Graphene can be used to create circuits that are almost superconducting, potentially speeding electronic components by as much as 1000 times [1]. Such blazing speed might also help produce ever-tinier computing devices with more power than your clunky laptop [2]. Graphite is a polymorph of the element carbon [3]. Graphite is made up of tiny sheets of graphene. Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm, which means that a stack of 3 million sheets would be only one millimeter thick. [1] This nano scale 2 dimensional sheet is graphene. Novoselov and Geim's discovery is now the stuff of scientific legend, with the two men being awarded the Nobel Prize in 2010 [4]. In 2004, two Russian-born scientists at the University of Manchester stuck Scotch tape to a chunk of graphite, then repeatedly peeled it back until they had the tiniest layer possible [2]. Graphene has exploded on the scene over the past couple of years. "Six years ago, it didn't exist at all, and next year we know that Samsung is planning to release their first mobile-phone screens made of graphene." - Dr Kostya Novoselov [4]. It is a lattice of hexagons, each vertex tipped with a carbon atom. At the molecular level, it looks like chicken wire [4]. There are two common lattice formations of graphene, armchair and zigzag. The most studied edges, zigzag and armchair, have drastically different electronic properties. Zigzag edges can sustain edge surface states and resonances that are not present in the armchair case Rycerz et al., 2007 [5]. This research focused on the armchair graphene nanoribbon formation (acGNR). Graphene has several notable properties that make it worthy of research. The first of which is its remarkable strength. Graphene has a record breaking strength of 200 times greater than steel, with a tensile strength of 130GPa [1]. Graphene has a Young's modulus of 1000, compared to just that of 150 for silicon [1]. To put it into perspective, if you had a sheet of graphene as thick as a piece of cellophane, it would support the weight of a car. [2] If paper were as stiff as graphene, you could hold a 100-yard-long sheet of it at one end without its breaking or bending. [2] Another one of graphene's attractive properties is its electronic band gap, or rather, its lack thereof. Graphene is a Zero Gap Semiconductor. So it has high electron mobility at room temperature. It's a Superconductor. Electron transfer is 100 times faster than Silicon [1]. With zero a band gap, in the massless Dirac Fermion structure, the graphene ribbon is virtually lossless, making it a perfect semiconductor. Even in the massive Dirac Fermion structure, the band gap is 64meV [6]. This research began, as discussed in Chapter 2, with an armchair graphene nanoribbon unit cell of N=8. There were 16 electron approximation locations (ψ) provided per unit cell that spanned varying Fermi energy levels. Due to the atomic scales of the nanoribbon, the carbon atoms are separated by 1.42Å. The unit vector is given as, ~a = dbx, where d = 3αcc and αcc = 1.42°A is the carbon bond length [5]. Because of the close proximity of the carbon atoms, the 16 electron approximations could be combined or summed with their opposing lattice neighbors. Using single line approximation allowed us to reduce the 16 points down to 8. These approximations were then converted into charge densities (ρ). Poisson's equation, discussed in Chapter 3, was expanded into the 3 dimensional space, allowing us to convert ρ into voltage potentials (φ). Even though graphene is 2 dimensional; it can be used nicely in 3 dimensional computations without the presence of a substrate, due to the electric field lines and voltage potential characteristics produced being 3 dimensional. Subsequently it was found that small graphene sheets do not need to rest on substrates but can be freely suspended from a scaffolding; furthermore, bilayer and multilayer sheets can be prepared and characterized.

Cette thèse est consacrée à l'étude de différents modèles de fluides quantiques, en particulier des modèles cinétiques, et aux liens entre ces modèles. La première partie est dédiée aux gaz de bosons. Nous nous intéressons d'abord à un fluide de bosons ayant une partie condensée, modélisé par deux équations couplées : une équation de Boltzmann quantique pour la partie normale, et une équation de Gross-Pitaevskii pour la partie condensée. Nous étudions formellement la limite hydrodynamique de ce système dans le scaling hyperbolique, couplée avec une limite semi-classique, et obtenons un système du type Euler compressible à deux fluides. Nous étudions le système limite dans l'approximation isentropique : hyperbolicité, solutions faibles, chocs, simulation numérique des chocs. Nous nous intéressons dans un deuxième temps à un modèle de type Boltzmann pour les bosons unidimensionnel et homogène en espace. Après avoir prouvé l'existence de solutions, nous montrons qu'elles convergent dans la limite des collisions rasantes (et dans un sens très faible) vers des solutions d'une équation de Fokker-Planck quantique. La deuxième partie est centrée sur l'équation de Boltzmann pour les fermions. Nous montrons un résultat d'existence de solutions vérifiant la conservation locale de la masse, du moment et de l'énergie cinétique dans un domaine à bord. Nous prouvons ensuite un résultat rigoureux de limite hydrodynamique dans le scaling Euler incompressible à l'aide de la méthode de l'entropie relative couplée à des techniques de filtrage des ondes acoustiques.

