Submitted by Biblioteca do Instituto de Física (bif@ndc.uff.br) on 2017-05-26T20:14:25Z No. of bitstreams: 1 TeseFranciscoLustosa.pdf: 726667 bytes, checksum: b1704d3cae6ec9a91da3b57f936bc53b (MD5) / Made available in DSpace on 2017-05-26T20:14:25Z (GMT). No. of bitstreams: 1 TeseFranciscoLustosa.pdf: 726667 bytes, checksum: b1704d3cae6ec9a91da3b57f936bc53b (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho estudamos o problema do Buraco Negro (BN) em um região contendo um Monopolo Global em uma teoria de gravidade f(R). Utilizando o formalismo da métrica, obtemos as equações de campo em termos de [Fórmula] e assumimos que F(R) seja uma fun c~ao de grau n da coordenada radial. Adotando uma aproximação, conseguimos obter soluções do tipo BN e analisamos suas quantidades termodinâmicas, como temperatura local, energia e capacidade térmica para qualquer n. Comparamos os resultados obtidos com o caso do BN de Scharzschild com um Monopo Global e também observamos se há influência do grau n nos efeitos termodinâmicos. / In this work we study the problem of a Black Hole (BH) in a region containing a Global Monopole in a f(R) gravity. We use the metric formalism to obtain the eld equations in terms of [Formula] and assume that F(R) is a n-degree function of the radial coordinate. Adopting an aproximation, we obtain BH solutions and analise the resulting thermodynamical quantities, such as local temperature, energy and heat capacity for all n's. We compare the results with the ones obtaines in the case of the Scharzschild BH with a Global Monopole and observe if there is an in uence of the degree n in the thermodynamical e ects.

Ces travaux sont consacrés à l'étude d'un gaz d'excitons bidimensionnel créé dans un double puits quantique de semi-conducteurs. Grâce à un champ électrique appliqué perpendiculairement au plan des puits, les deux composants de l'exciton, l'électron et le trou, sont chacun confinés dans deux puits séparés. Ceci donne lieu à des excitons avec un fort moment dipolaire qui sont piégés et refroidis à très basse température. Dans ce manuscrit, nous étudions les propriétés du gaz d'excitons à travers la photoluminescence émise lors de la recombinaison des paires électron-trou, que nous analysons grâce à des mesures spectroscopiques et interférométriques. Ainsi, nous avons étudié la thermodynamique du gaz d'excitons dans un piège harmonique et établi son équation d'état. Nous avons dévoilé l'universalité de l'équation d'état ce qui a rendu possible la première démonstration de l'équilibre thermodynamique du gaz et a aussi permis d'évaluer la force des interactions entre excitons. En associant des mesures de cohérence spatiale et l'étude de la distribution de défauts de densité dans la photoluminescence des excitons, nous avons montré que dans une zone centrale du piège de rayon R < 3 µm, il s'opère conjointement une augmentation du niveau de cohérence et une diminution de la densité de défauts. Des travaux précédents ayant montré que ces défauts pouvaient constituer des défauts topologiques appelés vortex, nos observations constituent ainsi un ensemble de preuves de l'établissement d'un état superfluide dans la partie centrale du piège, en accord avec la théorie prédite par Berezinskii-Kosterlitz et Thouless. / This work is devoted to the study of a two dimensional exciton gas created in a semiconductordouble quantum wells. Thanks to an electric field applied perpendicular to these layers,the exciton constituents, namely, the electron and the hole, are confined each in one quantumwell so that excitons inherit a strong electric dipole. In this manuscript, we study the propertiesof such exciton gas trapped at very low temperature, through the photoluminescence emittedby electron-hole recombinations. We particularly study the emitted light using spectroscopic andinterferometric techniques. Thus, we explore the thermodynamics of a trapped gas and quantifyits equation of state. We unveil an important feature: the universality of the equation of state,which allows the first demonstration of thermodynamic equilibrium for excitons, and we realizea direct measurement of the excitons dipolar interaction strength. By probing both the spatialcoherence and the density of defects of the excitons photoluminescence, we show that it exists acentral region (R < 3 μm) in an exciton trap where a high degree of spatial coherence is conditionedby a decrease of the defects density. Our experiments thus provide a set of evidences pointingtowards a Berezinskii-Kosterlitz-Thouless transition for trapped 2D exciton gas.

