Ces dernières années, la physique de la matière condensée a connu une profonde révolution de concepts par la découverte de nombreuses phases de la matière qui ne sont pas classifiables à la Landau, c’est à dire par leur groupe de symétrie. Si les premiers travaux remontent à ceux des effets Hall quantiques (entier et fractionnaire), ce n’est que récemment, avec l’avènement du graphène et des isolants topologiques que les physiciens ont réalisé que ces phases de la matière ne nécessitent, dans l’absolu, ni champ magnétique, ni basse température, par opposition aux effets Hall quantiques précédemment cités. Ces nouveaux états de la matière sont caractérisés non pas par la géométrie du problème mais plutôt par la topologie. Ici donc, la forme précise du spectre électronique n’est pas importante, seules certaines caractéristiques, comme la présence ou l’absence d’un gap, le sont. De manière similaire à la classification de Landau des groupes de symétries, il est possible de classifier ces nouveaux systèmes par l’intermédiaire de groupes topologiques. La branche mathématique invoquée est celle de la topologie algébrique. A travers les invariants qu’elle génère, il est possible de classer les états topologiquement non-triviaux. De plus, les transitions entre des états à topologies distinctes sont aussi accessibles par cette théorie. Les travaux réalisés dans le cadre de cette thèse s’intéressent aux effets topologiques dans la structure de bandes de matériaux bi-dimensionnels. Après une présentation du formalisme mathématique général, un premier chapitre s’intéressera à la topologie locale, c’est à dire pour une portion restreinte de la première zone de Brillouin, des points de croisements de bandes, dits points de Dirac. Un effort sera porté vers la classification de ces systèmes et des transitions associées. Le chapitre suivant mettra en lumière un moyen efficace de mesurer les effets de la topologie des électrons en deux dimensions. Il s’agit de l’étude des niveaux de Landau qui résultent de l’application d’un champ magnétique 5transverse au plan des électrons. Les points de Dirac se transmutent alors en niveaux à énergie nulle topologiquement stables, c’est à dire peu ou pas influencés par les diverses perturbations. L’étude des différents modèles justifiera la discrimination entre la physique à champ magnétique faible et celle à champ magnétique fort, faible ou fort étant très dépendant du système étudié. Enfin, dans un dernier chapitre plus prospectif on s’intéressera à la topologie globale, c’est à dire pour l’ensemble de la première zone de Brillouin. Ce type d’étude est surtout caractérisé par l’existence d’états de bords robustes. On en fera l’expérience d’une double manière. D’abord par l’étude un modèle à un électron, puis par celle d’un système en forte interaction de N électrons. A travers les différents exemples étudiés, on s’attachera à démontrer la puissance de l’outil topologique pour les problèmes de la matière condensée, phénomène qui devrait s’accentuer les prochaines années. / During the last few decades, condensed matter physics has witnessed a deep refoundation of its paradigms, through the discovery of many systems that the usual symmety classification à la Landau cannot handle properly. Although the first major breaktroughs were realized at the time of discovery of integer and fractional quantum Hall effects, only recently physicists have agreed that these peculiar phases of matter require neither a magnetic field nor low temperature. Those new states of matter cannot be caracterized by the geometric aspects of the model but rather by topological ones. The precise shape of the electronic spectrum is no longer relevant, but only particular features are, such as the presence or the absence of a gap. Similarly to the Landau classification scheme, one can achieve a construction through extensive use of topological groups. This is the realm of algebraic topology. Related generated topological invariants can hold a classification of non-trivial topological states, as well as of the accompanying transitions. This thesis focusses on peculiar topological features of two-dimesnsional electronic band structures. After a technical introduction to the underlying formalism, the first chapter is devoted to local topology, that is for a restricted piece of the first Brillouin zone, of band crossing points, also known as Dirac points. Special care is taken to classify these points and related transitions. The next chapter sheds some light on a particularly efficent way of measuring topology for two-dimensional electrons. This is achieved through measurements of Landau levels that are generated by a magnetic field applied perpendicular to a plane. Dirac points then generate zero Landau levels that are topologically stable, i.e. almost not influenced by perturbations at all. Distinctions between low and high magnetic fields will prove to be relevant, although very system-dependant. Through the several models studied, we particularly stress out the importance of the topological tool for condensed matter physics, past present... and future.

