SOUSA, Ariel Adorno de. Vazamentos de corrente e ineficiência de transporte em nanoestruturas semicondutoras investigadas através de propagação de pacotes de onda. 2015. 149 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2015. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-06-11T18:23:58Z No. of bitstreams: 1 2015_tese_aasousa.pdf: 11602478 bytes, checksum: 96b288e68aacaf0da271842e48706b70 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-06-11T18:24:41Z (GMT) No. of bitstreams: 1 2015_tese_aasousa.pdf: 11602478 bytes, checksum: 96b288e68aacaf0da271842e48706b70 (MD5) / Made available in DSpace on 2015-06-11T18:24:41Z (GMT). No. of bitstreams: 1 2015_tese_aasousa.pdf: 11602478 bytes, checksum: 96b288e68aacaf0da271842e48706b70 (MD5) Previous issue date: 2015 / Advances in growth techniques have made possible the fabrication of quasi one-dimensional semiconductor structures on nanometric scales, called quantum dots, wires, wells and rings. Interest in these structures has grown considerably not only due to their possible applications in electronic devices and to their easy chemical manipulation, but also because they offer the possibility of experimentally exploring several aspects of quantum confinement, scattering and interference phenomena. In particular, in this work, we investigate the electronic and transport properties in quantum wells, wires and rings, whose dimensions can be achieved experimentally. For this purpose, we solve the time-dependent Schrödinger equation using the split-operator method in two dimensions. We address four different problems: in the first one, the electronic transport properties of a mesoscopic branched out quantum ring are discussed in analogy to the Braess Paradox of game theory, which, in simple words, states that adding an extra path to a traffic network does not necessarily improves its overall flow. In this case, we consider a quantum ringindex{Quantum ring} with an extra channel in its central region, aligned with the input and output leads. This extra channel plays the role of an additional path in a similar way as the extra roads in the classical Braess paradox. Our results show that in this system, surprisingly the transmission coefficient decreases for some values of the extra channel width, similarly to the case of traffic networks in the original Braess problem. We demonstrate that such transmission reduction in our case originates from both quantum scattering and interference effects, and is closely related to recent experimental results in a similar mesoscopic system. In the second work of this thesis, we extend the first system by considering different ring geometries, and by investigating the effects of an external perpendicular magnetic field and of obstructions to the electrons pathways on the transport properties of the system. For narrow widths of the extra channel, it is possible to observe Aharonov-Bohm oscillations in the transmission probability. More importantly, the Aharonov-Bohm phase acquired by the wave function in the presence of the magnetic field allows one to verify in which situations the transmission reduction induced by the extra channel is purely due to interference. We simulate a possible closure of one of the paths by applying a local electrostatic potential, which can be seen as a model for the charged tip of an atomic force microscope (AFM). We show that positioning the AFM tip in the extra channel suppresses the transmission reduction due to the Braess paradox, thus demonstrating that closing the extra path improves the overall transport properties of the system. In the third work, we analyze the tunneling of wave packets between two semiconductor quantum wires separated by a short distance. We investigate the smallest distance at which a significant tunneling between the semiconduting wires still occur. This work is of fundamental importantance for the manufacturing of future nanostructured devices, since it provides information on the minimum reasonable distances between the electron channels in miniaturized electronic circuits, where quantum tunnelling and interference effects will start to play a major role. In the last work of this thesis, we investigate the binding energy of the electron-impurity pair in a GaN/HfO2 quantum well. We consider simultaneously the contributions of all interactions in the self-energy due to the dielectric constant mismatch between materials. We investigate the electron-impurity bound states in quantum wells of several widths, and compared the results for different impurity positions. / Os avanços nas técnicas de crescimento tornaram possível a fabricação de estruturas semicondutoras quase-unidimensionais em escalas nanométricas, chamadas pontos, fios, poços e anéis quânticos. Interesse nessas estruturas tem crescido consideravelmente, não só devido às suas possíveis aplicações em dispositivos eletrônicos e à sua manipulação química fácil, mas também porque eles oferecem a possibilidade de explorar experimentalmente vários aspectos de confinamento quântico, espalhamento