L'effet Nernst, bien que peu exploité depuis sa découverte en 1886, a acquis récemment une place importante dans le domaine des électrons corrélés. Au cours de cette thèse, nous avons utilisé l'effet Nernst afin d'étudier deux exemples de systèmes corrélés, un supraconducteur NbxSi1-x et un fermion lourd PrFe4P12. Dans l'étude des films amorphes supraconducteurs de Nb0.15Si0.85, le signal Nernst observé est en parfait accord avec la prédiction théorique de Ussiskhin, Sondhi et Huse (USH) dans la limite de faible champ magnétique et près de Tc. La théorie USH qui se fonde sur l'existence de paires de Cooper au temps de vie fini au-dessus de Tc, relie directement le coefficient Nernst à la longueur de corrélation à champ nul, c-à-d la taille des paires de Cooper fluctuantes. L'étude approfondie des données a montré que, de façon plus générale, le signal Nernst est déterminé par une seule longueur, la longueur de corrélation à toute température et tout champ magnétique. La théorie USH n'est que la limite bas champ d'une théorie plus générale qui relierait le coefficient Nernst à la longueur de corrélation. Ces résultats démontrent que le signal Nernst observé au-dessus de Tc jusqu'à très haute température (30 xTc) et jusqu'à très haut champ magnétique (3 X Bc2) dans les films amorphes de Nb0.15Si0.85 est généré par les fluctuations supraconductrices de type paires de Cooper fluctuantes. La seconde étude que nous avons effectuée dans le composé fermion lourd PrFe4P12 nous a permis de caractériser les phases qui apparaissent dans ce matériau à basse température. L'amplitude exceptionnelle de l'effet Nernst observée dans la phase ordonnée à bas champ magnétique est la conséquence de trois facteurs indépendants : une faible densité de porteurs, une augmentation de la masse effective et un grand libre parcours moyen. Ce comportement est caractéristique d'un fermion lourd semi-métallique. L'augmentation importante du pouvoir thermoélectrique dans la phase ordonnée est révélatrice d'une destruction importante de la surface de Fermi. La phase qui apparaît à haut champ magnétique pour la direction [111] semble également liée à une restructuration de la surface de Fermi, bien que moins importante, associée à un comportement non liquide de Fermi. Le changement de signe de l'effet Nernst lors de l'apparition de la phase à haut champ magnétique pourrait s'interpréter comme le signe d'une transition métamagnétique.

In this study we investigate the properties of trapped atoms subjected to rapid rotations. The study is divided into two distinct parts, one for fermions, another for bosons. In the case of the degenerate Fermi gas we explore the density structure of non-interacting cold atoms when they are rotated rapidly. On the other hand, for rapidly rotating two component Bose condensate, we search for new lattice structures in the presence of contact and dipolar interactions. First, the density structure of Fermi gases in a rotating trap is investigated. We focus on the anisotropic trap case, in which two distinct regimes, two and one dimensional regimes, depending on rotation frequency and anisotropy are observed. Two regimes can be illustrated by a simple description of maximum number of states between two Landau levels, which is strongly related to the dimensionality of the system. The regimes are separated from each other by a minimum point in this description. For small anisotropy values the density profiles show a step structure where each step is demonstrated by an elliptical plateau. Each plateau represents a Landau level with a constant density. The local density approximation describes the two dimensional regime with a perfect similarity in the structure of fermion density. The case for one dimensional regime is a little different from the two dimensional case. For large anisotropy values the Friedel oscillation is the dominant aspect of the density profiles. The density profiles show gaussian structure along the direction of strong trapping, and a semicircular form with prominent oscillations along the weak confining direction. Again, the system is nicely described by local density approximation in this regime. A smooth crossover between two regimes is observed, with a switching from a step structure profile to a soft edge transition with Friedel oscillations. At finite temperatures, the step structures are smeared out in two dimension. In one dimensional regime the Friedel oscillations are cleaned as soon as the temperature is turned on. The second part of the study is devoted to the investigation of different lattice structures in two component Bose condensates subjected to very fast rotation, this time in the presence of interactions. We explore the existence of new vortex lattice structures for dipolar two component condensates scanning a wide range of interaction strengths. We introduce a phase diagram as a function of intra and inter-component interactions showing different type of vortex lattice structures. New types of lattice structures, overlapped square and overlapped rectangular, emerge as a result of dipolar interactions and s-wave interaction for a two component condensate. The region where the attractive inter-component interactions dominate the repulsive interactions, the overlapped lattices are formed. The intra-component interactions, which defines the behavior of each component inside, result in different type of lattices by changing the strength of interactions. Two different limits of phase diagram reproduce the results of ordinary two component and dipolar one component Bose condensates. The results of calculation are in agreement with the results of previous studies for two regimes.