This dissertation describes the theoretic studies of magnetic moment and spinorbit interaction in vacuum (Dirac wavepacket) and solid state systems, such as semiconductors. The semiclassical approach developed here provides a simple and intuitive picture for the origin of spin and spin-orbit coupling. In the Dirac model, the spin magnetic moment is originated from the self-rotating Dirac wavepacket with a correct g-value. The spin-orbit interaction is related to Berry connection (gauge potential) and the model is generalized to solid state systems. The Rashba effect caused by the spin-orbit coupling in a crystal with asymmetric potential in heterostructure quantum well is calculated by semiclassical spindependent scattering. The exact treatment of interface phase accumulation provides a justification of spin-dependent boundary condition at interface derived in previous treatment using Löwdin decomposition. Other spin-orbit coupling related phenomena in solid state system are also discussed in this thesis. / text

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2016-10-14T12:48:52Z No. of bitstreams: 1 TeseVLON.pdf: 12327358 bytes, checksum: 6fe55d85e4aff3ba5318f9671501f27c (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-21T13:10:16Z (GMT) No. of bitstreams: 1 TeseVLON.pdf: 12327358 bytes, checksum: 6fe55d85e4aff3ba5318f9671501f27c (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-21T13:10:23Z (GMT) No. of bitstreams: 1 TeseVLON.pdf: 12327358 bytes, checksum: 6fe55d85e4aff3ba5318f9671501f27c (MD5) / Made available in DSpace on 2016-10-21T13:10:31Z (GMT). No. of bitstreams: 1 TeseVLON.pdf: 12327358 bytes, checksum: 6fe55d85e4aff3ba5318f9671501f27c (MD5) Previous issue date: 2016-03-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this thesis, the electronic and structural properties of nanostructured systems were studied aiming to get a realistic model for quantum rings, potentially adaptable for quantum dots. To attain these goals, several studies supported by experimental results were carried out that allowed the introduction to the building blocks for the theoretical models such as: the envelope function approach within the k.p approximation in quantum wells, and quantum ring/dot with perpendicular magnetic field and without spin-orbit interaction. In these models, the effects of size, strain and localization were subsequently introduced to understand the ring formation process and their effects in the photoluminescence and magneto-photoluminescence. The experimental results of atomic force microscopy indicated the importance of structural properties and the types of asymmetries possibly found in quantum rings after the growth process. The understanding of these effects and the evidence of the anisotropy in a preferential direction of the ring helped building more realistic models for the potential profiles. Various systems were then studied with success. They also included a controllably magnetic field (both in magnitude and orientation), beside the geometric deformation, making the ring ellipsoidal, and taking into account the spin-orbit interaction. The most realistic model was used to analyze the Berry phase generation and the relative weight of the contribution of each term of the Hamiltonian. / Nesta tese de doutorado, as propriedades eletrônicas e estruturais de sistemas nano estruturados foram estudadas visando a obtenção de um modelo realístico para anéis quânticos potencialmente adaptáveis a pontos quânticos. Para alcançar este objetivo, foram feitos alguns estudos, apoiados por resultados experimentais, que permitiram a construção passo a passo do modelo teórico, como: aproximação da função envelope na representação k.p em poços quânticos e anéis/pontos quânticos com campo magnético perpendicular e sem interação spin-órbita. Nestes modelos, os efeitos do tamanho, tensão e localização foram introduzidos subsequentemente para entender o processo de formação do anel e os resultados apresentados na fotoluminescência e na magneto-luminescência. O resultado experimental da microscopia de força atômica nos levou a analisar a importância das propriedades estruturais e os tipos possíveis de assimetria encontrados em anéis quânticos devido ao processo de crescimento. O entendimento desses efeitos e a evidência de anisotropia em uma direção preferencial do anel ajudou na construção de modelos mais realísticos para os perfis de potencial. Deste modo, vários sistemas foram estudados com sucesso. Eles também possuíam um campo magnético controlável (ambas, magnitude e orientação), além da deformação geométrica, que torna o anel elipsoidal, e a interação spin-órbita. O modelo mais realístico foi usado para analisar a geração da fase de Berry e o peso da contribuição de cada termo do Hamiltoniano.