e fenômenos de interferência. Em particular, neste trabalho, investigamos as propriedades eletrônicas e de transporte em poços quânticos, fios e anéis, cujas dimensões podem ser alcançados experimentalmente. Para isto, resolvemos a equação de Schrödinger dependente do tempo utilizando o método Split-operator em duas dimensões. Nesta tese, abordamos quatro trabalhos, sendo o primeiro uma analogia ao Paradoxo de Braess para um sistema mesoscópico. Para isso, utilizamos um anel quântico com um canal adicional na região central, alinhado com os canais de entrada e saída. Este canal extra faz o papel do caminho adicional em uma rede de tráfego na teoria dos jogos, similar ao caso do paradoxo de Braess. Calculamos as auto-energias e a evolução temporal para o anel quântico. Surpreendentemente, o coeficiente de transmissão para algumas larguras do canal extra diminuiu, semelhante ao que acontece com redes de tráfego, onde a presença de uma via extra não necessariamente melhora o fluxo total. Com a analise dos resultados obtidos, foi possível determinar que neste sistema o paradoxo ocorre devido a efeitos de interferência e de espalhamento quântico. No segundo trabalho, foi feita uma extensão do primeiro, (i) aplicando-se um campo magnético, onde foi possível obter o efeito Aharonov-Bohm para pequenos valores do canal extra e controlar efeitos de interferência responsáveis pelo paradoxo mencionado, e (ii) fazendo também a aplicação de um potencial que simula a ponta de um microscópio de força atômica (AFM) interagindo com a amostra - este potencial é repulsivo e simula um possível fechamento do caminho em que o pacote de onda se propaga. Assim, neste trabalho, realizamos uma contra-prova do primeiro, onde observamos que com o posicionamento da ponta do AFM sobre canal extra, se diminui o efeito de redução de corrente devido ao paradoxo de Braess. No terceiro trabalho, realizamos uma análise de tunelamento entre dois fios quânticos separados por uma certa distância e calculamos qual a menor distância para qual ocorre tunelamento significativo nesse sistema eletrônico. Este trabalho é de fundamental importância para o manufaturamento de dispositivos nanoestruturados, porque nos permite investigar qual a distância mínima para a construção de um circuito eletrônico sem que haja interferências nas transmissões das informações. No quarto e último trabalho desta tese, investigamos a energia de ligação do elétron-impureza em GaN/HfO2 para um poço quântico. Consideramos simultaneamente as contribuições de todas as interações das auto-energias devido ao descasamento das constantes dielétricas entre os materiais. Foram estudados poços largos e estreitos, comparando os resultados para diferentes posições da impureza e a contribuição da auto-energia para o sistema.

Neste trabalho utilizamos o método k.p na aproximação de função envelope, que é uma ferramenta muito útil para a solução de problemas relacionados a heteroestruturas em geral. Apresentamos a análise de heteroestruturas semicondutoras com confinamento espacial nas três direções de crescimentos {Quantum Dots}, utilizando o Hamiltoniano de Kane (8x8) em sua forma generalizada para descrever os estados do elétrons na banda de condução e na banda valência. Fazendo uso dessa ferramenta foram realizadas simulações de estruturas de banda em sistemas quase zero-dimensionais de InAs em matrizes de GaAs, em vários formatos e dimensões e sob diferentes estados de tensionamento. Um estudo sistemático de como as propriedades geométricas e as dimensões de um dado sistema podem influenciar os estados eletrônicos do mesmo foi também realizado, onde puderam ser confirmadas a presença de estados localizados e a sensibilidade do comportamento dos estados eletrônicos a estas propriedades. Pudemos observar um deslocamento para o vermelho no espectro de fotoluminescência com o aumento das dimensões do sistemas estudados. Foram ainda realizados cálculos de {Quantum Dots} de InN em matriz de GaN, que permitem explorar outras regiões do espectro eletromagnético e observamos o comportamento dos mesmos sob estados de tensionamentos diferentes. Com base nos autoestados do sistema foram calculados espectros de fotoluminescência para as heteroestruturas aqui estudadas, permitindo uma comparação direta com resultados experimentais. Como pode-se verificar o strain exerce importância primordial na determinação dos estados eletrônicos dos sistemas estudados e na presença do hidrostático pode-se verificar mudanças apreciáveis na resposta óptica do material, onde pode ser observado um deslocamento para o azul quando levado em consideração a presença de um hidrostático. / In this work, we use the k.p method in the approximation of the envelope function, that is a very useful tool, to the solution of heterostructure related problems. We present a semiconductor heterostructure analysis with confinement on the three directions (Quantum Dots), using the Kane Hamiltonian (8x8) on its generalized form to describe electron eigenstates on the conduction and valence bands. Using