Chiral magnets such as MnSi, FeGe or Cu2OSeO3 exhibit a non-centrosymmetric lattice structure which lacks inversion symmetry. The resulting Dzyaloshinskii-Moriya interaction originating from weak spin-orbit coupling stabilizes smooth modulated magnetic textures, namely helices and skyrmions. In this thesis, we study the properties of helimagnets which are systems with a magnetic helix as ground state. First, we examine the consequences of the helical texture for spin wave excitations, so-called helimagnons. We investigate magnon-focusing effects, i.e. magnon flow in very specific directions, which result from flat bands occurring in the helimagnon band structure when the momentum component perpendicular to the helix axis is large. We show that the softness of the Goldstone mode leads to a large dissipation even at very small frequencies cut off only by magnetocrystalline anisotropies or by a magnetic field. Finally, we discuss that dipolar interactions induce non-reciprocal behavior of the spectrum at finite fields and momenta, i.e. the spectrum is not symmetric under reversing the momentum anymore. We calculate the Brillouin light scattering cross section and compare it to experimental results obtained by N. Ogawa [1]. Then, we consider reorientation processes of the helix axis due to an applied magnetic field. We compare the results to magnetic force microscopy measurements in Cu2OSeO3 performed by P. Milde et al. [2]. Afterwards, we point out that the skyrmion lattice orientation has singular points, i.e. points where the orientation is not determined, as a function of the magnetic field direction which is a consequence of the Poincaré-Hopf theorem. Afterwards, we turn to excitations in the form of the basic defects in helimagnets: disclinations and dislocations. Due to the lamellar nature of the helimagnetic texture, analogies to liquid crystals can often be used. We present an analytic parameterization of dislocations transferred from smectic liquid crystals and illustrate that dislocations carry a topological skyrmion charge. We examine dislocation motion in the presence of weak pinning due to random impurities. We derive a Thiele-Langevin equation for the dislocation position which effectively describes one dimensional motion. When reducing the system to two dimensions, this reveals ultra slow anomalous Sinai diffusion which may explain the very long time scales observed in several experiments [3,4]. Eventually, we present our work on domain walls in helimagnets. In magnetic force microscopy experiments performed by P. Schoenherr [5], we have identified three domain wall types. At small angles between the two domains, curvature walls appear. At intermediate angles, one can observe zig-zag disclination walls and at large angles, dislocation walls occur. We present analytical descriptions for curvature and dislocation walls, which we compare to micromagnetic simulation results obtained by J. Masell [5], and comment on the non-trivial topology of helimagnetic domain walls. [1] N. Ogawa, L. Köhler, M. Garst, S. Toyoda, S. Seki, and Y. Tokura, In preparation (2019). [2] P. Milde, E. Neuber, P. Ritzinger, L. Köhler, M. Garst, A. Bauer, C. Pfleiderer, H. Berger, and L. M. Eng, In preparation (2019). [3] A. Dussaux, P. Schoenherr, K. Koumpouras, J. Chico, K. Chang, L. Lorenzelli, N. Kanazawa, Y. Tokura, M. Garst, A. Bergman, C. L. Degen, and D. Meier, Nature Communications 7, 12430 (2016). [4] A. Bauer, A. Chacon, M. Wagner, M. Halder, R. Georgii, A. Rosch, C. Pfleiderer, and M. Garst, Physical Review B 95, 024429 (2017). [5] P. Schoenherr, J. Müller, L. Köhler, A. Rosch, N. Kanazawa, Y. Tokura, M. Garst, and D. Meier, Nature Physics 14, 465 (2018).:Introduction 1. Introduction to chiral magnets 1.1. Helimagnets 1.1.1. Magnetic phase diagram of chiral magnets 1.2. Skyrmions 1.2.1. Topology 1.2.2. Magnetic skyrmions 1.2.3. Skyrmion motion 1.2.4. Emergent electrodynamics 1.3. Model for chiral magnets 2. Spin waves in helimagnets 2.1. Linear spin wave theory for helimagnons 2.1.1. Fluctuations in the harmonic approximation 2.1.2. Spectrum at small momenta and fields 2.1.3. Frequency broadening from Gilbert damping 2.2. Magnon-focusing effects 2.3. Enhanced local dissipation 2.3.1. Global static susceptibility in the limit k, k' → 0 2.3.2. Local damping 2.4. Non-reciprocity 2.4.1. Non-reciprocity of the spectrum 2.4.2. Brillouin light scattering cross section 3. Orientation of magnetic order 3.1. Helix reorientation transition in MnSi 3.1.1. Effective Landau potential for the helix pitch 3.1.2. Experimental results 3.2. Helix reorientation in Cu2OSeO3 3.3. Skyrmion lattice orientation 4. Disclinations and dislocations 4.1. Liquid crystals 4.1.1. Types of liquid crystals 4.1.2. Energetics of liquid crystals 4.2. Disclinations 4.2.1. Elasticity theory for disclinations 