M.Sc. / Spin-density-wave (SDW) effects are investigated in a Cr + 1.9 at.% Fe alloy single crystal, where the Fe concentration lies just below the triple point found in the temperatureconcentration magnetic phase diagram of the Cr-Fe alloy system. The crystal is expected to undergo a commensurate (C) SDW to an incommensurate (I) SDW phase transition at a temperature Tc, and an ISDW-P (paramagnetic) phase transition at the Neel temperature, TN. The magnetoelastic properties and the anharmonic behaviour of this crystal were studied with the aid of velocity of sound measurements as function of temperature and pressure. Electrical transport measurements were carried out using the standard fourprobe method. In order to determine the various phases present in the crystal a preliminary neutron-diffraction study was also done. Fe belongs to the group-8 magnetic transition metals, possessing localized magnetic moments. The SDW effects in the Cr + 1.9 at.% Fe crystal are therefore compared with that of Cr-Ru and Cr-Ir alloys, as Ru and Ir also belong to the group-8 transition metals, however these impurities are nonmagnetic. The following observations were made: The longitudinal mode elastic constants and the bulk modulus show a prominent change in the slope at Tc, and a sharp, deep minimum at TN. For the c' shear propagation mode peaks were seen at Tcl as well as TN and the c4 4 propagation mode showed no anomalies at either phase transition temperatures. The longitudinal ultrasonic wave velocities for the cL propagation mode were measured as a function of temperature at different constant pressures. TN obtained from these measurements varies linearly with increasing pressure. High-pressure ultrasonic wave velocity measurements were taken at various constant temperatures in the range of 230 K to 350 K for the C L, c44 and c' propagation modes of the Cr + 1.9 at.% Fe alloy single crystal. This was used to determine the pressure derivatives of the second order adiabatic elastic constants (acu /ap). The pressure derivatives of the second order adiabatic elastic constant are shown to be a very powerful tool for investigating the interaction of the SDW with the acoustic phonons in the Cr-Fe crystal. II The long-wavelength acoustic-mode Gitmeisen parameters, calculated from (acu/ap), showed that the SDW in the Cr + 1.9 at.% Fe alloy single crystal couples mainly with the longitudinal acoustic phonons. Coupling to the shear modes is relatively small. The mean acoustic-mode GrOneisen parameter shows a small maximum between Tc, and TN. It increases on heating through TN, reaching a large maximum value above TN, and then decreases with further increase in the temperature. The electrical resistivity was measured_in the temperature region of 4 Kt() 900 K in order to obtain the nonmagnetic component of the resistivity at all temperatures. Only the Neel phase transition was observed in these measurements with no resistivity anomalies taking place at -Va. The experimental results on the resisitivity were analyzed according the model of Chui et al.. The magnetic component of the electrical resistivity was calculated from the model with and without the inclusion of the effects of resonant impurity scattering of the conduction electrons by the local impurity states lying in the SDW energy gap. The magnetic contributions were found to be appreciable above TN, even up to temperatures as high as 1.5TN. The neutron-diffraction experiments show that the Cr + 1.9 at.% Fe crystal remains in the ISDW phase at all temperatures below TN. This is an unexpected result as a CSDW-ISDW phase transition is expected at To, the temperature of the observed anomaly in elastic constant and thermal expansion measurements on the crystal