this tool, we have made band structure simulations in quasi zero-dimensional systems of InAs in GaAs matrices, in diverse shapes and dimensions and on different tension states. A systematic study of how the geometrical properties and dimensions of a given system could influence the electronic states was also done. There can be confirmed the presence of localized states and the sensitivity of the electronic states to these properties.We could observe a deviation to the red on the photoluminescence spectrum with the increase of the system dimensions. There were also made calculations on InN dots in a GaN matrix, which allow to explore other electromagnetic spectral regions and we have studied their behavior under different tension states. From the system eigenvalues, we calculated the photoluminescence spectra from the heterostructures studied here, allowing a direct comparison with experimental results. It can be verified that the strain is is extremely important on the determination of the electronic states of the studied systems in the presence of an hydrostatic strain. We could observe important modifications on the optical responseof the material, where there is a deviation to the blue when it is considered the presence of the hydrostatic strain.

Orientadores: Peter Alexander Bleinroth Schulz, Ana Luiza Cardoso Pereira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-17T03:19:21Z (GMT). No. of bitstreams: 1 Munoz_WilliamArmando_M.pdf: 8434738 bytes, checksum: d59e43facc73d2ca570f8291de7f22cc (MD5) Previous issue date: 2010 / Resumo: Nós estudamos os efeitos da quebra de simetria e de desordem no espectro de energia de um elétron numa bicamada de grafeno. O problema foi abordado através de simulações numéricas considerando um Hamiltoniano tight-binding para uma rede retangular topologicamente equivalente à rede hexagonal do grafeno que nos permite incluir de forma simples os efeitos do campo magnético através da substituição de Peierls. O problema de quebra de simetria foi observado quando consideramos a aplicação de uma diferença de potencial entre as camadas. Neste contexto, é observada uma quebra completa na degenerescência do nível de Landau de energia zero devida à aplicação desta diferença de potencial entre as camadas. Acompanhamos este mecanismo de quebra de degenerescência para uma situação onde a diferença de potencial entre camadas é mantida fixa enquanto o campo magnético é aumentado. Isto mostra a possibilidade de controlar a abertura de gaps através da variação do campo magnético na bicamada de grafeno e está de acordo com o que foi recentemente observado experimentalmente. Observamos também um comportamento para a separação em energia desta quebra de degenerescência do tipo vB para valores do campo magnético B<60 Teslas, enquanto que para campos maiores é obtido um comportamento assintótico para energias próximas da separação (Vg) do desdobramento do nível de Landau central. Um mapeamento das funções de onda dos estados envolvidos nesta quebra de degenerescência, mostra um esquema diferente para regimes diferentes de campo magnético. Conseguimos verificar claramente como a quebra da degenerescência do nível de Landau central está relacionada com uma quebra da degenerêscencia entre as duas camadas da bicamada e também entre as duas sub-redes que formam o grafeno. O segundo problema abordado neste trabalho é relacionado à introdução de duas vacâncias acopladas na bicamada de grafeno. Em presença de um campo magnético perpendicular ao plano das camadas mostramos como estados localizados ao redor do defeito com energias entre os níveis de Landau são introduzidos pela presença das vacâncias acopladas. Estes estados para baixas energias formam uma molécula de vacâncias que pode ser facilmente polarizável pela aplicação de um potencial entre as camadas / Abstract: We studied the symmetry breaking and disorder effects on energy spectrum of an electron in a bilayer graphene. We used numerical calculation considering a 2D tight-binding model for a rectangular lattice which not changes the hexagonal lattice topology and where the magnetic field effects are easily calculated. The breaking symmetry problem was considered through the application of a potential difference between both layers in the bilayer graphene. In this case, we observe a complete degeneracy breaking of the energy-zero Landau level due to the application of this potential difference between the two layers. We followed this degeneracy breaking considering a potential difference constant while the magnetic field was increasing. That shows a possibility to control the opening of the gap by means of the magnetic fields in the bilayer graphene which is in agreement with recent experimental results. We also shown that this gap increases with a root of B for values of B<60T, while in the high magnetic field regime (B>60T) the energy dependency of the gap shows a asymptotic behavior with B, which tends to energy values close to Vg. We mapped the wave functions amplitudes of states related to the splitting of the