GaN is shown to be a highly important semiconductor material for the fabrication of electronic devices such as light emitting diodes, laser diodes and field effect transistors. In the main calculations are carried out using density functional theory. The details of the particular implementation used are given in chapter 2. This methodology is then used to investigate the formation energy of basal plane stacking faults in a selection of wurtzite materials, namely; GaN, AlN, InN, BeO and ZnO. The investigation explores the reasons for the range of stacking fault energies across the materials. This thesis also addresses the question of the influence of impurity doping on the formation of stacking faults in GaN. Experimental evidence has shown that the density of basal plane stacking faults is higher in silicon doped GaN compared to undoped GaN. Present calculations confirm that silicon encourages the formation of cubic material. The influence of carbon, magnesium, indium and aluminium is also investigated as is the relation between the wurtzite-sphalerite structural energy difference and the bonding characteristics of doped GaN. A pair potential model for the group-III nitrides is developed in chapter 4. The model is used to investigate the incorporation of indium and aluminium into GaN and the interaction between native defects and planar defects which requires the use of large supercells. It is shown that native defects have a positive binding energy to all three boundary structures considered and that the binding energy is highest for interstitial defects. Work in this thesis also investigates magnesium and carbon acceptors in GaN. The influence of indium and aluminium on the solubility and on the depth of the acceptor level is investigated in order to determine whether such elements can improve the properties of the acceptors. Chapter 6 looks at the formation energy and the electrical behaviour of metal impurities in GaN.

There is strong evidence that a common pairing mechanism is in operation in many classes of unconventional superconductor that is related to the proximity of a magnetic quantum critical point. Hydrostatic pressure has been shown to be an effective means to tune systems near to quantum critical regions and some of the most convincing evidence linking superconductivity to magnetism has emerged from such experiments. In this work, we describe the development of a unique system that couples this high pressure tuning technique with the powerful normal state probe of quantum oscillations, in order to test models of superconductivity that make quantitative predictions regarding the normal state. As a first application, we examine how the quantum oscillation spectrum of the exotic superconductor Sr<SUB>2</SUB>RuO<SUB>4</SUB> evolves up to pressures in excess of 30 kbar and through a region in the phase diagram previously thought to contain a quantum critical point. Combining these experiments with conventional low field measurements of the T<SUP>2</SUP> <I>A</I>-coefficient of the resistivity and the upper critical field, we discuss the implications of our new results to possible pressure phase diagrams in the context of the "Magnetic Interaction Model", and adaptation of BCS theory to magnetic interactions. As an extension, by analysing interference effects in the oscillation spectra, we have been able to extract extremely accurate values for cylindrically symmetric contributions to the c-axis dispersion in Sr<SUB>2</SUB>RuO<SUB>4</SUB>. Access to the total warping is restricted for the α and β sheets, but we find a striking reduction under pressure in the warping of the γ sheet, which is thought to be the active band in orbital dependent theories of superconductivity. In such a scenario, this indicates a reduction in the coupling between the active and passive bands. More generally, it implies a reduced effective dimensionality in the γ sheet, which might act to suppress superconductivity via fluctuation effects.

This thesis is a comprehensive study of the charged Bose-gas (CBG). Special attention has been paid to the role of Bose-Einstein condensation, and it's effect on the superconducting properties of the system. The main motivation for this work has been the relevance of the CBG as a model for the high temperature superconductors, within the context of the bipolaron theory[1], the experimental and theoretical evidence for which is discussed in the introductory chapters. By using standard many body theory relevant properties of the CBG have been derived. Much attention has been placed on how to deal with the condensate in an interacting system. The Bogoliubov-de Gennes (BdG) equations are formulated for the Charged Bose Gas (CBG), and their extension to the Ginzburg-Landau-Abrikosov-Gor'kov (GLAG) type theory is discussed. The temperature dependence of the condensate density for the Coulomb Bose-gas (CBG) was studied using the Bogoliubov approximation. This enabled the calculation of the London penetration depth as a function of temperature. Other thermodynamic variables, such as the free energy and specific heat, were also calculated. The nature of the Bose-Einstein condensation of the CBG in a magnetic field was investigated for ultra-low temperatures and ultra-high magnetic fields. The temperature dependence of the upper critical field was found to have positive curvature, one of the remarkable features of the high temperature superconductors. The difference between the resistive transition and the peak in the specific heat is also discussed.

