The analogy between the BCS theory of superconductivity and chiral symmetry breaking in QCD is reviewed and the Nambu-Jona-Lasinio model is introduced as a paradigm for both these phenomena. In Part I, the properties of quantum electrodynamics in (2+1)-dimensional spacetime (QED<SUB>3</SUB>) are investigated in detail. After describing the symmetry structure of the theory, the finite-temperature photon propagator is calculated at leading order in the large-<I>N</I> expansion and the effective attraction between static test charges is derived. The bound-state spectrum of the theory is discussed and the dynamical generation of a fermion mass is investigated analytically. The analysis of QED<SUB>3</SUB> concludes with an approximate treatment of the symmetry restoration transition, including a numerical solution of the finite-temperature gap equation. Part II begins with a brief review of the phenomenology of the quasi-planar high-<I>T<SUB>c</SUB></I> superconductors La<SUB>2</SUB>CuO<SUB>4</SUB> and YBa<SUB>2</SUB>CuO<SUB>6</SUB>. The two-dimensional Heisenberg antiferromagnet is introduced as a microscopic description of these materials and the nonlinear σ-model is derived as a long-wavelength limited in the undoped case. Following Shankar, the dynamics of holes in the antiferromagnet is modelled by coupling two species of Grassmann fields to the σ-model action. The long-wavelength limit of this system is found to be a 'pseudo-relativistic' quantum field theory of Dirac fermions interacting with an abelian gauge field. The results of Part I are applied to demonstrate the dynamical generation of a fermion mass, which corresponds to the opening of a superconducting gap in the 'quasi-hole' spectrum. The long-wavelength theory exhibits type-II superconductivity without parity or time-reversal symmetry violation, flux quantization with quantum <I>hc/</I>2<I>e</I> and a two-dimensional Meissner effect. The possible relevance of this model to high-<I>T<SUB>c</SUB></I> superconductivity is discussed and avenues for future investigation are suggested.

The compound Bi<SUB>2</SUB>Sr<SUB>2</SUB>CaCu<SUB>2</SUB>O<SUB>8+δ</SUB> is of special interest for two reasons: it is an important member of the family of cuprates who possess superconducting transitions at high temperatures, and it is an example of the class of layered compounds whose structures are distinguished by incommensurate modulation. The unique normal state and superconducting properties of the cuprates are intricately linked to their far from ideal disordered structures. The additional incommensurate nature of some compounds has greatly hampered the understanding of their novel behaviour. This thesis describes single crystal studies of Bi<SUB>2</SUB>Sr<SUB>2</SUB>CaCu<SUB>2</SUB>O<SUB>8+δ</SUB> using x-ray scattering techniques as a tool for establishing in detail those structural features of significance to the behaviour of this compound as a superconductor, and those of importance to its nature as an incommensurate. The thesis starts with the characterisation of the variations between crystals grown, using flux and floating zone methods, by four separate research groups. The inclusion of impurities is found to be a feature of flux grown crystals. The nature of the incommensurate modulation is also clarified, and defects associated with it are identified. The fundamental properties of the modulation are investigated by studying <I>in situ</I> the response of the structure to high temperature. It is demonstrated that the modulation is strongly pinned and that the incommensurate period of the modulation is not a continuous function of oxygen content; a possible oxygen deficient high temperature phase is tentatively identified. The inert nature of the incommensurability to temperature is also established at low temperature, down to 20K, limiting any possible direct involvement of the modulation in the superconducting transition. Oxygen content, on the other hand, is known to hold a major influence over both normal state and superconducting properties, and a study is made of the effects of nitrogen and oxygen annealing treatments. The results reveal modifications in microstructure associated with oxygen ordering, a result of potential importance to the understanding of transport properties.

The correlation between charge-density waves (CDWs) and superconductivity has been a subject of extensive study for a long time. This thesis describes a series of x-ray scattering experiments designed to study CDWs in perovskite superconductors. A review of the properties of CDW materials and the relationship between CDWs and superconductivity is given. Using x-ray scattering techniques the modulated structures caused by the formation of a CDW state have been clarified in a variety of single crystals of Ba<SUB>1-<I>x</I></SUB>K<I><SUB>x</SUB></I>BiO<SUB>3</SUB>. In low resolution measurements, the CDW satellites produce a superstructure doubling the unit cell existing in the range from the semiconducting state (0<x<0.37) to the metallic state (x>0.37), even in the low temperature superconducting state. Additional peaks with <I>G<SUB>2</SUB> </I>= 0.33a* were observed, which are only present in semiconducting samples. An attempt to determine the size of the modulated structure was undertaken using higher resolution x-ray scattering in the superconductor Ba<SUB>0.6</SUB>K<SUB>0.4</SUB>BiO<SUB>3</SUB>. In this study, the modulated structure was identified to be incommensurate with the host lattice with <I>G</I><SUB>1</SUB>=0.494a* ± 0.11b* and a rather short correlation length of ˜150Å limited by the CDW domain size. An unusual decrease in the intensities of the CDW superlattice reflections was also observed as the temperature was lowered. Evidence to support to the attribution of these satellites to a CDW distortion was obtained from measurements conducted under applied magnetic fields. Increased splitting of the CDW satellites was observed under a magnetic field of 0.8 T with an extremely long relaxation time when the field was removed. Such a long relaxation time is a characteristic of CDWs associated with metastable states.

The flux line lattice (FLL) of Type-II superconductors is a topic of much recent interest. On the one hand, the FLL orientation and shape provide insights into the properties of the underlying superconducting state. On the other hand, the quasi-2D flux line system itself provides a test-bed for theories of structural order in solids and glasses. We use small-angle neutron scattering (SANS) to study FLLs in elemental niobium, a conventional superconductor. Applying the magnetic field along the fourfold [001] direction of pure Nb crystals, we discover surprising new FLL shapes and orientations that spontaneously break the fourfold symmetry. We examine how the crystal symmetry affects the FLL as the field is rotated away from [001]. Pursuing the second theme, we develop a reverse Monte Carlo (RMC) method to uncover the correlations between flux lines from SANS data. For FLLs perturbed by weak disorder, contemporary theories predict the survival of. quasi-long range order in a Bragg glass phase. Strong disorder is anticipated to generate a variety of vortex glass phases.' . Our results show that complex FLL shapes are not exclusive to unconventional superconductors. The potential of our RMC technique for revealing unambiguously the structural nature of flux line glasses is demonstrated.

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The recent interest in developing highly controllable quantum bits (qubits) based on superconducting circuits makes it necessary to get a deeper understanding of the physics of small Josephson junctions. Such devices have to be wisely engineered and well isolated from the noisy environment to observe non-classical physics. In this thesis, a real-time noise analysis was implemented by an autocorrelation calculation to identify the type of environmental effects affecting a superconducting circuit. This was used during switching current measurements of small Josephson junctions to track the effects of unwanted signals and identify their frequency components. The temperature dependence of the switching current distribution was used to further characterise the small Josephson junctions. Furthermore the fabrication of smal1 Josephson junctions is further developed by analysing the reliability and reproducibility of them. A systematic approach is shown to solve typical fabrication problems for example identifying and reducing mechanical stress between resist layers. As Josephson junctions show quantum mechanical effects on a macroscopic scale they are used in a wide range of applications especially in superconducting circuits.

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