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Previous studies have suggested that the material graphene might transition into an electron-electron interaction driven, unconventional, time-reversal-symmetry-breaking, (d+id)wave superconducting state upon either significant electron or hole doping, and, in particular, upon doping to the Van Hove singularity. As defects are likely to be introduced in the doping process, we are, in this text, concerned with the effects of defects on this superconducting state near the Van Hove singularity doping. To investigate the effects we use a mean-field treatment of a phenomenological resonant-valence-bond model. We find that the resonant-valence-bond amplitudes, which in the defect free graphene sheet are proportional to the superconducting pairing-potential, are suppressed near the defects, and that the recovery is well described by an exponential, yet anisotropic, recovery. In general, we find that the (d+id)-wave, superconducting state is quite resilient, and that even for strong defects, such as a vacancy, the recovery length is of the order of one lattice constant when extrapolated to weak pairing-potentials; this is compared to a conventional superconducting state of an attractive Hubbard model for which the same decay length is found to be of the order of a half lattice constant. For the defect free graphene sheet the (d+id)-wave state is a completely gapped state. The introduction of vacancies is, however, found to be accompanied by the appearance of midgap states. These states are shown to be localized around the vacancies. In accordance with the nature of this text, we will, for the benefit of students and non-experts, include an introductory section on the fundamental methods and concepts used. It gives a short and hopefully pedagogical introduction to the rudimentary concepts of solid state theory and the microscopic BCS theory of superconductivity.

High resolution fluorescence spectra are presented of the sideband of the 5D0+ 7F0 transition of Sm++ in KBr and KCl. Several Van Hove singularities of the phonon spectrum of the host material are directly observed. They occur at slightly different frequenciesfromthose predicted by density of states calculations based on neutron diffraction measurements. Numerical calculations of both sidebands are given and compared with experiment, with quite good agreement. Sidebands observed for Eu++ in KBr and KCl are also presented and discussed. / Thesis / Doctor of Philosophy (PhD)

The most-discussed pairing symmetry in Sr₂RuO₄ is chiral p-wave, pₓ ± p[sub]y, whose degeneracy is protected by the lattice symmetry. When the lattice symmetry is lowered by the application of a symmetry-breaking field, the degeneracy can be lifted, potentially leading to a splitting of the superconducting transition. To lift the degeneracy, the symmetry breaking field used in this study is uniaxial stress. Uniaxial stress generated by a piezo-electric actuator can continuously tune the electronic structure and in situ lower the tetragonal symmetry in Sr₂RuO₄. Previous studies of magnetic susceptibility and resistivity under uniaxial stress have revealed that there is a strong peak in T[sub]c when the stress is applied along the a-axis of Sr₂RuO₄. In addition, it has been proposed that the peak in T[sub]c coincides with a van Hove singularity in the band structure, and measurements of Hc₂ at the maximum T[sub]c indicate the possibility of an even parity condensate for Sr₂RuO₄ at the peak in Tc. In this thesis, the heat capacity approach is used to study the thermodynamic behavior of Sr₂RuO₄ under uniaxial stress applied along the crystallographic a-axis of Sr₂RuO₄. The first thermodynamic evidence for the peak in T[sub]c is obtained, proving that is a bulk property. However, the experimental data show no clear evidence for splitting of the superconducting transition; only one phase transition can be identified within the experimental resolution. The results impose strong constraints on the existence of a second phase transition, i.e. the size of the second heat capacity jump would be small or the second T[sub]c would have to be very close to the first transition. In addition to these results, I will present heat capacity data from the normal state of Sr₂RuO₄. The experimental results indicate that there is an enhancement of specific heat at the peak in T[sub]c, consistent with the existence of the van Hove singularity. The possibility of even parity superconductivity at the maximum T[sub]c has also been investigated. However, the heat capacity measurements are shown to be relatively insensitive to such a change, so it has not been possible to obtain strong and unambiguous evidence for whether it takes place or not.