This thesis presents a novel device architecture allowing the monolithic integration of SAWs and semiconductors, which compensates for the inherent weakness of piezoelectric coupling in GaAs by relying on a strong non-local interaction mechanism. A special double-barrier quantum well RTS is designed so that large vertical currents can be sensitivity triggered by a small potential near the surface of the structure, such as the potential associated with a SAW. When a SAW beam is incident on the RTS mesa, the peaks ( and valleys) of the SAW electric field change the potential across the quantum well, resulting in local increases (and decreases) of the current through the structure. With the appropriate device design, the net effect of the SAW integrated over the entire RTS mesa will induce a microwave current in the receiving circuit connected to the RTS emitter. The basic linear and nonlinear properties of the microwave response have been investigated. Simple phenomenological models taking into account the spatial distribution of the SAW electric field and the nonlocality of the RTS conductivity have demonstrated good agreement with experimental results. The effect of varying the RTS layer structure on both the dc characteristics and the microwave response has been investigated theoretically, and experiments once again support the predictions. A process for non-annealed Ohmic contact to the RTS emitter has been optimized, in which Al is grown <I>in situ</I> on highly-doped GaAs incorporating several layers of <I>δ</I>-doping near the surface. The use of this contact method helps to eliminate the extrinsic instability observed in the negative differential resistance region of early devices. Finally, possible applications of the interaction are discussed, including a proposal for the parametric generation of very high frequency SAWs.

Local Hall probe measurements of the superconducting and magnetically ordered [RE]Ni<SUB>2</SUB>B<SUB>2</SUB>C series of materials are presented. These include HoNi<SUB>2</SUB>B<SUB>2</SUB>C, ErNi<SUB>2</SUB>B<SUB>2</SUB>C TmNi<SUB>2</SUB>B<SUB>2</SUB>C and YNi<SUB>2</SUB>B<SUB>2</SUB>C. Measurements in YNi<SUB>2</SUB>B<SUB>2</SUB>C are presented as a non-magnetic control member of the series against which the data from the magnetically ordered members may be compared. In HoNi<SUB>2</SUB>B<SUB>2</SUB>C an α-axis incommensurate order is confirmed to cause a dramatic enhancement of bulk pinning between around 5 K and 6 K. Samples of low quality show no evidence of such an enhancement, although these poorer samples show a higher intensity of incommensurate magnetic ordering.

In this research we have successfully developed a THS version of the Whole Wafer Process (WWP) to fabricate YBCO/PBCO/YBCO trilayer Josephson junctions using both c-axis and a-axis oriented single crystalline films. As in the case of LTS Niobium-based tunnel junction technology, the planar trilayer technology promises to be a good candidate for HTS electronics. Planar HTS Josephson junctions in the c-axis orientation are thought to be difficult to fabricate due to the low value of the coherence length in the c-direction (ξ<SUB>c</SUB>~0.3 nm) compared to ξ<SUB>ab</SUB>~1.6 nm along the <I>ab</I>-planes. While on the other hand, a-axis oriented planar junctions are difficult to fabricate. Other limitations include the difficulty associated with depositing high quality trilayer structures with well defined interfaces. PBCO was chosen as the barrier material due to its structural and chemical compatibility with YBCO. This allowed epitaxial multilayered integration with YBCO. The first c-axis oriented trilayers were prepared by high pressure dc-sputtering using a range of barrier thicknesses. Josephson behaviour was observed in some junctions which showed RSJ-like current-voltage characteristics (CVCs), Shapiro steps and Fraunhofer-like magnetic modulation of the critical current. The differences in junction properties were found to be related to microstructure and surface morphology. Using off-axis laser ablation, high quality smooth and outgrowth free c-axis trilayers were obtained. The CVCs for junctions with a 60 nm thick PBCO barrier were hysteretic RSJ-like at low temperatures (<20 K). In addition to high <I>I</I><SUB>c</SUB><I>R</I><SUB>N</SUB> products (8-18 mV), we observed an exponential dependent of <I>R</I><SUB>N</SUB> with decreasing temperature indicating transport through a semiconducting-like PBCO barrier. The conductance spectra revealed a pronounced BCS-like gap feature at 2Δ=10.5 mV giving 2Δ/<I>k</I><SUB>B</SUB><I>T</I><SUB>c</SUB>=1.3 which was found to be reproducible between different junctions.

