano-scale superconducting devices, the inclusion of the coherence length into electrodynamics calculations becomes paramount. In this thesis, we provide numerical calculations of various electrodynamic quantities of interest in the non-local regime, and discuss their implications for building superconducting devices. We place special emphasis on Superconducting QUantum Inteference Devices (SQUIDs), and their usage as flux quantum bits (qubits) in quantum computation. One of the main limitations of these flux qubits is the presence of intrinsic flux noise, which leads to decoherence of the qubits. Although the origin of this flux noise is not known, there is evidence that it is related to spin impurities within the superconducting material. We present calculations which show that the flux noise in the non-local regime is signi cantly different from the local case. We also demonstrate that non-local electrodynamics greatly affect the self-inductance of the qubit. / Graduate

Superconducting Quantum Interference Devices (SQUIDs) are currently being used as flux qubits and read-out detectors in a variety of solid-state quantum computer architectures. The main limitation of SQUID qubits is that they have a coherence time of the order of 10 us, due to the presence of intrinsic flux noise that is not yet fully understood. The origin of flux noise is currently believed to be related to spin impurities present in the materials and interfaces that form the device. Here we present a novel numerical method that enables calculations of the flux produced by spin impurities even when they are located quite close to the SQUID wire. We show that the SQUID will be particularly sensitive to spins located at its wire edges, generating flux shifts of up to 4 nano flux quanta, much higher than previous calculations based on the software package FastHenry. This shows that spin impurities in a particular region along the wire's surface play a much more important role in producing flux noise than other spin impurities located elsewhere in the device. / Graduate / 0611 / 0607 / 0753 / laforest@uvic.ca

<p>Dynamic properties of type-II superconductors have been experimentally studied in zero and low magnetic fields using SQUID magnetometry and <i>I–V</i> measurements.</p><p>In zero magnetic field close to the critical temperature, the physical properties of type-II superconductors are dominated by spontaneously created vortices. In three dimensions (3D) such vortices take the form of vortex loops and in two dimensions (2D) as vortex-antivortex pairs.</p><p>The 2D vortex dynamics has been probed using mutual inductance and flux noise measurements on YBa₂Cu₃O₇ (YBCO) and MgB₂ thin films in zero and low magnetic fields. In such measurements, information about vortex correlations is obtained through a temperature dependent characteristic frequency, below (above) which the vortex movements are uncorrelated (correlated). The results obtained in zero magnetic field indicate that sample heterogeneities influence the vortex physics and hinder the divergence of the vortex-antivortex correlation length.</p><p>In low magnetic fields the vortex dynamics is strongly dependent on the applied magnetic field and a power law dependence of the characteristic frequency with respect to the magnetic field is observed. The results indicate that there is a co-existence of thermally and field generated vortices.</p><p>The <i>I–V</i> characteristics of untwinned YBCO single crystals show that only a small broadening of the transition region influences the length scale over which the vortex movements are correlated. The dynamic and static critical exponents therefore exhibit values being larger in magnitude as compared to values predicted by relevant theoretical models. The results also suggest that the copper oxide planes in YBCO decouple slightly below the mean field critical temperature and hence, the system has a crossover from 3D to 2D behaviour as the temperature is increased. </p><p>From temperature dependent DC-magnetisation measurements performed on untwinned YBCO single crystals in weak applied fields, detailed information about the critical current density and the irreversibility line is obtained.</p>

Dynamic properties of type-II superconductors have been experimentally studied in zero and low magnetic fields using SQUID magnetometry and I–V measurements. In zero magnetic field close to the critical temperature, the physical properties of type-II superconductors are dominated by spontaneously created vortices. In three dimensions (3D) such vortices take the form of vortex loops and in two dimensions (2D) as vortex-antivortex pairs. The 2D vortex dynamics has been probed using mutual inductance and flux noise measurements on YBa2Cu3O7 (YBCO) and MgB2 thin films in zero and low magnetic fields. In such measurements, information about vortex correlations is obtained through a temperature dependent characteristic frequency, below (above) which the vortex movements are uncorrelated (correlated). The results obtained in zero magnetic field indicate that sample heterogeneities influence the vortex physics and hinder the divergence of the vortex-antivortex correlation length. In low magnetic fields the vortex dynamics is strongly dependent on the applied magnetic field and a power law dependence of the characteristic frequency with respect to the magnetic field is observed. The results indicate that there is a co-existence of thermally and field generated vortices. The I–V characteristics of untwinned YBCO single crystals show that only a small broadening of the transition region influences the length scale over which the vortex movements are correlated. The dynamic and static critical exponents therefore exhibit values being larger in magnitude as compared to values predicted by relevant theoretical models. The results also suggest that the copper oxide planes in YBCO decouple slightly below the mean field critical temperature and hence, the system has a crossover from 3D to 2D behaviour as the temperature is increased. From temperature dependent DC-magnetisation measurements performed on untwinned YBCO single crystals in weak applied fields, detailed information about the critical current density and the irreversibility line is obtained.