In this thesis, research starts by questioning Berry curvature dipole's role in electronic properties in solids. Strongly inspired by the recent studies, we discover a more profound interpretation of the Berry curvature dipole. It is demonstrated that the anomalous correction to the electron acceleration is proportional to the Berry curvature dipole and is responsible for the Non-linear Hall effect recently discovered in materials with broken inversion symmetry. This allows uncovering a deeper meaning of the Berry curvature dipole as a non-linear version of the Drude weight that serves as a measurable order parameter for broken inversion symmetry in metals. Later, we introduce the Quantum Rectification Sum Rule in time-reversal invariant materials is derived by showing that the integral over frequency of the rectification conductivity depends solely on the Berry connection and not on the band energies or relaxation rates. In the final part of the thesis, we use the Keldysch-Floquet formalism to obtain non-perturbative predictions of the optical responses in solids, mainly focusing on the clean limit response of systems with broken time-reversal symmetry.

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The prominent features of single molecule magnets (SMMs), such as the quantum tunneling of the magnetization (QTM), are conventionally understood through the giant spin approximation (GSA) which considers the molecule as a single rigid spin. This model often requires the inclusion of high order anisotropy terms in the Hamiltonian, a manifestation of admixing of low lying excited states that can be more naturally understood by employing a multi-spin (MS) description i.e. considering the individual spins and the interactions between ions within the molecule. However, solving the MS Hamiltonian for high nuclearity molecules is not feasible due to the enormous dimensions of the associated Hilbert space that put it beyond the capability of existing computational resources. In contrast, low nuclearity systems permit the complete diagonalization of the MS Hamiltonian required to sample the effect of internal degrees of freedom, such as exchange interactions and single ion anisotropies, on the QTM. This dissertation focuses on the study of low nuclearity SMMs in view of understanding these subtle quantum effects. To accomplish this, we have developed a series of magnetic characterization techniques, such as integrated microchip sensors resulting from the combination of two dimensional electron gas (2DEG) Hall-Effect magnetometers and microstrip resonators, capable of performing measurements of magnetization and EPR spectroscopy simultaneously. The thesis bases on a comparative study of two low nuclearity SMMs with identical magnetic cores (Mn4 dicubane) but differing ligands. Notably, one of these SMMs lacked solvent molecules for crystallization; a characteristic that gives rise to extremely sharp resonances in the magnetization loops and whose basic QTM behavior can be well explained with the GSA. On the contrary, the second SMM exhibited mixed energy levels, making a MS description necessary to explain the observations. We have also examined the role of internal degrees of freedom on more subtle QTM phenomena, leading to the explanation of asymmetric Berry-phase interference patterns observed in a Mn4 SMM in terms of a competition between different intermolecular magnetic interactions, i.e. non-collinear zero-field splitting tensors and intramolecular dipolar iii interactions, resulting in astonishing manifestations of the structural molecular symmetry on the quantum dynamics of the molecular spin.

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We investigate the geometric phase (GP) acquired by the states of a spin-1/2 nucleus which is subject to a static magnetic field. This nucleus as the carrier system of GP, is taken as coupled to a dissipative environment, so that it evolves non-unitarily. We study the effects of different characteristics of different environments on GP as nucleus evolves in time. We showed that magnetic field strength is the primary physical parameter that determines the stability of GP / its stability decreases as the magnetic field strength increases. (By decrease in stability what we mean is the increase in the time rate of change of GP.) We showed that this decrease can be very rapid, and so it could be impossible to make use of it as a quantum logic gate in quantum information theory (QIT). To see if these behaviors differ in different environments, we analyze the same system for a fixed temperature environment which is under the influence of an electromagnetic field in a squeezed state. We find that the general dependence of GP on magnetic field does not change, but this time the effects are smoother. Namely, increase in magnetic field decreases the stability of GP also for in this environment / but this decrease is slower in comparison with the former case, and furthermore it occurs gradually. As a second problem we examine the entanglement of two atoms, which can be used as a two-qubit system in QIT. The entanglement is induced by an external quantum system. Both two-level atoms are coupled to a third two-level system by dipole-dipole interaction. The two atoms are assumed to be in ordinary vacuum and the third system is taken as influenced by a certain environment. We examined different types of environments. We show that the steady-state bipartite entanglement can be achieved in case the environment is a strongly fluctuating, that is a squeezed-vacuum, while it is not possible for a thermalized environment.