This thesis is concerned with the synthesis of high critical temperature (T<SUB>c</SUB>) copper oxide superconductors and related materials. Details are given of a range of substituted phases based on the TBa<SUB>2</SUB>Cu<SUB>3</SUB>O<SUB>7</SUB> structure. Chapter 1 introduces the discovery and development of the high T<SUB>c</SUB> superconductors and describes their structural features. Theoretical considerations of the methods of structure determination are presented in Chapter 2 and the experimental techniques are detailed in Chapter 3. Chapter 4 gives the results of a study into the structural properties of borate substituted phases. The upper limit (x) of boron substitution in the YSr<SUB>2</SUB>Cu<SUB>3-x</SUB>B<SUB>x</SUB>O<SUB>7</SUB> structure was found to be ≈ 0.75. Rietveld refinement using X-ray diffraction data shows YSr<SUB>2</SUB>Cu<SUB>2.25</SUB>B<SUB>0.75</SUB>O<SUB>7</SUB> to be orthorhombic (a = 3.8176(2)Å, b = 3.8345Å, c = 10.9708Å). An electron microscopy study of this material showed a 4B:Cu ordering, giving an a x 5b x 2c supercell, consistent with an upper limit of x ≈ 0.8. Attempts to Rietveld refine the geometry of the borate group from neutron diffraction data were unsuccessful. Exploration of several mixed T1 or Bi copper oxoborate compositions did not yield any new phases. The effects of cation substitutions and inherent disorder in T1Sr<SUB>2</SUB>(Ca,Y)Cu<SUB>2</SUB>O<SUB>7</SUB> based materials are described in Chapter 5. 'T1Sr<SUB>2</SUB>(Ca<SUB>0.4</SUB>Y<SUB>0.6</SUB>)Cu<SUB>2</SUB>O<SUB>7</SUB>' was found, by resonant synchrotron X-ray diffraction, to be (T1<SUB>0.922(4)</SUB>Cu<SUB>0.078</SUB>)Sr<SUB>2</SUB>(Ca<SUB>0.195(5)</SUB>Y<SUB>0.805</SUB>)Cu<SUB>2</SUB>O<SUB>7</SUB>, with the inherent cross-substitution giving an optimally doped material with an average copper oxidation state of +2.14 and T<SUB>c</SUB> = 86K. A comparison of first row transition metal substituents in this structure shows Mn to be a particularly good substituent, yielding an almost phase pure material with a high T<SUB>c</SUB> (97K). Chapter 6 describes attempts to make the Mn analogue of YBa<SUB>2</SUB>Cu<SUB>3</SUB>O<SUB>7</SUB>, YBa<SUB>2</SUB>Mn<SUB>3</SUB>O<SUB>9-x</SUB>, which led to the discovery of a new tetragonal layered Mn oxide, YBaMn<SUB>2</SUB>O<SUB>5</SUB> (a = 3.9204Å, c = 7.6614Å). This material exhibits no oxygen non-stoichiometry and is a valence ordered, insulating ferrimagnet below 167K.

In superconductors, I set up the <I>free energy</I> of the system in terms of the macroscopic wavefunction and vector potential. I then computationally minimised the free energy to find the distribution of these quantities when the system is thermodynamically stable. This yielded the number density of superelectron distribution in space and the magnetic field distribution. The path that the system takes toward free energy minimisation gives its time evolution. I looked in particular at a force free case where both an external field and an external current are applied along the axis of a 3d superconducting cylinder. The current causes <I>rings</I> of magnetic field to form perpendicular to the applied field. I showed that, as expected, <I>vortices</I> tend to form along the local magnetic field direction. These vortices are tubes of normal material (with few superelectrons) surrounded by a whirlwind of supercurrent. The vortices repelled each other and formed a hexagonal lattice as expected. Normally, vortices will move under the influence of current causing a non-zero resistance, but I was able to show that the application of an additional magnetic field was enough to cause the vortices to be entangled and so pinned by each other. This effect could be useful in increasing J<SUB>c</SUB> in superconductors in future. Various different currents and fields were tried including high currents which result in a complex, highly twisted vortex pattern. Two different ways of meshing the sample were tried in the computer simulation.

