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Many important properties of transition metal oxides such as, copper oxide high- temperature superconductivity and colossal magnetoresistance (CMR) in manganites are due to strong electron-electron interactions, and hence these systems are called highly correlated systems. These materials are characterised by the coexistence of different kinds of order, including charge, orbital, and magnetic moment. This thesis contains high-resolution X-ray scattering studies of charge ordering in such systems namely the high-T(_c) copper oxides isostructural system, La(_2-x)Sr(_x)NiO(_4)) with various Sr concentrations (x = 0.33 - 0.2), and the CMR manganite system, Nd(_1/2)Sr(_1/2)MnO(_3)). It also includes a review of charge ordering in a large variety of transition metal oxides, such as ferrates, vanadates, cobaltates, nickelates, manganites, and cuprates systems, which have been reported to date in the scientific literature. Using high-resolution synchrotron X-ray scattering, it has been demonstrated that the charge stripes exist in a series of single crystals of La(_2-x)Sr(_x)NiO(_4)) with Sr concentrations (x = 0.33 - 0.2) at low temperatures. Satellite reflections due to the charge ordering were found with the wavevector (2Ɛ, 0, 1) below the charge ordering transition temperature, Tco, where 2 Ɛ is the amount of separation from the corresponding Bragg peak. The charge stripes are shown to be two-dimensional in nature both by measurements of their correlation lengths and by measurement of the critical exponents of the charge stripe melting transition with an anomaly at x = 0.25. The results show by decreasing the hole concentration from the x = 0.33 to 0.2, the well-correlated charge stripes change to a glassy state at x = 0.25. The electronic transition into the charge stripe phase is second-order without any corresponding structural transition. Above the second-order transition critical scattering was observed due to fluctuations into the charge stripe phase. In a single-crystal of Nd(_1/2)Sr(_1/2)MnO(_3) a series of phase transitions were observed using high-resolution synchrotron X-ray scattering. Above the charge ordering transition temperature, Tco, by measuring the peak profiles of Bragg reflections as a function of temperature, it was found that this crystal undergoes two transitions corresponding to the transition from a paramagnetic- to a ferromagnetic state at T ≈ 252 K, and the formation of a mixture of the antiferromagnetic and ferromagnetic phases below T ≈ 200 K. Below the charge ordering temperature, Tco =162 K, additional satellite reflections with the wavevector, q = (1/2, 0, 0), were observed due to Jahn-Teller distortion of the MnO(_6) octahedra caused by charge- and orbital ordering in sample. This transition was observed to be of first-order with a hysteresis width of 10 K. In addition, another very weak satellites with wavevector (1/2, 1, 1/2) were observed possibly due to spin ordering.

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The study is an investigation of the nucleation of quantised vortices in mesoscopic superconducting discs and superconducting nanowires. Vortices nucleate in these systems when an applied magnetic fleld penetrates into the systems. A quantised vortex always carries a discrete quantum of flux. The vortex lattices in bulk samples are known to be triangular. However, in a small confined superconductor, the pattern of the vortices will be different. This is due to the fact that the effect of the boundary effect cannot be ignored in the small sample. It is interesting to understand how the presence of a boundary influences the pattern of vortices in a mesoscopic superconducting disc. To start with, we shall use London's equations. To study the systems at finite temperatures, one needs to include the entropy associated with the configuration of vortices. We also study the systems using Ginzburg-Landau equations. Recent experimental studies on Pb (lead) superconducting nanowires has found that at low temperatures far from the superconducting transition temperature, the response of the wires to a transverse applied magnetic field shows hysteresis, namely Type II response: the magnetisation curves are different under magnetic heating and cooling. Lead is a Type I superconductor and the experimental results are puzzling. The research involves a detailed numerical study of the response of Pb nanowires in applied magnetic fields at different temperatures using Ginzburg-Landau equations.