This study looks at the fluid interactions from the wake of a sail boat performing the heaving-to storm tactic in heavy weather seas with the waves. This interaction causes the wave height in the wake to be reduced. The fluid flow in the top layer of the wave is seen to move with the wake as the hull drifts with the wind. This movement of the top layer of the wave provides a vertical momentum cancelation affect with the portion of the wave that it moves over reducing the wave height. STAR-CCM+ CFD software is used to perform the simulations of the steep waves with wavelength of 25 meters, 55 meters, and 67 meters. In the simulation, a propulsive force is used to simulate the wind force on the boat. / Master of Science

<p> The influence of a logarithmically dependent (van Hove singularity) electronic density of states is studied in the weak-coupling limit. Through analytic and numerical analysis it is found that the model can give rise to temperatures in the 100 K range, and that universal BCS ratios such as 2Δ/kBTC and ΔC/γTC do not change essentially from their constant BCS values. The consequences of this model on the calculation of the isotope effect and specific heat are discussed in detail and compared to recent experimental results.</p> / Thesis / Master of Science (MSc)

De plus en plus de metteurs en scène ont aujourd’hui recours à la vidéo en direct dans leurs spectacles. De manière générale, le recours à ce type de dispositifs pendant la représentation permet d’offrir au spectateur des possibilités de perception qu’il n’a habituellement pas au théâtre : voir le plus infime détail d’un visage, ou une action au plus près, accéder visuellement à tout espace extérieur à la scène lorsque l’action scénique s’y déroule, percevoir sur le visage d’un acteur sa réaction devant l’action qui se tient sous ses yeux ou encore avoir une multiplicité de points de vue simultanés sur un même objet. Pour autant, peut-on dire que la fonction des images en direct au théâtre se réduise à ces quelques principes utilitaires dans la représentation ? En donnant aux spectateurs la possibilité de voir simultanément les acteurs et leur image filmée et projetée et/ou diffusée en direct sur le plateau, les artistes jouent de plus en plus du potentiel performatif du dispositif vidéo dans la représentation théâtrale. Ils ne s’arrêtent pas à redoubler la scène par l’image mais mettent en avant la déconstruction de l’image et la construction du réel ou, du moins, d’une réalité dans et par l’image. C’est pourquoi le recours aux images en direct au théâtre appelle inévitablement à en interroger les enjeux à la fois esthétique, narratif, dramaturgique et proxémique dans la représentation théâtrale. Sans prétendre à une quelconque exhaustivité, cette thèse vise à proposer, à partir de certains spectacles d’Ivo van Hove et de Guy Cassiers, quelques pistes permettant de mesurer l’étendue possible du potentiel performatif des images en direct dans la représentation. / Today, more and more directors include live video in their performances. The use of such devices offers new possibilities of perception to the spectators, which usually are not available in a theatrical representation such as to look at the smallest details of an action or on the performer’s face; to access visually to peripheral areas of the stage when a dramatic action takes place there; to notice the reaction of an actor who listens to the main protagonist, as well as to have different simultaneous viewpoints on the same object. Nevertheless, can we reduce the function of live images on stage to these few utilitarian principles in the performance? Allowing spectators to see, in the same time, the actors and the images of themselves, many artists exploit more than ever the performative potential of video in theatrical representations. Live video does not only reproduce on the screen what happens on the scene, but it also highlights on one hand the deconstruction of the image and, on the other, the construction of a reality in and by images. That is why the uses of live video on stage unavoidably lead to question issues related to the aesthetic, narrative, dramaturgical and proxemic aspects of theatrical performances. Based on the analysis of different performances staged by Ivo van Hove and Guy Cassiers, this thesis aims to measure the extent of the performative potential of live video on stage.