Dans cette thèse, nous présentons des mesures de conductivité thermique (κ) dans les supraconducteurs à fermions lourds PrOs4Sb12 (Tc~1.75K) et<br />CeCoIn5 (Tc~2.35K). Après une courte<br />introduction aux composés, nous décrivons notre technique expérimentale, qui a permis des mesures fiables jusqu'à 10mK et dans un champ magnétique allant jusqu'à 6.5T. Le développement d'une méthode de<br />caractérisation (quantitative) des résistances de contact<br />électriques et thermiques du montage constitue une partie originale de ce travail.<br /><br />Une forte augmentation de κ avec le champ à basse température dans PrOs4Sb12 et CeCoIn5 révèle l'existence d'une échelle de champ caractéristique beaucoup plus faible que Hc2. Cette haute sensibilité au champ de κ ne correspond ni aux prédictions pour un supraconducteur ordinaire de type II ni au cas où le gap présente des nœuds, mais souligne plutôt le caractère multibande de la supraconductivité, comme dans MgB2. En outre, dans Pr PrOs4Sb12, la dépendance en<br />température de κ indique des gaps complètement ouverts sur toute la surface de Fermi, alors que dans CeCoIn5 la suppression de diffusions inélastiques rend impossible une conclusion sur la topologie du gap.

Topological insulators (TI) are a new phase of matter with very exotic electronic properties on their surface. As a direct consequence of the topological order, the surface electrons of TI form bands that cross the Fermi surface odd number of times and are guaranteed to be metallic. They also have a linear energy-momentum dispersion relationship that satisfies the Dirac equation and are therefore called Dirac fermions. The surface Dirac fermions of TI are spin-polarized with the direction of the spin locked to momentum and are immune from certain scatterings. These unique properties of surface electrons provide a platform for utilizing TI in future spin-based electronics and quantum computation. The surface bands of 3D TI can be directly mapped by angle-resolved photoemission spectroscopy (ARPES) and the spin polarization can be determined by spin-resolved ARPES. These types of experiments are the first to establish the 3D topological order, which demonstrates the power of ARPES in probing the surface of strongly spin-orbit coupled materials. Extensive investigation of TI has ranged from understanding the fundamental electronic and lattice structure of various TI compounds to building TI-based devices in search of more exotic particles such as Majorana fermions and magnetic monopoles. Surface-sensitive techniques that can efficiently disentangle the charge and spin degrees of freedom have been crucially important in tackling the multi-faceted problems of TI. In this thesis, I show that laser-based ARPES in combination with a time-of-flight spectrometer is a powerful tool to study the spin structure and charge dynamics of the Dirac fermions on the surface of TI. Chapter 1 gives a brief introduction of TI. Chapter 2 describes the basic principles behind ARPES and time-resolved ARPES (TrARPES). Chapter 3 provides a detailed account of the experimental setup to perform laser-based ARPES and TrARPES. In Chapters 4 and 5, how these two techniques are effectively applied to investigate two unique electronic properties of TI is elaborated. Through these studies, I have obtained a complete mapping of the spin texture of several prototypical topological insulators and have uncovered the cooling mechanism governing the hot surface Dirac fermions. / Physics

No description available.

Seltenerd-Eisenpniktide ziehen gegenwärtig großes wissenschaftliches Interesse auf sich, da sie wegen der bei ihnen beobachteten Hochtemperatursupraleitung eine vielversprechende Alternative zu den herkömmlichen Kuprat-Supraleitern darstellen. Neben der Supraleitung weisen diese Systeme ein breites Spektrum magnetischer Eigenschaften auf, die auf dem Wechselspiel von Eisen 3d- und Seltenerd-4f-Elektronen beruhen und teils in Konkurrenz zu, teils aber auch in Koexistenz mit der Supraleitung auftreten. Das theoretische Verständnis dieser Phänomene lässt noch viele Fragen offen, da sich vor allem die 4f-Elektronen infolge ihrer starken räumlichen Lokalisierung und der damit verbundenen hohen Coulomb-Korrelationsenergien einer einfachen Behandlung im Rahmen von Bandstrukturtheorien weitgehend entziehen. Die vorliegende Arbeit beschäftigt sich mit winkelaufgelösten Photoemissionsuntersuchungen an CeFe2P2, CeFePO und CeFeP0.3As0.7O, bei denen Schwer-Fermionen-Verhalten bzw. Ferromagnetismus beobachtet werden kann. Die Wechselwirkung der 4f-Elektronen mit dem überwiegend von Fe 3d-Orbitalen abgeleiteten Valenzband spiegelt sich in den Spektren durch das Auftreten dispergierender Strukturen im Bereich der Kondoresonanz wider. Diese werden in der Arbeit auf der Grundlage von LDA-Bandstrukturrechnungen und dem Periodischen Andersonmodell, welches für einfache Fallbeispiele mittels der DMFT (Dynamical Mean Field Theory) gelöst wird, diskutiert. Anhand der experimentellen Beobachtungen wird ein Mechanismus für die in der Verbindungsklasse beobachteten magnetischen Übergänge, basierend auf charakteristischen Unterschieden in der Bandstruktur, vorgeschlagen sowie ein möglicher Zusammenhang mit der Supraleitung diskutiert.