zero-energy Landau level and we found that this electronic charge distribution is different depending on magnetic field regime. We verified clearly as this splitting is related to a layers degeneracy breaking as well as a sublattice (valley) degeneracy breaking. The second problem considered in this thesis is related to the introduction of two coupled vacancies in the bilayer graphene. In presence of a perpendicular magnetic field, we show that two coupled vacancies in the bilayer graphene introduce states with a charge-density distribution localized close to the defect and energies between consecutives Landau levels. These states for lowest energies form a vacancy molecule which can be easily polarized by applying of a potential between the two layers in bilayer graphene / Mestrado / Física da Matéria Condensada / Mestre em Física

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-10-22T19:24:12Z No. of bitstreams: 2 Dissertação - Roger Otávio Pires Montes - 2015.pdf: 8169771 bytes, checksum: e580ffb280dfa5136f41ab38cf0aec4e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-23T11:04:48Z (GMT) No. of bitstreams: 2 Dissertação - Roger Otávio Pires Montes - 2015.pdf: 8169771 bytes, checksum: e580ffb280dfa5136f41ab38cf0aec4e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-23T11:04:48Z (GMT). No. of bitstreams: 2 Dissertação - Roger Otávio Pires Montes - 2015.pdf: 8169771 bytes, checksum: e580ffb280dfa5136f41ab38cf0aec4e (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-05-25 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / This master’s thesis analyses the free and forced nonlinear vibrations of a simply supported functionally graded cylindrical shell which the material’s properties are described by gradient’s law along the shell’s thickness. The nonlinear equations of motion are obtained using nonlinear theories Donnell and Sanders, where the field displacements and field strain of nonlinear Donnell’s shallow shell theory is obtained as a simplification of the nonlinear Sanders’s formulation. The effects of the internal fluid, that is incompressible, irrotational and inviscid and it has been described as a potential velocity to consider the fluid-structure interaction, and the influence of a thermal field in the nonlinear dynamic behavior of the functionally graded cylindrical shell will be investigated. It is developed a low-dimensional model, wherein the shell of the system equilibrium equations is solved by an analytical procedure, which yields the longitudinal and circumferential displacement field as a function of transverse displacement, satisfying the boundary conditions problem. The determination of transverse displacement is obtained by the perturbation techiniques, which enables the achievement of the main nonlinear modes that should be present in the displacement fields of the functionally grade cylindrical shell. To analyze the nonlinear free vibration, it is applied the Galerkin-Urabe method to obtain the system of non-linear algebraic equations, and then resolved by the Newton-Raphson method. The results show the influence of functional gradation, geometry, the effect of the internal fluid, considering a fluid-filled shell, and the thermal action of the nonlinear free vibrations of the shell by the frequency-amplitude relations. Finally, a parametric analysis to study the nonlinear forced vibrations of the cylindrical shell subjected to a harmonic loading side for some geometric relations is conducted. In this case the system of ordinary differential equations of second order in time is obtained from the application of the Galerkin method and integrated over time from the Runge-Kutta fourth order method. The results evaluates the influence of the internal fluid and the thermal effects in the nonlinear oscillation of functionally graded cylindrical shell, using the resonances’ curves, the basins’ attraction, time responses and the phase portraits. / Nesta dissertação são analisadas as vibrações, livres e forçadas, não lineares de uma casca cilíndrica simplesmente apoiada feita com um material com gradação funcional, que as propriedades dos materiais constituintes são descritas por determinadas leis de gradação ao longo da espessura. As equações não lineares de movimento são obtidas utilizando-se as teorias não lineares de Donnell e de Sanders, sendo que os campos de deslocamentos e as deformações referentes à teoria não linear de Donnell para cascas abatidas podem ser obtidos como uma simplificação da formulação não linear de Sanders. Serão investigados os efeitos da presença de um fluido interno, incompressível, não viscoso e irrotacional, sendo descrito a partir de um potencial de velocidade, considerando a interação fluido-estrutura, além da influência de um campo térmico no comportamento dinâmico não linear da casca cilíndrica com gradação funcional. É desenvolvido um modelo de baixa dimensão, em que o sistema de equações de equilíbrio da casca é resolvido através de um procedimento analítico, o qual permite obter os campos de deslocamento axial