Les couches de graphene épitaxiées sur la face carbone du carbure de silicium sont tournées les unes par rapport aux autres. Cette rotation préserve la structure de bande linéaire du graphene mono-couche et permet un transport balistique des porteurs de charge. Parmi les propriétés intéressantes développées dans le chapitre 2, la possibilité de former de pleines couches de graphene sur le substrat isolant qu'est le SiC est un avantage majeur de cette technique comparé aux autres méthodes de croissance du graphene (exfoliation et épitaxie en phase vapeur sur métaux). Les grandes surfaces produites permettent aux expérimentateurs de faire facilement des mesures STM car la localisation de la partie utile de l’échantillon n'est pas un problème dans ce cas.Dans ce travail de thèse, j'ai réalisé la croissance de graphene sur la face carbone du SiC dans le but d'étudier la supraconductivité induite dans le graphene par la proximité d'un supraconducteur. Cette supraconductivité induite dont le principe expliqué dans le chapitre 3 se développe d'autant plus loin de l'interface que le matériau non supraconducteur possède un grand libre parcours moyen. D'où notre choix du graphene. Dans le chapitre 3 je présente aussi les efforts que j'ai mené pour fabriquer des jonctions graphene/supraconducteur par une technique de lithographie propre : la lithographie par microsphères. Cette méthode utilise des micro-sphères de silice comme masque dur durant le dépôt par évaporation d'un matériaux supraconducteur tel le vanadium. Malgré la propreté de cette méthode telle qu'avérée par les images STM des échantillons, nous n'avons pas réussi à induire la supraconductivité dans le graphene. Suite à ce résultat négatif, nous avons développé une seconde approche décrite dans le chapitre 4. Un matériau supraconducteur réfractaire, le niobium, est cette fois-ci déposé sur le substrat avant la croissance du graphene. A l'issue de la croissance, nous avons eu la surprise de constater que la température critique du matériaux supraconducteur s'était élevée de 7 à 12 K. Cela s'explique par la carburation du Niobium lors du recuit. Par ailleurs, nous avons bien démontré que des couches graphitiques sont aussi crues sur le NbC permettant ainsi de réaliser des jonctions. Néanmoins, nous n'avons à nouveau pas réussi à observer de supraconductivité induite dans le graphene.Outre les propriétés intéressantes pour l'étude de la supraconductivité induite, les couches de graphene en rotation constituent en elle même un sujet d'étude intéressant. En effet, la densité d'état de ce système présente des singularités de van Hove dont la position en énergie dépend de l'angle de rotation. Ce système ouvre donc la porte à l'étude de la physique associée à ces singularités (supraconductivité, magnétisme) à des énergies accessibles par dopage électrostatique. De plus, une localisation des fonctions d'onde électroniques a été prédite pour les faibles angles de rotation et cette localisation a été confirmée par des résultats expérimentaux préliminaires. Cependant, il manquait une étude systématique des propriétés électriques des systèmes à faible angle de rotation. Les mesures que j'ai réalisé dans ce régime sont présentées dans la dernière partie de ce mémoire. Ces mesures de spectroscopie sont comparées à un modèle de liaison fortes. Le modèle sans désordre et en présence de désordre ne permettent pas de décrire correctement les expériences menées pour des angles inférieurs à 2°. Mon travail souligne qu'une physique riche existe aux faibles angles de rotation et qu'il reste encore beaucoup de travail à faire pour la comprendre. / Epitaxial graphene on carbon-terminated face (C-face) of SiC substrates consists of graphene layers rotated from each other. This rotation of layers grants this material single-layer like properties, such as a linear dispersion band structure and a ballistic transport. As discussed in chapter 2, the full-wafer size and the insulating SiC substrate are two of many advantages of graphene films grown on SiC compared to those prepared differently (exfoliation method and chemical vapour deposition method). These two advantages allow experimentalists to perform scanning tunneling microscopic (STM) experiments and to study graphene properties easily.In this PhD work, we grew graphene on C-face of SiC substrates to investigate the induced superconducting proximity effect in ballistic regime. The physics of this phenomenon is explained in chapter 3 as the formation of time-reversed pairs of electrons and holes. Concerning the superconducting materials, we relied on vanadium and niobium carbide to induce the proximity effect. These two approaches are discussed in detail in chapter 3 (for V) and chapter 4 (for NbC). STM characterizations performed on fabricated samples show a superconducting gap in V and a part of the NbC surface, but no induced gap in graphene. Several possible reasons, like a poor interface between superconductors and graphene, the unability of the STM to reach the true graphene-superconductor interface, and the degradation of the surface of NbC, were suggested and discussed. However, our high-quality epitaxial NbC films meet the requirements for hot-electron bolometers.Besides their single-layer like properties, the rotation of layers also leads to tunable van Hove singularities and the localization of states, which are thoroughly discussed in chapter 5 and 6. Once one of these singularities stays at the Fermi level, graphene is predicted to gain intrinsic superconductivity and magnetic properties. This condition can be achieved by reducing the rotation angle towards zero, as these singularities converge to the Dirac point or the Fermi level for undoped graphene. In addition to the intrinsic superconductivity, the localization of states also appears for layers rotated with a small angle, as observed in several STM experiments. Experimentally, we found regions in rotated layers, which appear as periodic Moiré patterns in our STM images. The rotation angles were estimated from the Fast Fourier Transform of the recorded STM images. Comparing our experimental results with tight-binding calculations for disorder-free layers rotated with the same angles leads to a qualitatively good agreement for the positions of van Hove peaks. However, the appearance of new peaks in proximity to the Dirac point for layers rotated with θ=1.5º and a spatial evolution of of spectroscopic features for the small rotation angles cannot be explained by the calculations for disorder-free layers. In order to explain these two phenomena, we considered the influence of disorder. This indeed improved the agreement between theoretical and experimental results. But, since no electronic disorder could be evidenced from our STM images, other explanations, like strain, need to be considered too.