4.3. Dislocations 4.3.1. Volterra process and Burgers vector 4.3.2. Elasticity theory for dislocations 4.3.3. Mermin-Ho relation in helimagnets 4.3.4. Topological skyrmion charge 5. Dislocation motion 5.1. Thiele approach for one helimagnetic dislocation 5.1.1. Motion in the presence of pinning 5.1.2. Corrections from elastic deformations 5.2. Dislocation diffusion 5.2.1. Sinai diffusion and toy model simulations 5.2.2. Susceptibility with Sinai diffusion 5.2.3. Dislocation string 6. Domain walls 6.1. Experimental and numerical methods 6.2. Domain wall types in helimagnets 6.3. Energetics of helimagnetic domain walls 6.3.1. Curvature wall 6.3.2. Dislocation wall 6.4. Topological domain wall structures 7. Discussion and outlook Appendix A. Details on helimagnons B. Formalism of linear-spin wave theory in helimagnets C. Deviations from the helix Bibliography List of Figures Index Danksagung

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In my thesis I will discuss some aspects of collective dynamics of excitons and exciton-polaritons in nanoscale heterostructures. In the first Chapter I will make a brief introduction to the modern semiconductor physics and willdescribe the general elements and notions which will be used further. Other four chapters would be devoted to four works in which I participated, notably, in Chapter 2 I will speak about the coherent interactions between phonons and exciton orexciton-polariton condensates, in Chapter 3 I will discuss the quantum dots lasing and its amplification by an acoustic pulse. Chapter 4 and 5 will be devoted respectively to the polariton multistability and to the condensates of indirect excitons.

Ces travaux concernent l’étude expérimentale des textures se développant dans les ménisques de films smectiques de cristaux liquides thermotropes. Ces fluides complexes nous servent de système modèle pour l’étude des couplages élasto-capillaires qui se manifestent dans certaines conditions par des déformations périodiques de l’interface cristal liquide-air. Dans un premier temps, à partir de l’étude détaillée de la topographie de l’interface par une méthode interférométrique, nous caractérisons les différents types de structures, puis, identifions les principaux paramètres impliqués dans le processus d'apparition des défauts dans le ménisque de films libres suspendus. Ces résultats nous servent de base pour discuter des mécanismes physiques qui génèrent les différents types de défauts observés. Nous regardons en particulier, comment la diminution d’épaisseur de couche associée à une transition de phase va induire une instabilité mécanique responsable de l’apparition des ondulations de l’interface. Dans un deuxième temps, afin d’aller plus loin dans la compréhension des mécanismes, nous avons utilisé des films minces de cristaux liquides déposés sur des substrats solides microstructurés par des plots fabriqués par des techniques photolitographiques. Une telle géométrie permet de générer un ménisque autour de chaque plot et surtout de faire varier un plus grand nombre de paramètres comme par exemple l’ancrage sur le substrat via un traitement chimique de surface. L’ensemble de nos résultats apportent un éclairage nouveau sur la caractérisation et la compréhension des déformations spécifiques aux ménisques de fluides complexes. / The present work is an experimental study of the textures that appear in the meniscus of free standing smectic films with thermotropic liquid crystals. These complex fluids serve as model systems to investigate elasto-capillary phenomena which, under certain conditions, manifest themselves through periodic deformations of the liquid crystalair interface. In the first part of the thesis, we focus our attention on meniscus structures whose interfacial topographies are thoroughly characterized thanks to an in-house optical interferometry technique. Our study allows us to identify the main parameters involved in the development of meniscus structures and to discuss the physical mechanisms that are likely to be responsible for their formation. In particular, we show how a phase transition-induced layer shrinkage triggers a mechanical instability leading to interfacial undulations of the smectic free surface. In the second part of the manuscript, we address the case of thin liquid crystal films deposited on solid patterned solid substrates. The latter consist of regular arrays of microposts fabricated through photolithographic techniques. Such a geometry allows a meniscus to be formed around each micropost and makes it possible to examine the influence of other parameters such as the anchoring conditions on the solid substrate. The results gathered so far are able to shed some light on the characterization and the understanding of the specific deformations and textures that appear in the menisci of complex fluids.