Density wave oscillations (DWO) are a class of two-phase flow instabilities which can pose significant safety concerns to boiling water reactors (BWR). During an anticipated transient without scram (ATWS) while operating in the proposed extended operating domain MELLLA+, natural circulation conditions can potentially lead to DWO-type instabilities which have the capability to develop into cycles of fuel surface dryout and rewet, damaging core integrity. In order to provide data on these phenomena, a series of tests were performed at the KATHY facility during which DWO was developed with and without simulated neutronic feedback. In this dissertation, the data provided by these tests is analyzed to determine the onset conditions for DWO. Following this, several models are assessed for their capability in predicting this stability boundary compared to the experimental results. The models were chosen in order to provide a suitably large range of prediction methodologies. Two analytical drift-flux models developed with and without thermal equilibrium are shown, with respective differences compared. A computational model of the full KATHY natural circulation loop is built using the 1D thermal-hydraulics code TRACE. This is adapted with a point-kinetics model for neutronic feedback for experimental comparison. With both the analytical models and the TRACE model, a series of parametric studies are performed showing the effects of inlet/outlet flow restrictions, pressure, channel geometry, and axial power profile on the stability boundary. Finally, two machine learning neural network-based models are developed and trained on various subsets of the experimental data. The results from each model showed certain benefits and drawbacks based on model complexity and physicality. / Doctor of Philosophy / Certain conditions in the core of a boiling water reactor (BWR) can lead to unstable flows due to the high ratio between the power and the coolant flow rate. These instabilities, called density wave oscillations (DWO), have been shown to occur during a specific accident scenario known as an anticipated transient without scram (ATWS) when the reactor is operating in a lower flow domain called MELLLA+. In this accident, pump flow through the core is halted, but the reactor is not shut down. This can lead to serious safety concerns if left unaddressed. To analyze these instabilities, the KATHY facility performed a series of tests with and without power feedback from simulated neutron response. In this dissertation, the onset conditions from these tests are given and compared to several models for predicting the stability boundary. Two analytical models proposed by Ishii and Saha are compared and the effect of certain parameters on the stability is assessed. Next, a model of the KATHY loop is built using the thermal-hydraulics code TRACE both with and without simulated power feedback. Finally, two types of machine learning models are developed to determine their accuracy in predicting the instability conditions. The overall performance of each is compared and their benefits and drawbacks are highlighted.

The study of cuprate high-temperature superconductors has undergone a recent resurgence due to the discovery of charge order in several families of cuprate materials. While its existence is now well established, little is known about its microscopic origins or its relationship to high-temperature superconductivity and the pseudogap. The aim of the research presented in this thesis is to address these questions. In this thesis I will report on the use of spectroscopic-imaging scanning tunnelling microscopy (SI-STM) to visualise the short-ranged charge density wave (CDW) in Bi₂Sr₂CaCu₂O₈₊ₓ and NaxCa₂₋ₓCuO₂Cl₂. Building on previous measurements of the intra unit-cell electronic structure of cuprates, I introduce sub-lattice segregated SISTM to individually address the atomic sub-lattices in the CuO₂ plane with spatial phase sensitivity. Using this technique I establish that the CDW in Bi₂Sr₂CaCu₂O₈+x and NaxCa₂₋ₓCuO₂Cl₂ has a previously unobserved d-symmetry form factor, where a breaking of rotational symmetry within the unit cell is modulated periodically in space. Towards identifying a mechanism of CDW formation, I establish that the amplitude of CDW modulations in the electronic structure are maximal at the pseudogap energy-scale and that these modulations exhibit a spatial phase difference of π between filled and empty states. Together with the doping evolution of the CDW wave-vector this highlights the role of the low-energy electronic structure of the pseudogap regime in CDW formation. To elucidate the relationship between the CDW and the superconducting condensate I will introduce nanometer resolution scanned Josephson tunnelling microscopy (SJTM). In this approach the Cooper pair (Josephson) tunnelling current between a Bi₂Sr₂CaCu₂O₈₊ₓ sample and a scan-able Bi₂Sr₂CaCu₂O₈₊ₓ nano-flake STM tip is used to directly visualise the superconducting condensate. I will report the observation of a periodic modulation in the Cooper pair condensate at the same wave-vector as the CDW, the first direct detection of a periodically modulating condensate in any superconductor.

