Please read the abstract in the front of the document. / Dissertation (MSc)--University of Pretoria, 2009. / Physics / unrestricted

There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.

This thesis describes two topological phases of matter, the Weyl semimetal and the line node semimetal, that are related to but distinct from topological insulator phases. These new topological phases are semimetallic, having electronic energy bands that touch at discrete points or along a continuous curve in momentum space. These states are achieved by breaking time-reversal symmetry near a transition between an ordinary insulator and a topological insulator, using a model based on alternating layers of topological and ordinary insulators, which can be tuned close to the transition by choosing the thicknesses of the layers. The semimetallic phases are topologically protected, with corresponding topological surface states, but the protection is due to separation of the band-touching points in momentum space and discrete symmetries, rather than being protected by an energy gap as in topological insulators. The chiral surface states of the Weyl semimetal give it a non-zero Hall conductivity, while the surface states of the line node semimetal have a flat energy dispersion in the region bounded by the line node. Some transport properties are derived, with a particular emphasis on the behaviour of the conductivity as a function of the impurity concentrations and the temperature.

This thesis describes two topological phases of matter, the Weyl semimetal and the line node semimetal, that are related to but distinct from topological insulator phases. These new topological phases are semimetallic, having electronic energy bands that touch at discrete points or along a continuous curve in momentum space. These states are achieved by breaking time-reversal symmetry near a transition between an ordinary insulator and a topological insulator, using a model based on alternating layers of topological and ordinary insulators, which can be tuned close to the transition by choosing the thicknesses of the layers. The semimetallic phases are topologically protected, with corresponding topological surface states, but the protection is due to separation of the band-touching points in momentum space and discrete symmetries, rather than being protected by an energy gap as in topological insulators. The chiral surface states of the Weyl semimetal give it a non-zero Hall conductivity, while the surface states of the line node semimetal have a flat energy dispersion in the region bounded by the line node. Some transport properties are derived, with a particular emphasis on the behaviour of the conductivity as a function of the impurity concentrations and the temperature.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 118-122).

Title: Algebraic Approaches to Elementary Excitations in Media with Broken Spatial or Time-reversal Symmetry Author: Kay Condie Erb Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: Ing. Jiří Hlinka, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: Structural phase transitions with macroscopic symmetry breaking can be divided into 212 non-magnetic species according to the mutual spatial orien- tation of the point groups of both phases. Classification into the given species implies a set of universal transition properties such as the number of macroscopic domain states of the low-symmetry phase and their distinguishability by order parameter. In this work, the distinguishability of macroscopic domain states by all order pa- rameters which transform as vectors or vectorlike quantities (called bidirectors) was studied. For solving this task, a computer algorithm was designed which enabled an explicit listing of all vector and vectorlike order parameters, not only for the 212 non-magnetic species, but even for all 1602 magnetic species which includes transitions between crystallographic gray and bicolor point groups. In addition, irreducible representations of the 122 magnetic crystallographic point groups which transform as vectors or vectorlike quantities are...

In absence of external fields, vibrational modes of periodic systems are usually considered as linearly polarized and, as such, they do not carry angular momentum. Our work proves that non-adiabatic effects due to the electron-phonon coupling are time-reversal symmetry breaking interactions for the vibrational field in systems with non-collinear magnetism and large spin-orbit coupling. Since in these systems the deformation potential matrix elements are necessarily complex, a nonzero synthetic gauge field (Berry curvature) arises in the dynamic equations of the ionic motion. As a result, phonon modes are elliptically polarized in the non-adiabatic framework and intrinsic vibrational angular momenta occur even for non-degenerate modes and without external probes. These results are validated by performing fully relativistic ab-initio calculations on two insulating platinum clusters and a metallic manganese compound, with non-collinear magnetism. In both cases, non-adiabatic vibrational modes carry sizeable angular momenta comparable to the orbital electronic ones in itinerant ferromagnets.