As a result of the computing power provided by the current technology, computational methods now play an important role in modeling and designing materials at the nanoscale. The focus of this dissertation is two-fold: first, new computational methods to model nanoscale transport are introduced, then state-of-the-art tools based on density functional theory are employed to explore the properties of phosphorene, a novel low dimensional material with great potential for applications in nanotechnology. A Wannier function description of the electron density is combined with a generalized Slater-Koster interpolation technique, enabling the introduction of a new computational method for constructing first-principles model Hamiltonians for electron and hole transport that maintain the density functional theory accuracy at a fraction of the computational cost. As a proof of concept, this new approach is applied to model polythiophene, a polymer ubiquitous in organic photovoltaic devices. A new low dimensional material, phosphorene - a single layer of black phosphorous - the phosphorous analogue of graphene was first isolated in early 2014 and has attracted considerable attention. It is a semiconductor with a sizable band gap, which makes it a perfect candidate for ultrathin transistors. Multi-layer phosphorene transistors have already achieved the highest hole mobility of any two-dimensional material apart from graphene. Phosphorene is prone to oxidation, which can lead to degradation of electrical properties, and eventually structural breakdown. The calculations reported here are some of the first to explore this oxidation and reveal that different types of oxygen defects are readily introduced in the phosphorene lattice, creating electron traps in some situations. These traps are responsible for the non-ambipolar behavior observed by experimental collaborators in air-exposed few-layer black phosphorus devices. Calculation results predict that air exposure of phosphorene creates a new family of two-dimensional oxides, which has been later confirmed by X-ray photoemission measurements. These oxides can form protective coatings for phosphorene and have interesting tunable electronic properties. Finally, Wannier function interpolation has been used to demonstrate that a saddle-point van Hove singularity is present near the phosphorene Fermi energy, as observed in some layered cuprate high temperature superconductors; this leads to an intriguing strain-induced ferromagnetic instability.

Les systèmes quantiques d'interactions répétées sont des modèles à la fois simples et flexibles qui apparaîssent de façon naturelle dans plusieurs domaines, dont notamment l'optique quantique et la théorie des bruits quantiques. Dans cette thèse, on s'est intéressé à leur étude perturbative. On a généralisé un théorème dû a Attal et Joye [Attal and Joye, Weak Coupling and Continuous Limits for Repeated Quantum Interactions, J. Stat. Phys., 126, (2007)] sur l'existence de limite de van Hove pour ces systèmes au cadre des algèbres de von Neumann quelconques. Ensuite, on a montré que si le système de référence est de dimension fini, alors l'existence d'un état asymptotique unique pour la limite de van Hove implique la convergence vers un état asymptotique périodique unique pour le système de référence, pourvu que le paramètre de perturbation soit suffisamment petit. De plus, le terme d'ordre zéro du développement en puissances du paramètre de perturbation de cet état asymptotique périodique coïncide avec l'état asymptotique de la limite de van Hove, sauf pour la différence d'échelle temporelle qui doit être prise en compte (donnant lieu à la periodicité). Ce résultat est important pour la justification physique de l'utilisation du formalisme thermodynamique dans le régime de couplage faible développé dans [Lebowitz and Spohn, Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs, Adv. Chem. Phys. 38 (1978)].