<p> The interplay between superconductivity, magnetism and crystal structure is a central issue in the study of the high Tc cuprates. The transition metal compound La2-xBaxCuO4 (LBCO) was the very first high Tc superconductor, discovered by J. G. Bednorz and K. A. Muller in 1986. However, it has been much less extensively studied than other high Tc materials, due to the difficulty of growing large single crystals. With our Image Furnace facility, we have successfully grown high quality, large LBCO crystals (with x~0.095 , 0.08, 0.05 and 0.025) on the underdoped side of the well known 1/8 (x=0.125) anomaly in this material's phase diagram.</p> <p> Using our rotating anode X-ray source at McMaster University we have performed high-resolution X-ray diffraction studies on our x=0.095 and 0.08 samples and on a 1/8 doped LBCO (x=0.125) crystal grown by our collaborators. The X-ray study mapped out a sequence of tetragonal and orthorhombic crystal structures with temperature, which were known from earlier measurements.</p> <p>We have also performed neutron scattering studies at several Laboratories on x=0.095 , 0.08, 0.05 and 0.025 samples. We observed elastic spin incommensurate Bragg peaks in all samples, and inelastic measurements on the x=0.095 sample allowed us to explore the material's low energy spin fluctuations. The elastic neutron scattering results of higher doped samples (x=0.095 and 0.08) indicate that "collinear" static incommensurate magnetic ordering develops below the low temperature structural phase transition, and this order persists into the superconducting state. Static incommensurate magnetic order is also observed in the La2-xBaxCuO4 (x=0.05 and 0.025) compounds with ordering wavevectors which are rotated by 45° about the commensurate (0.5 ,0.5 ,0) position, with respect to that in the superconducting x=0.095 and 0.08 samples. These spin modulations are one dimensional in the x=0.05 and 0.025 samples, with ordering wavevectors lying along the orthorhombic b* direction. Such a rotation in the orientation of the static spin ordering as a function of increasing Ba doping, from diagonal to collinear is roughly coincident with the transition from an insulating to a superconducting ground state and is similar to that observed in the related La2-xSrxCuO4 system. The low energy, inelastic neutron scattering studies show that the dynamic spin susceptibility for x=0.095 is constant within the superconducting state and decreases as the temperature rises above Tc. </p> / Thesis / Doctor of Philosophy (PhD)

We study a Ginzburg--Landau model for an inhomogeneous superconductor in the singular limit as the Ginzburg--Landau parameter tends to infinity. The inhomogeneity is represented by a potential term which vanishes when the order parameter equals a given smooth function, the pinning term, which is assumed to become negative in finitely many smooth subdomains, the ''normally included'' regions. For large exterior magnetic field, we study the Gamma-limit of this inhomogeneous Ginzburg-Landau functional. The vanishing of the given smooth function near the inner boundaries imply that the associated operators are strictly but not uniformly elliptic, leading to many questions to be resolved near the boundaries of the normal regions. The method we use is an extension of many techniques including the product estimate from Sandier-Serfaty, Jacobian estimates from Jerrard-Soner and an appropriate Hodge decomposition adapted to our problem. To resolve these problems, we first study the Gamma-limit in the simpler case when the pinning term is varying but bounded below by a positive constant. Second, we consider singular limits of the three-dimensional Ginzburg-Landau functional for a superconductor with thin-film geometry, in a constant external magnetic field. The superconducting domain is multiply connected and has a small characteristic thickness, and we consider the simultaneous limit as the thickness tends to zero and the Ginzburg-Landau parameter to infinity. We do this when the applied field is strong in its components tangential to the film domain. Finally, we study the Gamma-limit of the inhomogeneous superconducting Ginzburg-Landau model with the pinning term vanishing on the boundary of the normal regions. / Thesis / Doctor of Science (PhD)