e circunferencial em função dos deslocamentos transversais, além de atender as condições de contorno do problema. A determinação dos deslocamentos transversais é feita a partir do método da perturbação, o qual possibilita a obtenção dos principais modos não lineares que devem estar presentes nos campos de deslocamentos da casca cilíndrica. Para analisar as vibrações livres não lineares, aplica-se o método de Galerkin-Urabe para se obter o sistema de equações algébricas não lineares, sendo, em seguida, resolvido a partir do método de Newton-Raphson. Os resultados mostram a influência da gradação funcional, da geometria, do efeito do fluido interno, considerando uma casca totalmente preenchida, e da ação térmica nas vibrações livres não lineares da casca por meio das relações frequência-amplitude. Por fim, é feita uma análise paramétrica das vibrações forçadas não lineares da casca cilíndrica submetida a um carregamento lateral harmônico para algumas relações geométricas. Neste caso o sistema de equações diferenciais ordinárias de segunda ordem no tempo é obtido a partir da aplicação do método de Galerkin e integrado ao longo do tempo a partir do método de Runge-Kutta de quarta ordem. Da mesma forma avalia-se a influência do fluido interno e dos efeitos térmicos nas oscilações não lineares da casca cilíndrica com gradação funcional, utilizando-se as curvas de ressonância, as bacias de atração, as respostas no tempo e os planos fase.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-03-29T15:39:07Z No. of bitstreams: 2 Dissertação - Henrique Araujo Rodrigues Sattler - 2015.pdf: 3327262 bytes, checksum: 1c260793f2aa5b49f25d29e6835ab326 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-03-29T15:41:36Z (GMT) No. of bitstreams: 2 Dissertação - Henrique Araujo Rodrigues Sattler - 2015.pdf: 3327262 bytes, checksum: 1c260793f2aa5b49f25d29e6835ab326 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-03-29T15:41:37Z (GMT). No. of bitstreams: 2 Dissertação - Henrique Araujo Rodrigues Sattler - 2015.pdf: 3327262 bytes, checksum: 1c260793f2aa5b49f25d29e6835ab326 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-08-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work is a study of linear and nonlinear free vibration of a cylindrical panel simply supported subjected to a dependent loading time. From the full potential and kinetic energy functional of a cylindrical panel to determine the system's equations of motion, whereas the field of deformations of the cylindrical panel follows the non-linear theory for Donnell shallow shell. For discretization of the cylindrical panel moving system of equations is performed a test procedure able to obtain the fields axial and circumferential displacements from a modal expansion radial displacement field, creating a low-dimensional discretized model. Determine the radial displacement field from perturbation techniques that provides the nonlinear modes which couple to the linear vibration mode of the system from the quadratic and cubic non-linearities present in the cylindrical panel equilibrium equations. With this system of equations is reduced to a partial differential equation as a function of the expansion of the modal amplitudes for the radial displacement being discretized then the Galerkin method. They present the results of various free, linear and non-linear vibrations, and forced into a cylindrical simply supported panel, showing the remarkable influence of the modal coupling in modal solution to this radial displacement and the panel geometry. / Neste trabalho, realiza-se um estudo das vibrações livres, lineares e não lineares, e forçadas de um painel cilíndrico simplesmente apoiado submetido a um carregamento dependente do tempo. A partir dos funcionais de energia potencial total e cinética de um painel cilíndrico, determinam-se as equações de movimento do sistema, considerando que o campo de deformações do painel cilíndrico segue a teoria não linear de Donnell para cascas abatidas. Para obter a discretização do sistema de equações de movimento do painel cilíndrico, realiza-se um procedimento analítico capaz de obter os campos de deslocamentos axial e circunferencial a partir de uma expansão modal para campo de deslocamento radial, criando um modelo discretizado de baixa dimensão. Determina-se o campo de deslocamentos radiais a partir de técnicas de perturbação que fornece os modos não lineares que se acoplam ao modo linear de vibração do sistema a partir das não linearidades quadráticas e cúbicas presentes nas equações de equilíbrio do painel cilíndrico. Com isto o sistema de equações é reduzido para uma equação diferencial parcial em função das amplitudes modais da expansão para o deslocamento radial, sendo discretizada, em seguida, pelo método de Galerkin. Apresentam-se diversos resultados das vibrações livres, lineares e não-lineares, e forçadas para um painel cilíndrico simplesmente apoiado, mostrando a marcante influência do acoplamento modal presente na solução modal para os deslocamentos radiais e da geometria do painel.