Within condensed matter physics, systems with strong electronic correlations give rise to fascinating phenomena which characteristically require a physical description beyond a one-electron theory, such as high temperature superconductivity, or Mott metal-insulator transitions. In this thesis, a class of strongly correlated electron systems is considered. These systems exhibit fractionally charged excitations with charge +e/2 or -e/2 in two dimensions (2D) and three dimensions (3D), a consequence of both strong correlations and the geometrical frustration of the interactions on the underlying lattices. Such geometrically frustrated systems are typically characterized by a high density of low-lying excitations, leading to various interesting physical effects. This thesis constitutes a study of a model of spinless fermions on the geometrically frustrated kagome lattice. Focus is given in particular to the regime in which nearest-neighbour repulsions V are large in comparison with hopping t between neighbouring sites, the regime in which excitations with fractional charge occur. In the classical limit t = 0, the geometric frustration results in a macroscopically large ground-state degeneracy. This degeneracy is lifted by quantum fluctuations. A low-energy effective Hamiltonian is derived for the spinless fermion model for the case of 1/3 filling in the regime where |t| << V . In this limit, the effective Hamiltonian is given by ring-exchange of order ~ t^3/V^2, lifting the degeneracy. The effective model is shown to be equivalent to a corresponding hard-core bosonic model due to a gauge invariance which removes the fermionic sign problem. The model is furthermore mapped directly to a Quantum Dimer model on the hexagonal lattice. Through the mapping it is determined that the kagome lattice model exhibits plaquette order in the ground state and also that fractional charges within the model are linearly confined. Subsequently a doped version of the effective model is studied, for the case where exactly one spinless fermion is added or subtracted from the system at 1/3 filling. The sign of the newly introduced hopping term is shown to be removable due to a gauge invariance for the case of hole doping. This gauge invariance is a direct result of the bipartite nature of the hole hopping and is confirmed numerically in spectral density calculations. For further understanding of the low-energy physics, a derivation of the model gauge field theory is presented and discussed in relation to the confining quantum electrodynamic in two dimensions. Exact diagonalization calculations illustrate the nature of the fractional charge confinement in terms of the string tension between a bound pair of defects. The calculations employ topological symmetries that exist for the manifold of ground-state configurations. Dynamical calculations of the spectral densities are considered for the full spinless fermion Hamiltonian and compared in the strongly correlated regime with the doped effective Hamiltonian. Calculations for the effective Hamiltonian are then presented for the strongly correlated regime where |t| << V . In the limit g << |t|, the fractional charges are shown to be effectively free in the context of the finite clusters studied. Prominent features of the spectral densities at the Gamma point for the hole and particle contributions are attributed to approximate eigenfunctions of the spinless fermion Hamiltonian in this limit. This is confirmed through an analytical derivation. The case of g ~ t is then considered, as in this case the confinement of the fractional charges is observable in the spectral densities calculated for finite clusters. The bound states for the effectively confined defect pair are qualitatively estimated through the solution of the time-independent Schroedinger equation for a potential which scales linearly with g. The double-peaked feature of spectral density calculations over a range of g values can thus be interpreted as a signature of the confinement of the fractionally charged defect pair. Furthermore, the metal-insulator transition for the effective Hamiltonian is studied for both t > 0 and t < 0. Exact diagonalization calculations are found to be consistent with the predictions of the effective model. Further calculations confirm that the sign of t is rendered inconsequential due to the gauge invariance for g in the regime |t| << V . The charge-order melting metal-insulator transition is studied through density-matrix renormalization group calculations. The opening of the energy gap is found to differ for the two signs of t, reflecting the difference in the band structure at the Fermi level in each case. The qualitative nature of transition in each case is discussed. As a step towards a realization of the model in experiment, density-density correlation functions are introduced and such a calculation is shown for the plaquette phase for the effective model Hamiltonian at 1/3 filling in the absence of defects. Finally, the open problem of statistics of the fractional charges is discussed.

Thesis (M.SC.) - Carleton University, 2007. / Includes bibliographical references (p. 103-107). Also available in electronic format on the Internet.