A series of neutron scattering studies of unconventional superconductors is presented. These measurements are split into two parts. The first part considers the purely magnetic scattering in low-doped $La_{2−x}Ba_{x}CuO_{4}$. This study is comprehensive and elucidates much of the doping and temperature dependence of the low energy magnetic scattering in this system. It also clearly demonstrates that two dimensional incommensurate magnetic order in this system forms at the expense of three dimensional commensurate magnetic order. The remainder of the thesis is concerned with characterizing and determining the physics underlying pronounced enhancements of the inelastic scattering found to exist at 20 meV at equivalent two dimensional magnetic zone centers in both $La_{2−x}Ba_{x}CuO_{4}$ and $La_{2−x}Sr_{x}CuO_{4}$. Arguments are presented to interpret these features as a result spin-phonon hybridization in 214 cuprate superconductors. The measurements also explore the temperature and doping dependence of these features, determining that the enhancements are largely insensitive to doping and only present parametric response at temperatures relevant for three dimensional magnetic order in this system. In addition, the first evidence for a superconducting spin gap in $La_{2−x}Ba_{x}CuO_{4}$ is presented. The implications of these findings are discussed. / Thesis / Doctor of Philosophy (PhD) / This thesis discusses a series of measurements using brand new state of the art facilities to re-examine the family of high temperature superconductors with the simplest structure. By taking advantage of these new facilities and applying their capabilities to a, relatively speaking, simpler material family, the goal is to try and learn more about what may be the cause of high temperature superconductivity - a magnetism based phenomenon with profound implications for energy efficiency, energy storage, diagnostic healthcare, quantum computing and much more. While many interesting effects were observed, two of the more important findings were observations that unify the physical descriptions of $La_{2−x}Ba_{x}CuO_{4}$ and $La_{2−x}Sr_{x}CuO_{4}$, as is necessary to have a truly universal understanding of high temperature superconductivity, and a detailed characterization we interpret as hybridization. It is clear from this work that any complete solution of superconductivity must also explain this part magnetic and part crystalline structural hybridization phenomenon.

<p> In this thesis, we investigate the possibility that a purely electronic mechanism is the cause of superconductivity in C60 materials. Several computational methods are adopted to calculate the pair-binding energy. They are perturbation theory, exact diagonalization, Gutzwiller projection, and auxiliary field Monte Carlo. Results from these different methods are compared with each other both in a C60 molecule and in other smaller molecules in order to test conclusions about whether or not a purely electronic mechanism can lead to an attractive interactions between electrons in C60 molecules.</p> <p> Besides this test of the superconductivity mechanism, we also explain in detail how to apply these different computational methods to C60 for the specific geometry of C60. Clearly illustrating these computational methods is the second goal of this thesis.</p> <p> Our final conclusion is that for both small and large Hubbard interaction U, there is pair binding in a single C60 molecule. For intermediate Hubbard interaction strength, there is no clear evidence for pair binding for the range of temperatures we explored. We suggest that the truncation of the Coulomb interaction, which is implicit in the Hubbard Hamiltonian, may suppress pair-binding of electrons in C60 and that it may be necessary to consider a model that includes the long range character of Coulomb interaction. This is a subject for further study.</p> / Thesis / Master of Science (MSc)

Since the high $T_c$ superconductivity was discovered in iron pnictides in 2008, the interplay between the reduced dimensionality, magnetism and unconventional superconductivity has been attracting renewed interest. Recently, Bao et al. and Tang et al. discovered a series of quasi-one-dimensional (quasi 1D) superconductors: \K($T_c=6.1 K$), \Rb($T_c=4.8 K$), and \Cs($T_c=2.2 K$). In this thesis, we will discuss microscopic investigation of \Cs based on nuclear magnetic resonance techniques. The first chapter is a brief introduction to this series of superconductors. The second chapter is a summary of NMR techniques and theory. In the third part, I summarize $^{133}$Cs NMR and $^{75}$As Nuclear Quadrupole Resonance (NQR) measurements on a powder sample of \Cs ($T_c < 1.6$~K). From the $^{133}$Cs NMR Knight shift $^{133}K$ measured at the Cs1 site, we show that the uniform spin susceptibility $\chi_{spin}$ increases from 295~K to $\sim$ 60~K, followed by a mild suppression; $\chi_{spin}$ then levels off below $\sim$10~K. Low frequency Cr spin dynamics, reflected on $^{75}$As $1/T_1T$ (the nuclear spin-lattice relaxation rate $1/T_1$ divided by temperature $T$), shows an analogous trend as $\chi_{spin}$. Comparison with the results of $1/T_1T$ near $T_c$ with \K($T_c=6.1$~K) and \Rb($T_c=4.8$~K) establishes a systematic trend that substitution of K$^{+}$ ions with larger alkali ions progressively suppresses Cr spin fluctuations together with $T_c$. / Thesis / Master of Science (MSc)