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We report on the fabrication and properties of state-of-the-art nanocrystalline Nb₃ (A1₁₋xGex) superconductors with 0 ≤ x ≤ 1. High-energy ball milling was used to produce disordered nanocrystalline powders from binary compounds and from pure elemental powders. A detailed analysis of powders milled for up to 30 h was performed using X-ray diffraction, differential scanning calorimetry and AC magnetic moment measurements. Powders milled for 6 h (bcc) and 20 h (amorphous) were consolidated using a hot isostatic press (HIP) operating at 2000 atm in a temperature range from 600°c to 1200°c. The role of isochronal post-HIP heat treatments was investigated for those materials HIP'ed at 600°c and 1200°c. For comparison purposes, heat treatments were also performed on milled powders. Nanocrystalline bulk materials were characterized using a.c. magnetometry, resistivity and SQUID measurements in magnetic fields up to 9 T to measure the critical temperature and the upper critical field. X-ray diffraction and scanning electron microscopy coupled with energy dispersive X-ray analysis were used to investigate the constituent phases, the distribution of compositions and to estimate the volume phase percent of each phase. Bulk materials fabricated from milled compounds showed a partial crystallisation recovery after HIP'ing at 600°c but subsequent annealing does not further improve the superconducting properties. For material fabricated from elemental powders, after equivalent processing using milling and HIP'ing, the material is more disordered. In contrast to compound precursors, post-HIP annealing produces significant changes in the superconducting properties. In particular, a strong enhancement of Tc and Bc₂ was achieved after a post HIP anneal of nanophase Nb₃Ge and Nb₃A1₁₋xGex materials. In this work, bulk material fabricated from milled elemental powders and HIP'ed at 600°c produced Nb₃Ge (A15) in bulk form with record Tc values of ~ 12 K and Bc₂(T) ~ 13 T. We find that the role of the optimal post HIP anneal of highly disordered material is to enhance the A15 crystal nucleation while minimising the crystallisation of oxides and secondary phases that occurs at higher temperatures and competes with superconductivity.

In this thesis we study two different aspects of holographic superconductivity. First we study fully backreacting Gauss-Bonnet (GB) holographic superconductors in 5 bulk spacetime dimensions. We explore the system’s dependence on the scalar mass for both positive and negative GB coupling, α. We find that when the mass approaches the Breitenlohner-Freedman (BF) bound and α→(L^2)/4 the effect of backreaction is to increase the critical temperature, Tc , of the system: the opposite of its effect in the rest of parameter space. We also find that reducing α below zero increases Tc and that the effect of backreaction is diminished. We study the zero temperature limit, proving that this system does not permit regular solutions for a non-trivial, tachyonic scalar field and constrain possible solutions for fields with positive masses. We investigate singular zero temperature solutions in the Einstein limit but find them to be incompatible with the concept of GB gravity being a perturbative expansion of Einstein gravity. We study the conductivity of the system, finding that the inclusion of backreaction hinders the development of poles in the conductivity that are associated with quasi-normal modes approaching the real axis from elsewhere in the complex plane. In the latter part of the thesis we investigate asymptotically anti de-Sitter (adS) and Lifshitz black holes in a bulk gravitational model that has a consistent embed-ding in string theory and that permits an arbitrary dynamical exponent, z ≥ 1. We find numerically that for both types of asymptotic spacetime there exists a two parameter family of black hole solutions. In the adS case these numerical solutions are supported by analytic solutions in the ‘probe’ or non-backreacting limit. Finally, we study the dependence of the black hole’s temperature on these two parameters.

This thesis is concerned with the fundamental physics of the superconducting-to-normal transition (sn-transition), particularly the mechanisms which give rise to massive gauge bosons and applications of the superconducting-to-normal transition, particularly in the form of superconducting radiation detectors.The basics of three of the most common types of superconducting particle detectors are discussed in Chapter 2: Superconducting Tunnel Junctions (STJs), Transition Edge Sensors (TESs), and Metallic Magnetic Calorimeters (MMCs). The chapter continues with an investigation of the phenomenon of TES excess noise, a white noise source of uncertain origin apparently intrinsic to the device [1]. The current theories of Phase Slip Shot Noise (PSSN) and percolation noise are discussed and the quantitative analytical model proposed by Fraser [2] is extended to include the magnetic field dependence of the noise spectral current density. An analytical expression for the dependence of the percolation noise spectral current density on experimental parameters is derived. In Chapter 3 the author addresses the question of whether quantum mechanical fluctuations of the vacuum energy can influence the sn-transition. The existing theory is refined by developing a treatment of the system using superconductor-specific electrodynamics. A mathematical model of the relevant vacuum interactions is derived and a quantitative estimate of the magnitude of the coupling is presented. In superconductors photons have a non-zero rest mass arising from the Higgs mechanism. Chapter 4 discusses the optical properties of a hypothetical transparent superconductor and finds practical applications. In Chapter 5 it is found that the Higgs mechanism applies to any gauge field generated by the superconducting electrons, including their gravitational field and a theory of massive gravity is developed. The massive gravitational field is propagated by non-zero rest mass gravitons, and the theory predicts the sum of gravitomagnetic flux and magnetic flux through a superconducting ring to be quantised. Some of the implications and possible experiments are explored.

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