This work focuses on the optimisation of critical current density, <i>J_c </i>of bulk polycrystalline MgB₂ via studying the influence of boron precursor powder, nominal Mg non-stoichiometry and finally by chemical modification. On the influence of the nature of the boron precursor on the superconducting properties of MgB₂, <i>J</i>_c’s for the MgB₂ made from high purity amorphous boron are at least a factor of three higher than typical values measured for standard MgB₂ samples made from amorphous precursors. Two possible mechanisms are proposed to account for this difference. Samples made from crystalline boron powders have around an order of magnitude lower <i>J</i>_c’s compared to those made from amorphous precursors. X-ray, superconducting transition temperature, <i>T_c</i>and resistivity studies indicate that this is as a result of reduced current cross section due to the formation of (Mg)B-O phases. The samples made from amorphous B contain far fewer Mg(B)-O phases than crystalline B despite the fact that the amorphous B contains more B₂O₃. The different reactivity rates of the precursor powders can account for this anomaly. The influence of Mg content was investigated in a series of samples with systematic variation of nominal Mg non-stoichiometry. <i>J</i>_c(<i>H</i>) was found to be influenced significantly with variation of Mg while leaving <i>T_c </i>unchanged. Mg deficient samples show higher degree of disorder as inferred from the Raman spectroscopy data. The Mg deficient samples also show higher <i>H</i>_irrand <i>H</i>_c2compared to samples with reduced Mg vacancy as the Mg nominal content increases. Based on the results from Raman spectroscopy studies, XRD, resistivity and normalised <i>J_c</i>(<i>H</i>), a phase diagram for Mg<i>_x</i>B­₂ – Mg is proposed. For chemical modification, different reaction conditions and amount of Cu, GaN and Dy₂O₃ additions into MgB­­₂ during the <i>in situ</i> reaction enhance <i>J_c</i> at 6k and 20K up to 5T without changing <i>T_c</i> appreciably compared to undoped samples whereas ZrO₂ additions combined with ball milling degrade <i>T_c</i> and <i>J</i>_c. Attempt of Cu substitution in varying annealing temperatures does not result in doping of lattice structure. The optimisation of <i>J_c</i> is found to rest on the competing effects between the improved grain connectivity and MgB₂ phase formation versus Mg-Cu secondary phase formation which decreases <i>J_c</i>. Additions of Ga in the form of GaN into MgB₂ produce plate-like grains and enhance <i>J_c</i>. Dy­₂O₃ additions result in the highest <i>J_c</i> at both 6K and 20K up to 5T among the additives studied. The best sample (only 0.5 wt.% Dy₂O₃) had a <i>J_c</i> ~ 6.5 X 10⁵ Acm^-2 at 6K, 1T and 3.5 x 10⁵ Acm^-2 at 20K, 1T, around a factor of 4 higher compared to the best pure sample, and equivalent to hot-pressed or nano-Si added MgB₂ at ≤ 1T. Even distributions of nano-scale precipitates of DyB₄ and MgO were observed within the grains. The room temperature resistivity decreased with Dy₂O₃ indicative of improved grain connectivity.

The magnetotransport properties of three new superconducting compounds (Y<SUB>1-x</SUB>Ca<SUB>x</SUB>Ba<SUB>2</SUB>Cu<SUB>3</SUB>O<SUB>7-δ</SUB>, TI<SUB>2</SUB>Ba<SUB>2</SUB>CuO<SUB>6+δ</SUB> and RNi<SUB>2</SUB>B<SUB>2</SUB>C) have been investigated. The study has principally involved measurements of the anisotropic resistivity, magnetoresistance, and Hall effect of these compounds. Results for sintered and thin film samples of Y<SUB>1-x</SUB>Ca<SUB>x</SUB>Ba<SUB>2</SUB>Cu<SUB>3</SUB>O<SUB>7-δ</SUB> are presented. The Hall coefficient of the fully oxygenated overdoped material is smaller in magnitude and has a weaker temperature dependence than that of optimally doped material, while the resistivity has an upward curvature and can be well fitted by A + BT + CT<SUP>2</SUP>. Despite these large changes in ρ and R<SUB>H</SUB>, cot(θ<SUB>H</SUB>) shows remarkably little variation with doping, as is also the case for underdoped YBa<SUB>2</SUB>Cu<SUB>3</SUB>O<SUB>7-δ</SUB>. By fitting the small downturn in the resistivity above T<SUB>c</SUB> to 3D Gaussian fluctuation theory, it is possible to estimate the c-axis coherence length ξ<SUB>c</SUB>, and it is shown that the planar hole concentration has a much stronger effect on ξ<SUB>c</SUB> than had previously been thought. In addition, it is shown that overdoping Y<SUB>1-x</SUB>Ca<SUB>x</SUB>Ba<SUB>2</SUB>Cu<SUB>3</SUB>O<SUB>7-δ</SUB> causes the mixed-state resistivity to mainly shift rather than broaden in applied magnetic fields. Measurements of the c-axis magnetoresistance of single crystals of TI<SUB>2</SUB>Ba<SUB>2</SUB>CuO<SUB>6+δ</SUB>(TI-2201) reveal a striking four-fold angular dependence as the magnetic field is rotated in the ab-plane. A metallic c-axis resistivity (dρ<SUB>c</SUB>/dT > 0) indicates that the out-of-plane transport may be coherent, and based on this assumption a simple model with an anisotropic relaxation time τ is developed. Calculations based on this model using Boltzmann transport theory are used to interpret the data and obtain values of the mean free path for carrier motion parallel and perpendicular to the CuO<SUB>2</SUB> planes. Although the ab-plane value is consistent with other estimates, the c-axis mean free path is smaller than the distance between adjacent CuO<SUB>2</SUB> planes (in the experimental temperature range). In addition, it is shown that changes in the anisotropy in τ with temperature cannot fully account for the observed temperature dependence of the in-plane Hall coefficient.