Achieving electrostatic control of quantum phases is at the heart of condensed matter physics allowing us to interface fundamentally different electronic orders and observe their interplay with one another. Recent investigations have revealed emergent superconductivity tuned by the electric field effect in two-dimensional (2D) semimetals and moiré heterostructures. Through electrical transport measurements, we investigate superconductivity in few-layered Td - MoTe2 in this dissertation. Given its sensitivity to the ambient, a process to encapsulate and simultaneously electrically contact the material is developed to preserve the innate properties of MoTe2. At the outset, we observe a dramatic enhancement of superconducting critical temperature (Tc) in few-layered MoTe2. Monolayer’s Tc of ∼ 7.5 K is about 60x higher than the bulk. Reflecting its relatively small Fermi surface, superconductivity is tunable with electrostatic gating andresponse to in-plane magnetic fields reveals a tilted Ising spin texture. Some 2D crystal systems exhibit a polar crystal structure resulting in a robust, nonvolatile and bistable interlayer polarization giving rise to electric-field tunable ferroelectricity. Remarkably, we show that noncentrosymmetric bilayer Td - MoTe2 exhibits such ferroelectric switching while simultaneously being a superconductor, two electronic orders conventionally thought to be incompatible with one another. Further, electrostatic doping unveils a superconductingdome. It is found that the maximum Tc is concomitant with compensated electron and hole carrier densities and vanishes when one of the Fermi pockets disappears with doping pointing towards a pairing mechanism mediated by Fermi surface nesting between electron and hole pockets. Finally, in-plane magnetotransport measurements reveal a two-fold symmetric superconductivity around the crystal axes for bilayer MoTe2. Superconductivity is maximized when magnetic field is parallel to the ?-axis of the crystal and minimized for b-axis. Although unsurprising given the ?2 crystal symmetry, these results lend further credence to the tilted Ising spin texture, as unveiled from Hc2|| measurements on the monolayer.

We analyze the distribution of coherent terahertz radiation from a regular hexagonal microstrip antenna (MSA) made from the high-Tc superconductor Bi2Sr2CaCu2O8+x (BSCCO). We discuss the C6v symmetry of the solutions of the wave equation on a hexagonal domain and distinguish between the closed-form and non-closed-form solutions. The closed-form wavefunctions of the transverse magnetic (TM) electromagnetic cavity modes are presented and formulas for the radiated power arising from the uniform part of the AC Josephson current and from the resonant cavity modes are derived. The wavefunctions and angular distribution of radiation from both sources are plotted for sixteen of the lowest-energy modes. Finally, we comment on the relevance of these power distributions to hexagonal arrays of equilateral triangular MSAs and propose a strategy for studying the non-closed-form modes.

The first project of this dissertation focuses on an extension of the Path Integral Renormalization Group (PIRG) method to the extended Hubbard model (EHM) including on-site U and a nearest-neighbor interaction V. The PIRG method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. A major advantage of the PIRG is that it is free from the Fermion sign problem. Many observables can be calculated using Wick’s theorem. The EHM is particularly important in models of charge-transfer solids (CTS) and at 1/4illing the V interaction drives a charge-ordered state. We test the method with comparisons to small two-dimensional (2D) clusters and long one-dimensional (1D) chains. The second project of this dissertation focuses on the Coulomb enhancement of superconducting pair-pair correlations in frustrated quarterilled band lattice systems. A necessary condition for superconductivity (SC) driven by electron correlation is that electronelectron (e-e) interactions enhance long range superconducting pair-pair correlations relative to the noninteracting limit. We present high-precision numerical calculations within the 2D Hubbard model on up to 100 sites showing that long range superconducting pair correlations are enhanced only for electron density 0.5. At all other fillings e-e interactions suppress pair correlations. We argue that the enhancement of pairing is due to a tendency to form local spin singlets at density 0.5. Our work provides a key ingredient to the mechanism of SC in the 2D organic-CTS superconductors, as well as in many other unconventional superconductors with frustrated crystal lattices and density 0.5. In the third project we apply our proposed concept to a real material, kappa-(BEDTTTF)2X. We present numerical results for 32 and 64 site lattices using the Constrained Path Monte Carlo and PIRG methods over a wide range of carrier density. We show that superconducting pair-pair correlations in this model are enhanced by e-e interactions for d-wave pairing symmetry uniquely for a hole density close to quarterilling. Our results indicate that this enhancement of superconductivity is not related to the presence of antiferromagnetic order, but to the strong tendency to spin-singlet formation in the quarterilled band.

No description available.

No description available.