Non-Abelian excitations, including Majorana fermions, parafermions, and Fibonacci anyons, provide potential new settings for realizations of topological quantum computation operations. Topological quantum systems have the advantage of being protected against some types of entanglement with the surrounding environment, but their elusive nature has inspired many to pursue rare systems in which they may be physically realized. In this work we present a new platform for production of parafermions in the ν=1/3 fractional quantum hall effect regime in a two-dimensional hole gas in a Gallium Arsenide quantum well, where spin transitions in the rich Γ₈ Luttinger ground state can be manipulated by gate-controlled electric fields. When numerical and analytical calculations of many-particle interactions combine with a proximity-induced superconducting pairing potential in this system, the spin transition we observe gives rise to a superconducting gap with an onset of six-fold degenerate ground state which disappears at critical values of the gap parameter Δ_k, the energetic signature associated with parafermion production.<br>

O presente trabalho consiste na expansão1/N de uma versão estendida do modelo de Nambu-Jona-Lasinio SU(3) no contexto de integrais funcionais. A equação de gap propagadores mesônicos, decaimentos e espalhamentos, aparecem naturalmente como ordens diferentes na expansão. A característica nova nesta abordagem é a inclusão de correções de ordem superior à ordem dominante, que nunca foram consideradas anteriormente. O método também permite a construção de uma densidade de Lagrangeana quiral mésons interagentes baseada no modelo Nambu-JonaLasinio SU(3) aqui obtida pela primeira vez. / The present work consists in 1/N expansion extended version of the SU(3) Nambu-Jona-Lasinio model in the context of the Functional Integral. The gap equations, meson propagators, triangle diagram, etc, appear quite naturally as different orders in the expansion. The new features of this approach in the inclusion of high order corrections in the I/N leading orders, which have never been included in the previous one. The method also allows for the construction of a chical Lagrangean of interacting mesons based on the SU(3) NJL model, here obtained for the first time.

O presente trabalho consiste na expansão1/N de uma versão estendida do modelo de Nambu-Jona-Lasinio SU(3) no contexto de integrais funcionais. A equação de gap propagadores mesônicos, decaimentos e espalhamentos, aparecem naturalmente como ordens diferentes na expansão. A característica nova nesta abordagem é a inclusão de correções de ordem superior à ordem dominante, que nunca foram consideradas anteriormente. O método também permite a construção de uma densidade de Lagrangeana quiral mésons interagentes baseada no modelo Nambu-JonaLasinio SU(3) aqui obtida pela primeira vez. / The present work consists in 1/N expansion extended version of the SU(3) Nambu-Jona-Lasinio model in the context of the Functional Integral. The gap equations, meson propagators, triangle diagram, etc, appear quite naturally as different orders in the expansion. The new features of this approach in the inclusion of high order corrections in the I/N leading orders, which have never been included in the previous one. The method also allows for the construction of a chical Lagrangean of interacting mesons based on the SU(3) NJL model, here obtained for the first time.

<p>This thesis describes the experimental results of liquid polymer droplets levelling on thin films of identical polymer liquid. Through varying the thickness of the underlying polymer film relative to the size of the droplet height, we have observed a crossover in the dynamics between droplets spreading on very thin films to droplets levelling on films thicker than the droplet itself. In the thin film regime, the underlying film behaves as a pre-existing precursor film and the droplet spreads according to the well-known Tanner's law where the droplet height, d₀, decreases in time as d₀ ~ t^-1/5. In the opposite regime, when the film thickness is much greater than the initial droplet height, the droplet levels with a much stronger time dependence compared to Tanner's law spreading, d₀ ~ t^-1/2. Not only have we observed the two extreme cases, we have also experimentally observed levelling behaviour of intermediate systems, where the droplet height and film height are on the same order. We have captured experimentally the crossover behaviour of droplets spreading on thin films to droplets levelling on thick films. In addition, we have developed a theoretical model that accurately captures the physics of this crossover using the lubrication approximation for thin film flows. The relevant background information will be presented as well as a detailed description of the sample preparation techniques required to fabricate spherical caps atop thin films of identical material.</p> / Master of Science (MSc)