Une théorie des champs quantique topologique (TQFT) en dimension 3 est un foncteur monoidal symétrique de la catégorie des cobordismes de dimension 3 vers celle des espaces vectoriels. Une TQFT fournit en particulier un invariant scalaire des variétés fermées de dimension 3 ainsi que des représentations du groupe de difféotopie des surfaces fermées.Turaev explique en 1994 comment construire à partir d'une catégorie modulaire une TQFT qui étend l'invariant scalaire de 3-variétés fermées introduit en 1991 par Reshetikhin et Turaev. Dans cette thèse, nous généralisons cette construction à l'aide d'une catégorie C en ruban avec coend. On représente un cobordisme par un enchevêtrement d'un type particulier (enchevêtrement de cobordisme) et on associe à celui-ci un morphisme défini entre puissances tensorielles de la coend comme décrit par Lyubashenko en 1995. A l'aide de l'extension du calcul de Kirby aux cobordismes de dimension 3, cette construction nous permet de produire un invariant de cobordismes puis une TQFT à valeurs dans la sous-catégorie monoïdale symétrique des objets transparents de C.Dans le cas où C est une catégorie modulaire, cette sous-catégorie s'identifie à celle des espaces vectoriels et on retrouve ainsi la TQFT de Turaev. Dans le cas où C est une catégorie prémodulaire modularisable, notre TQFT est un relèvement de la TQFT de Turaev associée à la modularisée de C. / A 3-dimensional topological quantum field theory (TQFT) is a symmetric monoidal functor from the category of 3-cobordisms to the category of vector spaces. Such TQFTs provide in particular numerical invariants of closed 3-manifolds and representations of the mapping class group of closed surfaces.In 1994, Turaev explains how to construct a TQFT from a modular category; the scalar invariant is then the Reshethikhin-Turaev invariant introduced in 1991. In this thesis, we describe a generalization of this construction starting from a ribbon category C with coend. We present a cobordism by a certain type of tangle (cobordism tangle) and we associate to such a tangle a morphism between tensor products of the coend as described by Lyubashenko in 1994. Extending the Kirby calculus to 3-cobordisms, we obtain in this way an invariant of cobordisms and a TQFT which takes values in the symmetric monoidal subcategory of transparent objects of C. If the category C is modular, this subcategory can be identified with the category of vector spaces, and we recover Turaev's TQFT. If the category C is modularizable, our TQFT is a lift of the Turaev TQFT for the modularization of C.