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-18T12:28:21Z No. of bitstreams: 1 arquivototal.pdf: 2590482 bytes, checksum: a72ba5c8c44731f3cffe38777111a92d (MD5) / Made available in DSpace on 2017-09-18T12:28:21Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2590482 bytes, checksum: a72ba5c8c44731f3cffe38777111a92d (MD5) Previous issue date: 2011-04-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Aspects of the physics of nematic liquid crystals are studied in this thesis from the viewpoint of riemannian geometry through analogue models of gravitation. The topics chosen for study were: geometric and wave optics, elastic waves, hydrodynamics and heat conduction. The main analogue model used is based on the interpretation of Fermat’s principle as a process to obtain null geodesics, where the liquid crystalline material is seen as a riemannian manifold. This approach predicts that the metric effectively felt by the light ray depends on the configuration of molecules in the liquid crystal and on the parallel and perpendicular refractive indexes to the axis of symmetry of the liquid-cristal molecule. It is known that, for the particular case of the existence of topological defects within the material, effective metric similar to cosmological defects (like global monopoles and cosmic strings) are obtained. This thesis develops itself on the situation where there are topological defects of hedgehog type and (k = 1, c = 0) disclination type in the nematic phase of the liquid crystalline material. The first problem studied, as a review, deals with the wave optics, with respect to the light diffracted by the cited defects. Since plane waves of small wavelength have identical trajectories to light rays, the use of analog model is therefore justified. Thus, we show that light scattered by these defects generates a characteristic diffraction pattern, being the location given by an algebraic expression dependent on the parallel and perpendicular refractive indexes to the axis of symmetry of the molecule. We also show how theses patterns depend on the temperature of the material. The second studied problem deals with the geometrical optics and hydrodynamics of the nematic liquid crystals. From a molecular configuration similar to a (k = 1, c = 0) disclination, we let the material flow radially towards the axis of the defect. Then, using the hydrodynamic fact that velocity gradients in the material locally change the refractive index of the molecule, we find the velocity profile that must exist around the defect so that the metric actually experienced by light traveling in the plane perpendicular to the axis the defect is the Schwarzschild one in the equatorial plane, with the Schwarzschild radius interior to the object. We found that the absolute values of the velocity of liquid crystalline fluid can be order of a few meters per second, differing greatly from the values obtained by Gordon metric for an isotropic fluid under identical conditions. The third studied problem deals with the elastic oscillations in the presence of topological defects. Similarly to the first problem, the trajectory of the sound is obtained by an elastic version of Fermat’s principle and, then, compared with a null geodesic. We show how topological defects influence the sound trajectories and the sound diffracted by them. The fourth problem deals with the heat conduction in the vicinity of defects. Considering that the defects come from an addition or removal of portion of the material, letting the medium relaxes elastically, effective metric of the space disturbed by the defect are found, with expressions similar to those obtained by the analogous model based on Fermat’s principle. These metrics generate a modified thermal conductivity tensor, allowing the study of the temperature field in this situation. We show that, depending on the values of parallel and perpendicular thermal conductivity to the axis of symmetry of the molecule and on the defect in question, the temperature gradient can be accentuated or attenuated on the defect, allowing control of the response thermal temperature of the material, according to the presence of defects. Encouraging a greater understanding of the physics of liquid crystals and its use as a background in analogue models of gravity is the main theme of each analyzed problem. / Aspectos da física dos cristais líquidos nemáticos são estudados nesta tese do ponto de vista da geometria riemannina, por meio de modelos análogos de gravitação. Os tópicos escolhidos para estudo foram: óptica geométrica e ondulatória, ondas elásticas, hidrodinâmica e condução de calor. O principal modelo análogo empregado baseia-se na interpretação do princípio de Fermat como um processo de obtenção de geodésicas nulas, onde o material líquido-cristalino é visto como sendo uma variedade riemanniana. Esta abordagem prevê que a métrica efetivamente sentida pelo raio luminoso dependa da configuração das moléculas dentro do cristal líquido e dos índices de refração paralelo e perpendicular ao eixo de simetria da molécula líquido-cristalina. É sabido que, para o caso especial da existência de defeitos topológicos dentro do material, métricas efetivas semelhantes às de defeitos cosmológicos (como monopolos globais e cordas cósmicas) são obtidas. Esta tese desenrola-se sobre a situação onde existem defeitos topológicos do tipo ouriço e do tipo desclinação (k = 1, c = 0) na fase nemática do material líquido-cristalino. O primeiro problema estudado, em caráter de revisão, trata da óptica ondulatória, no que concerne a difração de luz pelos defeitos citados. Uma vez