<p>In this thesis we present a ⁷⁷Se NMR study of the iron selenide based high-temperature superconductor K_xFe_2−ySe₂ (T_c = 33 K). We observe NMR lineshapes as narrow as ∼ 4.5 kHz with an applied field along the crystal c-axis, and find no evidence for the co-existence of magnetic order with superconductivity. With an applied field along the ab plane, however, the lineshape splits into two peaks of equal intensities at all temperatures, suggesting that the tetragonal fourfold symmetry of the average structure may be locally lowered by vacancy superstructure. Knight shift data indicate that spin susceptibility decreases progressively with temperature, similar to other iron arsenide high-T_c systems. In the nuclear spin-lattice relaxation rate 1/T₁ we observe no Hebel-Slichter coherence peak, nor any enhancement in low frequency antiferromagnetic spin fluctuations in 1/T₁T. We also report on the effects of sulphur (S) substitution on the selenium sites in this system by conducting ⁷⁷Se NMR measurements on K_xFe_2−ySe_2−zS_z (z = 0.8, 1.6). We find that both spin susceptibility and low frequency spin fluctuations are suppressed with increasing S content along with T_c.</p> / Master of Science (MSc)

<p>The purpose of this thesis is twofold and motivated by recent developments in string theory and extra dimensional models. The first objective is to describe the development and progress in the codimension-2 brane paradigm as a potential cosmological scenario. Secondly, it presents the Antide Sitter/Conformal Field Theory (AdS/CFT) conjecture, also known as holography, as a tool for calculating physical quantities in condensed matter system and goes on to model the quantum Hall effect. We first describe the initial development of treating back-reaction in codimension-2 branes systems with a scalar and gauge field. The purpose of this is to examine the low-energy effective dynamics on the brane. Furthermore, applications are then explored for D7-branes in F-theory as well as D3-branes in large extra dimensional scenarios explored as a model for the cosmological constant problem. The result of this work is that the higher and lower dimensional scenarios are consistent with each other once brane back-reaction is considered in these models. This work led to a number of future works one of which is in relation to the cosmological constant problem. While the subsequent work is beyond the scope of this thesis, we present a picture and further references for the reader. The larger, later, portion of this thesis introduces the concept of holography, its origins, and the applicability to condensed matter systems. Furthermore, we discuss the applicability in particular to the quantum Hall effect (QHE) and present a model in the holographic language that correctly reproduces some of the physics of the QHE. This includes a paper in which we introduce the model, along with demonstration of symmetry properties and conductivity calculations, as well as a paper which examines the finite size scaling behaviour of the model. As a benefit to the reader, we present a `starter edition guide' to the AdS/CFT dictionary preceding these papers for non-experts such that this thesis is self-contained. The upshot is that these avenues of work, in particular quantum Hall-ography, have been very successful in modeling physics using tools originally developed by string theory. As such, it provides support for string theory as a model and framework, as well as providing more opportunities for future predictions of physical quantities.</p> / Doctor of Philosophy (PhD)

<p>In Part I, the relationship between the topology of the Fermi surface and the entanglement entropy S is examined. Spinless fermionic systems on one and two dimensional lattices at fixed chemical potential are considered. The lattice is partitioned into sub-system of length L and environment, and the entanglement of the subsystem with the environment is calculated via the correlation matrix. S is plotted as a function of the next-nearest or next-next nearest neighbor hopping parameter, t. In 1 dimension, the entanglement entropy jumps at lifshitz transitions where the number of Fermi points changes. In 2 dimensions, a neck-collapsing transition is accompanied by a cusp in S, while the formation of electron or hole-like pockets coincides with a kink in the S as a function of the hopping parameter. The entanglement entropy as a function of subsystem length L is also examined. The leading order coefficient of the LlnL term in 2 dimensions was seen to agree well with the Widom conjecture. Of interest is the difference this coefficient and the coefficient of the term linear in L near the neck-collapsing point. The leading order term changes like |t-t_c|^1/2 whereas the first sub-leading term varies like |t-t_c|^1/3, where t_c is the critical value of the hopping parameter at the transition.</p> <p>In Part II, we study the statistics of fractionalized excitations in a bosonic model which describes strongly interacting excitons in a N-band insulator. The elementary excitations of this system are strings, in a large N limit. A string is made of a series of bosons whose flavors are correlated such that the end points of a string carries a fractionalized flavor quantum number. When the tension of a string vanishes, the end points are deconfined. We determine the statistics of the fractionalized particles described by the end points of strings. We show that either bosons or Fermions can arise depending on the microscopic coupling constants. In the presence of the cubic interaction in the Hamiltonian as the only higher order interaction term, it was shown that bosons are emergent. In the presence of the quartic interaction with a positive coupling constant, it was revealed that the elementary excitations of the system possess Fermion statistics.</p> / Master of Science (MSc)