We perform microscopic mean-field studies of topological order in a two-dimensional topological superconductor in the Bogoliubov-de Gennes (BdG) formalism. By adopting a two-dimensional s-wave topological superconductivity (TSC) model on a minimal tight-binding system, we solve the BdG equations self-consistently to obtain not only the superconducting order parameter, but also the Hartree potential. By computing the Thouless, Kohmoto, Nightingale, and den Nijs (TKNN) number and investigating the bulk-boundary correspondence, we study the nature of Abelian and non-Abelian TSC in terms of self-consistent solutions to the BdG equations. In particular, we examine the effects of temperature and a single non-magnetic impurity deposited in the centre of the system and how they vary depending on topology. We find that the non-Abelian phase exhibits signs of unconventional superconductivity, and by examining the behaviour of this phase under both low and high Zeeman field conditions, we show that the magnitude of the Zeeman field largely dictates the susceptibility of the system to temperature. Furthermore, we investigate the possible interplay of charge density waves (CDW) and TSC. By self-consistently solving for the mean fields, we show that TSC and topological CDW are degenerate ground states---with the same excitation spectrum in the presence of surfaces---and thus can coexist in the Abelian phase. The effects of a non-magnetic impurity, which tends to pin the phase of charge density modulations, are examined in the context of topological CDW.

We have studied the charge density wave (CDW) repolarization dynamics in blue bronze (K0.3MoO3) by applying symmetric bipolar square-wave voltages of different frequencies to the sample and measuring the changes in infrared transmittance, proportional to CDW strain. The frequency dependence of the electro-transmittance was fit to a modified harmonic oscillator response and the evolution of the parameters as functions of voltage, position, and temperature are discussed. We found that resonance frequencies decrease with distance from the current contacts, indicating that the resulting delays are intrinsic to the CDW with the strain effectively flowing from the contact. For a fixed position, the average relaxation time for most samples has a voltage dependence given by τ0 ∼ V −p, with 1 < p < 2. The temperature dependence of the fitting parameters shows that the dynamics are governed by both the force on the CDW and the CDW current: for a given force and position, both the relaxation and delay times are inversely proportional to the CDW current as temperature is varied. The long delay times (∼ 100 μs) for large CDW currents suggest that the strain response involves the motion of macroscopic objects, presumably CDW phase dislocation lines. We have done frequency domain simulations to study charge-density-wave (CDW) polarization dynamics when symmetric bipolar square current pulses of different frequencies and amplitudes are applied to the sample, using parameters appropriate for NbSe3 at T = 90 K. The frequency dependence of the strain at one fixed position was fit to the same modified harmonic oscillator response and the behavior of the parameters as functions of current and position are discussed. Delay times increase nonlinearly with distance from the current contacts again, indicating that these are intrinsic to the CDWwith the strain effectively flowing from the contact. For a fixed position and high currents the relaxation time increases with decreasing current, but for low currents its behavior is strongly dependent on the distance between the current contact and the sample ends. This fact clearly shows the effect of the phase-slip process needed in the current conversion process at the contacts. The relaxation and delay times computed (∼ 1 μs) are much shorter than observed in blue bronze (> 100 μs), as expected because NbSe3 is metallic whereas K0.3MoO3 is semiconducting. While our simulated results bear a qualitative resemblance with those obtained in blue bronze, we can not make a quantitative comparison with the K0.3MoO3 results since the CDW in our simulations is current driven, whereas the electro-optic experiment was voltage driven. Different theoretical models predict that for voltages near the threshold Von, quantities such as the dynamic phase velocity correlation length and CDW velocity vary as ξ ∼ |V/Von − 1| −ν and v ∼ |V/Von − 1|ξ with ν ∼ 1/2 and ζ = 5/6. Additionally, a weakly divergent behavior for the diffusion constant D ∼ |V/Von − 1|−2ν+ζ is expected. Motivated by these premises and the fact that no convincing experimental evidence is known, we carried out measurements of the parameters that govern the CDW repolarization dynamic for voltages near threshold. We found that for most temperatures considered the relaxation time still increases for voltages as small as 1.06Von indicating that the CDW is still in the plastic and presumably in the noncritical limit. However, at one temperature we found that the relaxation time saturates with no indication of critical behavior, giving a new upper limit to the critical regime, of |V/Von − 1| < 0.06.