que ondas planas de comprimento de onda pequeno possuem trajetórias idênticas aos raios luminosos, o emprego do modelo análogo é justificado. Assim, mostramos que a luz espalhada por esses defeitos gera padrões de difração bem característicos, sendo a localização dada por expressão algébrica dependente dos índices de refração paralelo e perpendicular ao eixo de simetria da molécula líquido-cristalina. Também mostramos de que forma esses padrões dependem da temperatura do material. O segundo problema estudado trata da óptica geométrica e da hidrodinâmica dos cristais líquidos nemáticos. A partir de uma configuração de moléculas semelhantes à de uma desclinação (k = 1, c = 0), permitimos que o material flua radialmente na direção do eixo do defeito. Em seguida, fazendo uso do fato hidrodinâmico de que gradientes de velocidade no material modificam localmente os índices de refração da molécula, encontramos o perfil de velocidade que deve existir em torno do defeito para que a métrica efetivamente sentida pela luz, que viaja no plano perpendicular ao eixo do defeito, seja a de Schwarzschild no plano equatorial, com raio de Schwarzschild interior ao objeto. Encontramos que os valores absolutos da velocidade de fluido líquido-cristalino podem ser da ordem de alguns metros por segundo, diferindo enormemente dos valores obtidos pela métrica de Gordon para um fluido isotrópico em condições idênticas. O terceiro problema estudado aborda as oscilações elásticas na presença de defeitos. Semelhantemente ao primeiro problema, a trajetória do som é obtida por uma versão elástica do princípio de Fermat e, então, comparada com uma geodésica nula. Mostramos como defeitos topológicos influenciam nas trajetórias sonoras, assim como no som difratado por eles. O quarto problema trata da condução de calor na vizinhança de defeitos. Considerando que os defeitos são resultantes de uma adição ou remoção de porção de material, dando-se seguimento a uma relaxação elástica do meio, métricas efetivas do espaço perturbado pelo defeito são encontradas, com expressões semelhantes às obtidas pelo modelo análogo baseado no princípio de Fermat. Essas métricas geram um tensor condutividade térmica modificado, dando cabo ao estudo do campo de temperatura nessa situação. Mostramos que, dependendo dos valores da condutividade térmica perpendicular e paralela ao eixo de simetria da molécula líquido-cristalina e do defeito em questão, o gradiente de temperatura pode ser acentuado ou atenuado sobre o defeito, permitindo o controle da resposta térmica do material à temperatura, de acordo com a presença de defeitos. Suscitar um entendimento maior da física dos cristais líquidos e de seu emprego como background em modelos análogos de gravitação é o tema principal de cada um dos problemas analisados.

Les cristaux liquides ont été tout le long un terrain fertile pour la recherche scientifique, des mathématiques à la science des matériaux, à l'optique. Leur utilisation ne se limite pas seulement à l'optique d'afficheurs mais s'étend à l'optique non linéaire, par exemple, à la commutation et au routage de faisceaux optiques. En raison de leur extrême sensibilité aux champs électriques, et ce sur une plage de fréquences allant du continu aux fréquences optiques, ils sont aussi utilises comme milieu non linéaires aptes à générer des faisceaux optiques auto-confinés, appelés solitons spatiaux optiques, à de très faibles puissances. Ces faisceaux ont la propriété de se propager sans diffraction, du fait que cette dernière est compensée par l’auto-focalisation non linéaire du milieu, avec formation de guides d'onde auto-induites. Dans les cristaux liquides nématiques, ces guides d'ondes peuvent à leur tours confiner et guider d’autres signaux optiques et peuvent être reconfigurés, soit optiquement, soit électriquement, du fait que la trajectoire des solitons peut être contrôlée par d'autres champs, ouvrant ainsi la voie à la manipulation tout-optique. Récemment, les cristaux liquides nématiques ont été également utilisés avec succès dans l'optique dite singulière, dans laquelle le paramètre clef est la singularité topologique portée par la phase de l'onde électromagnétique. Dans cette thèse, je rendrai compte de mon travail sur les solitons optiques spatiaux et les singularités optiques dans les cristaux liquides nématiques. / Liquid crystals have been all along a fertile background for scientific research, from mathematics to material science and optics; their use is not limited to displays but extends to nonlinear optics, for instance, to switching and routing of optical beams. Due to their extreme sensitivity to electric fields, and this at frequencies ranging from continuous to optical ones, they are also nonlinear media supporting the generation and propagation of self confined beams, called spatial optical solitons, at very low powers. Spatial optical solitons have the property to propagate without diffraction, since this is compensated by nonlinear self-focusing in the medium, resulting in self-induced waveguides. In nematic liquid crystals, these waveguides can in turn confine and route other optical signals and can be reconfigured, either optically or electrically, as soliton trajectories can be controlled by other fields, paving the way to all-optical manipulation. Nematic liquid crystals have also been recently employed with success in the so-called singular optics, in which the key parameter is the topologic singularity carried by the phase of an electromagnetic wave. In this thesis I will report on my work on spatial optical solitons and optical singularities in nematic liquid crystals.