<p>The study of ultrathin magnetic films offers novel magnetic phenomena due to the reduced symmetry of these 2D systems. The magnetic anisotropy differentiates behaviour in ultrathin films from the bulk environment, as additional anisotropies emerge from the ultrathin film thickness and the inherent strain of ultrathin films. In this work, the in-plane magnetic anisotropy of strained ferromagnetic (FM) ultrathin Co(0001) films grown on a W(110) substrate is measured over a range of temperatures (150-320 K). Low energy electron diffraction (LEED) and Auger electron spectroscopy (AES) were used to determine the film structure and thickness. The anisotropy is derived from the quotient of the saturation magnetization and the transverse susceptibility, which are measured using the surface magneto-optic Kerr effect (SMOKE).</p> <p>This work’s second objective is to study the Néel transition in antiferromagnetic (AFM) ultrathin films. The zero net magnetization of AFM materials and the minute sample size of ultrathin films make magnetic measurements impossible with conventional methods. An alternative approach is to study a single AFM ultrathin film that is coupled by the interfacial exchange interaction to a FM ultrathin film. The upper layers of ultrathin Co/W(110) films were oxidized to produce ultrathin CoO/Co/W(110) films, creating an AFM/FM bilayer system. SMOKE measurement of the transverse magnetic susceptibility of the FM Co layer reveal the Néel transition of the AFM layer indirectly through the interfacial exchange interaction.</p> / Master of Science (MSc)

<p>In this thesis, we present the results for the finite frequency response of a variety of materials. These materials all share the common theme that their low energy excitations are Dirac-like. This coincidence was not by design, and highlights the now-ubiquitous nature of Dirac-quasiparticles in condensed matter physics. We present results for graphene, the high temperature superconducting cuprates, and Weyl semi metals. For graphene, our calculations revolve around a new experimental technique: Near field infrared spectroscopy. Conventionally it is ok to use the $\vec{q}\rightarrow 0$ limit when calculating the low energy optical response. This new technique is able to directly probe the finite $\vec{q}$ response by using an atomic force microscope tip as an antenna. We computed the optical conductivity of graphene at finite wavevector and studied how the quasiparticle peak is altered by disorder and the electron-phonon interaction. The calculations on the high $T_c$ cuprates use a model of the pseudogap phase known as the Yang, Rice and Zhang (YRZ) model. We employed the model to study the resistivity in the pseudogap regime, both in-plane and along the c-axis. We used a coherent tunneling matrix element to describe transport along the c-axis. We found that the model was able to reproduce the metaliclike behavior in the plane while being resistive out of plane. We then extended the model to the finite frequency response, as well as the superconducting phase. We found a pseduogap feature at finite frequency that was previously explained through an interlayer collective mode. We also found that microwave spectroscopy puts strong limits on the form of the scattering rate. Finally, we computed the optical response of Weyl semimetals subjected to an applied magnetic field. Weyl semimetals are a topological phase of matter that have yet to be observed. The form of the conductivity contains a series of asymmetric peaks, whose spacing is a signature of the underlying relativistic dispersion. These peaks remain robust, even with moderate disorder.</p> / Doctor of Philosophy (PhD)