Thesis advisor: Stephen D. Wilson / This dissertation investigates the cubic type II superconductor, Ca₃Ir₄Sn₁₃, discovered by Remeika and the coauthors more than 30 years ago. It was originally discovered be to a superconductor and later suggested to host ferromagnetic spin fluctuations, which lead to a peak-like anomaly in thermodynamic and transport measurements. Later detailed x-ray single crystal structural refinement associated the peak-like anomaly in transport and magnetization measurements with a charge density wave phase transition at the same temperature. The potential charge density wave phase transition T* can be suppressed either by pressure or chemical potential through substitution on the Ca and Ir site such that a temperature-pressure/composition phase diagram can be constructed. Upon investigating magnetism in this compound, polarized neutron scattering and μSR data from our group and other researchers did not reveal any magnetic order or magnetic spin fluctuations at the time scale of μSR . However, through the partial substitution of Ir by Rh, we realized a structural quantum critical point at ambient pressure with 30% of Ir substituted by Rh--providing the research community a valuable material's platform for studying the interplay between 3D charge density wave order and superconductivity. On the other hand, our surprising discovery of the weak HHL (L=odd) type of super-lattice peaks from neutron scattering led us to a tentative model of a distorted Ca sublattice in this material. The similarity of the lattice instabilites of the Remeika compound and A15 superconductors are discussed, which may give us more insight into its role in the formation of the superconducting phase. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

No description available.

No description available.

Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.

Recent studies of the transition metal dichalcogenide niobium diselenide have led to debate in the scientific community regarding the mechanism of the charge density wave (CDW) instability in this material. Moreover, whether or not CDW boosts or competes with superconductivity (SC) is still unknown, as there are experimental measurements which supports both scenarios. Motivated by these measurements we study the interplay of charge density modulations and superconductivity in the context of the Bogoliubov de-Gennes (BdG) equations formulated on a tight-binding lattice. As the BdG equations require large numerical demand, software which utilizes parallel algorithms have been developed to solve these equations directly and numerically. Calculations were performed on a large-scale Beowulf-class PC cluster at the University of Saskatchewan.<p> We first study the effects of inhomogeneity on nanoscale superconductors due to the presence of surfaces or a single impurity deposited in the sample. It is illustrated that CDW can coexist with SC in a finite-size s-wave superconductor. Our calculations show that a weak impurity potential can lead to significant suppression of the superconducting order parameter, more so than a strong impurity. In particular, in a nanoscale d-wave superconductor with strong electron-phonon coupling, the scattering by a weakly attractive impurity can nearly kill superconductivity over the entire sample.<p> Calculations for periodic systems also show that CDW can coexist with s-wave superconductivity. In order to identify the cause of the CDW instability, the BdG equations have been generalized to include the next-nearest neighbour hopping integral. It is shown that the CDW state is strongly affected by the magnitude of the next-nearest neighbour hopping, while superconductivity is not. The difference between the CDW and SC states is a result of the anomalous, or off-diagonal, coupling between particle and hole components of quasiparticle excitations. The Fermi surface is changed as next-nearest neighbour hopping is varied; in particular, the perfect nesting and coincidence of the nesting vectors and the vectors connecting van Hove singularities (vHs) for zero next-nearest neighbor hopping is destroyed, and vHs move away from the Fermi energy. It is found that within our one-band tight-binding model with isotropic s-wave superconductivity, CDW and SC can coexist only for vanishing nearest neighbor hopping and for non-zero hopping, the homogeneous SC state always has the lowest ground-state energy. Furthermore, we find in our model that as the magnitude of the next-nearest neighbor hopping parameter increases, the main cause of the divergence in the dielectric response accompanying the CDW transition changes from nesting to the vHs mechanism proposed by Rice and Scott. It is still an open question as to the origin of CDW and its interplay with SC in multiple-band, anisotropic superconductors such as niobium diselenide, for which fundamental theory is lacking. The work presented in this thesis demonstrates the possible coexistence of charge density waves and superconductivity, and provides insight into the mechanism of electronic instability causing charge density waves.