L’apport principal de cette thèse réside dans l’évaluation de la vulnérabilité d’un certain nombre de règles de voteà la violation de deux propriétés ; nous nous appuyons pour cela sur l’approche axiomatique de la théorie du choixsocial, qui permet d’étudier le comportement d’un mécanisme de choix social vis-à-vis d’un jugement de valeurémis par l’économiste. La symétrie inverse ("reversal symmetry") est la première propriété examinée. A la suite destravaux de Saari [150], nous évaluons deux catégories de règles de vote en prenant cette propriété comme critèrede décision : d’une part, les règles positionnelles simples et d’autre part les règles positionnelles à deux tours. Plusprécisément, nous calculons la probabilité d’occurrence de ce phénomène à la fois en domaine universel (c’est-à-direlorsque les individus peuvent exprimer n’importe quel ordre de préférence), et en domaine restreint (lorsque deshypothèses supplémentaires sont introduites sur la manière dont les votants classent les « candidats » à l’élection).Nous examinons le cas de trois candidats, de quatre candidats ainsi que le contexte d’élections à un très grandnombre de votants, en faisant tendre ce nombre vers l’infini.La seconde thématique est consacrée à l’examen du comportement de la règle de Dodgson face à la propriété d’homogénéité.Nous proposons une méthode de calcul simple et systématique du score de Dodgson. Nous distinguonsensuite différentes classes de profils pour lesquels cette règle est susceptible d’être vulnérable à cette propriété. Afinde compléter notre recherche, des fréquences de violation de cette propriété par la règle de Dodgson sont fournies. / The contribution of this thesis lies in the evaluation of the vulnerability of a number of voting rules to the violationof two properties of the theory of social choice. We rely on the axiomatic approach of social choice theory to examinethe behavior of a social choice procedure according to a value judgment (or axiom) emitted by the economist.Reversal symmetry is the first property studied. Following the works of Saari [150], we evaluate two families ofvoting by using this property as the decision criterion : the simple scoring rules on the one hand, and the scoringrules with runoff on the other hand. We do probability calculations to evaluate how frequent this phenomenon is,in the three-candidate case under universal domain as well as under a restricted domain, and we also tackle thefour-candidate case and the infinite number of voters case.The second topic is devoted to the study of the Dodgsonrule according to the homogeneity axiom. We introduce a simple and systematic method for the computation ofthe Dodgson score. We distinguish various classes of profiles at which that rule may be vulnerable to this property.Further, frequencies of violation of this property by the Dodgson rule are provided.

O presente trabalho é um estudo sobre a importância da informação dos orbitais atômicos no cálculo de propriedades optoeletrônicas de heteroestruturas semicondutoras de baixa dimensionalidade. O trabalho é dividido em duas partes: na primeira parte, é estudada a simetria de reversão temporal no hamiltoniano k . p, analisando a preservação da informação de spin presente nos orbitais atômicos. O hamiltoniano obtido é inserido na equação de massa efetiva expandida para superredes. São calculadas estruturas de bandas de alguns poços quânticos de semicondutores III-V e grupo-IV. Compara-se o novo método com os tradicionais, e então são analisadas algumas grandezas que apresentam alteração significativa entre os métodos usados; A segunda parte é composta por um estudo detalhado do potencial de troca-correlação em semicondutores dopados. A matriz que descreve este potencial é escrita usando a distribuição de portadores presentes nos orbitais atômicos da rede cristalina, e os coeficientes desta matriz foram calculados usando quatro modelos para a correção de muitos corpos, baseadas nas aproximações LDA (Local density approximation) e LSDA (Local spin density approximation), com o objetivo de comparar as diversas parametrizações. Usando o método k . p tradicional, expandido para superredes, foram simulados sistemas δ-doped e hMni-δ-doped de Si, através de um cálculo autoconsistente baseado na equação de Poisson. A magnetização dos portadores é descrita por um modelo de campo médio. Foram analisados os perfis de potencial, estruturas de bandas, polarização de portadores e espectros de fotoluminescência para determinar as diferenças entre as aproximações utilizadas. / This work is a study about the atomic orbitals information importance in the calculation of optoelectronics properties of low dimensionality semiconductors. The work is divided in two parts. In the first one, a study of the time reversal symmetry of the k . p Hamiltonian is realized analyzing the preservation of the spin information present in the atomic orbitals. The obtained Hamiltonian is applied in the effective mass equation expanded to superlattices. Some calculations of quantum wells band structures are made using III-V and group-IV semiconductors, comparing the new method with the conventional ones to obtain an analysis of the difference of some physics properties. The second part is a detailed study of the exchangecorrelation potential in doped semiconductors. The matrix coefficients are calculated using the charge distribution of the crystalline lattice atomic orbitals, applied in some LDA (Local density approximation) and LSDA (Local spin density approximation) parameterizations to compare them. Using the conventional k . p method expanded to superlattices, Si δ-doped and hMni-δ-doped systems were calculated through a self consistent calculation based on Poissons equation. The carriers magnetization is described by an average field model. The potential profiles, band structures, carrier polarization and photoluminescence spectra were analyzed to obtain the difference between the approaches.