<p>This thesis details a collection of experiments performed on two condensed matter systems, Co-doped BaFe₂As₂ and URu₂Si₂. These two materials are related by their structural type (<em>ThCr₂Si₂</em>-type) serving as great examples of the diversity of material properties present in this family. They are also both superconducting materials and belong to the collection of strongly-correlated electron systems. The interest in studying the Ba(Fe,Co)₂As₂ group of materials is due to the high superconducting transition temperature in these (and related) materials, while the compound URu₂Si₂ was studied due to the presence of a poorly-understood 'hidden order' phase.</p> <p>Muon spin relaxation/rotation/resonance (µSR) was used to measure several single crystals of the series Ba(Fe_2-<em>x</em>Co<em>_x</em>)₂As₂ with Cobalt concentrations <em>x </em>= 0.038, 0.047, 0.061, 0.074, 0.107 and 0.114, and a single crystal of Sr(Fe_0.87Co_0.13)₂As₂. The two samples with the lowest doping, <em>x </em>= 0.038 and <em>x </em>= 0.047, showed strong c-axis magnetism occurring below the magnetic transition, T_SDW. The measurements suggest that the local magnetic field is increasingly disordered as the concentration of Co increases. These samples were shown to exhibit both superconductivity and magnetism, but that the entire sample contains non-zero local magnetic fields, meaning that superconductivity exists in or near regions of strong magnetic order.</p> <p>The remaining compounds (with <em>x </em>= 0.061, 0.074, 0.107, 0.114 and Sr(Fe_0.87Co_0.13)₂As₂) were measured with zero-field (ZF)-µSR and no magnetic ordering was found down to T = 1.65 K. An analytic Ginzburg-Landau model was used to fit the data and obtain absolute values for the penetration depth, λ. A model for the temperature dependence of the density of superconducting carriers, n_s ≈ λ², based on two <em>s</em>-wave gaps describes the data well. Below T_SC, a paramagnetic frequency shift was observed indicative of field-induced magnetism along the c crystallographic direction.</p> <p>Measurements of URu₂Si₂ under chemical and hydrostatic pressure have focused on measuring the spin correlations that are present in the hidden order phase. The chemical pressure that is induced by 5% Re doping perturbs, but does not destroy, the commensurate spin excitations. The spin gap that is present in the parent material is also present under this chemical doping. The hidden order phase survives at least halfway to the quantum critical point to ferromagnetism, but is weakened by the Re substitution.</p> <p>Under hydrostatic pressure of 10.1 kbar, URu₂Si₂ becomes antiferromagnetic, but the spin correlations are found to be qualitatively similar to those of the hidden order phase. The width in reciprocal space (Q-width) of the excitations and their gapped nature remains unchanged upon entering the antiferromagnetic phase. Quantitatively, there is an increase in the magnitude of the gap at Q = (1.4 0 0). This may be a result of the increase in the transition temperature preceding the entry to the antiferromagnetic phase.</p> <p>Due to the large difference in their properties, and hence the motivation for studying Ba(Fe_1-<em>x</em>Co<em>_x</em>)₂As₂ and URu₂Si₂, they will be introduced and presented separately. Chapter 1 will provide the necessary background material on Ba(Fe,Co)₂As₂, while Chapter 2 will provide the background for the work on URu₂Si₂. Chapter 3 will describe the experimental techniques that were used to study these systems.</p> <p>Original research results on Ba(Fe,Co)₂As₂ are presented in Chapter 4. This is mainly focused on µSR measurements of dopings that display superconductivity. Samples that did not order magnetically were measured in the mixed state to measure the vortex lattice to extract the various properties, including the superconducting pairing symmetry. Samples that did order magnetically were measured to analyze the amount of magnetic disorder and discover the extent of coexistence or phase separation between magnetism and superconductivity.</p> <p>Chapter 5 details the original research results on URu₂Si₂. This involved crystal growth of these compounds, and two neutron scattering experiments to measure the spin correlations while perturbing the hidden order state. The first experiment was done on a Re-doped crystal, URu_1.9Re_0.1Si₂. Doping with Re suppresses the hidden order, eventually leading to ferromagnetism at higher dopings. This work showed that the spin correlations are also suppressed, but not as quickly as the hidden order. The second experiment was on pure URu₂Si₂ under hydrostatic pressure. Applied pressure increases the hidden order transition, but eventually leads to antiferromagnetism, the phase in which the experiment was performed.</p> / Doctor of Philosophy (PhD)