Cette thèse a pour objet l’étude des effets de cohérence de la propagation d’ondes en milieu désordonné, à l’aide d’atomes ultrafroids. Ces systèmes permettent un contrôle précis de paramètres clés, tels que la dimensionnalité, les interactions, la vitesse initiale des atomes et le potentiel externe. Utilisant cette flexibilité, il a été possible de réaliser des expériences en régime fortement et faiblement localisé. La première expérience traite de l’expansion d’un condensat, dont une fraction maximale de 20% est localisée, permettant ainsi l’observation de la localisation d’Anderson en 3D. Lors de la seconde expérience, les atomes ont été envoyés dans un désordre quasi 2D avec une vitesse initiale bien définie. Il a été possible d’observer la distribution en impulsions des atomes, et ainsi de mesurer le temps de libre parcours moyen et le temps de transport. La rétrodiffusion cohérente s’est clairement manifestée sous la forme d’un pic dans la direction opposée à la direction initiale. L’amplitude et la largeur de ce pic ont été étudiées, et les résultats sont en accord avec la théorie. Microscopiquement, la rétrodiffusion cohérente a pour origine l’interférence constructive entre chemins à diffusions multiples symétriques par renversement du temps (symétrie T). Cette symétrie de la propagation d’ondes a été ensuite manipulée. Un déphasage précis a été introduit grace à un pulse de gradient de champ magnétique, qui détruit la symétrie T ainsi que la rétrodiffusion cohérente, sauf pour un bref instant : une résurgence du pic est alors observée. Ce nouvel effet démontre explicitement le rôle de la cohérence et de la symétrie T dans la localisation faible. / In this manuscript the coherence effects of wave propagation in disordered potentials is studied. Our experiment uses ultracold atoms as a probe, a system allowing for a very good control over parameters such as the dimensionality, interactions, initial velocity of the atoms, and the potential landscape. Exploiting this flexibility we were able to perform experiments in the strongly and the weakly localized regime. In the former the 3D expansion of a BEC was monitored in real space, resulting in the observation of 3D Anderson localization with a maximum localized fraction of about 20%. In the latter the atoms were launched into a quasi-2D disorder with a well defined initial velocity. Monitoring the momentum space distribution the mean scattering time and the transport time can be directly measured, and coherent backscattering (CBS) is clearly visible as a peak in the backwards direction. In a first set of experiments the evolution of the CBS amplitude and width were recorded and found to be in good agreement with theory. Microscopically, CBS stems from the constructive interference of time-reversed multiply scattered paths. In a second set of CBS experiments we manipulated the time-reversal symmetry (TRS) of the wave propagation. A surgical dephasing was introduced via a shortly pulsed gradient field, which brakes TRS and suppresses CBS except for a brief moment, when a revival of CBS is observed. This novel effect showcases explicitly the role of coherence and TRS in Coherent Backscattering and weak localization.