Orientadores: Ana Luiza Cardoso Pereira, Luiz Eduardo Moreira Carvalho de Oliveira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-28T09:45:49Z (GMT). No. of bitstreams: 1 SolisLerma_DanielAlejandro_M.pdf: 11339360 bytes, checksum: 0efee568f2b70411f8fcb14075392b26 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho foram estudados os efeitos de bordas com terminações perfeitamente definidas de uma rede de grafeno no regime Hall quântico sobre as propriedades eletrônicas deste sistema. O problema foi abordado com uso da aproximação tight-binding incluindo os efeitos do campo magnético e desordem no modelo. Estudou-se primeiramente o efeito das bordas nos níveis de energia do sistema, em espectros tipo borboleta de Hofstadter. Então o foco foi analisar as propriedades de localização eletrônica dos estados de borda, e as particularidades da distribuição das funções de onda nestes casos. Para investigar os estados de borda e determinar, para cada um dos estados eletrônicos, o quanto da função de onda encontra-se localizada nas bordas, foi criada uma quantidade nomeada Edge Fraction, denida como a somatória das amplitudes da função de onda na região das bordas, que numa aproximação semiclássica foi aqui considerada como a região delimitada por uma distância 2'B das bordas, onde 'B é o comprimento magnético. Com o uso do Edge Fraction, analisando-se as contribuições armchair e zigzag separadamente, em redes de grafeno quadradas, encontrou-se que há regiões de energia onde as funções de onda claramente cam mais localizadas num determinado tipo de borda. Este comportamento presume-se que é produto da competição que existe entre os potenciais devidos à presença de bordas e desordem no sistema, que evidenciam-se também no espectro de energia tipo borboleta de Hofstadter. Os resultados obtidos contribuem para o entendimento das propriedades de localização em redes de grafeno com bordas / Abstract: In this work the effects of sharp edges in the electronic properties of graphene lattices in the quantum Hall regime were studied. The problem was addressed using the tight-binding approximation including the effects of the magnetic eld and disorder in the model. It was studied at rst the effect of the edges in the energy levels of the system, through Hofstadter's buttery-like spectrum. Then we focused on analysing the localization properties of edge states and the particularities of the wave function distributions for these cases. To investigate the edge states and to determine, for each electronic state, how much of the wave function is localized at the edges, it was created a quantity called Edge Fraction. This quantity was dened as the probability density sum in the edge region, which in a semi-classical approximation, was considered here as the region limited by a distance 2'B from the edges, where 'B is the magnetic length. Using the Edge Fraction and analysing the contributions of armchair and zigzag edges separately, in squared lattices, it was found that there are energy regions where the wave functions are clearly more localized in a specic edge type. This behaviour is believed to be a result of the competition between the potential due to the presence of the edge and the potential due to the disorder in the system, which are also present in the Hofstadter energy spectrum. The results obtained contribute to the understanding of the localization properties of graphene lattices with edges / Mestrado / Física / Mestre em Física / 1247644 / CAPES

In this dissertation we reported our experimental investigation of the magnetic properties of nine low-dimensional vanadium compounds. Two of these materials are completely new (Pb2V5O12 and Pb2VO(PO4)2) and were found during our search for new low-dimensional vanadium oxides. Among the other seven vanadium compounds studied, three were physically investigated for the first time (Sr2VO(PO4)2, BaZnVO(PO4)2 and SrZnVO(PO4)2). Two had hitherto only preliminary, and wrongly interpreted, susceptibility measurements reported in the literature (Sr2V3O9 and Ba2V3O9) while the remaining two (Li2VOSiO4 and Li2VOGeO4) were previously investigated in some detail but the interpretation of the data was controversial. We investigated the magnetic properties of these materials by means of magnetic susceptibility and specific heat (Cp(T)) measurements (as well as single crystal ESR measurements in the case of Sr2V3O9). We synthesized the samples necessary for our physical studies. That required a search of the optimal synthesis conditions for obtaining pure, high quality, polycrystalline samples. Single crystals of Sr2V3O9 and Pb2VO(PO4)2 were also successfully grown. Pb2VO(PO4)2, BaZnVO(PO4)2, SrZnVO(PO4)2, Li2VOSiO4 and Li2VOGeO4 were found to be experimental examples of frustrated square-lattice systems which are described by the J1-J2 model. We found that Li2VOSiO4 and Li2VOGeO4 posses a weakly frustrated antiferromagnetic square lattice while Pb2VO(PO4)2, BaZnVO(PO4)2 and SrZnVO(PO4)2 form a more strongly frustrated ferromagnetic square lattice. Pb2V5O12 is structurally and compositionally related to the two dimensional A2+V4+nO2n+1 vanadates. Its structure consists of layers formed by edge- and corner-shared square VO5 pyramids. The basic structural units are plaquettes consisting of six corner-shared pyramids pointing in the same direction, which form a spin lattice of novel geometry. / In dieser Dissertation berichteten wir über unsere experimentelle Untersuchung der magnetischen Eigenschaften von neun Niedrigdimensionalen vanadiumverbindungen. Zwei dieser Materialien sind vollständig neu (Pb2VO12 und Pb2VO(PO4)2) und wurden während unserer Suche nach neuen Niedrigdimensionalen Vanadiumoxiden gefunden. Unter den anderen sieben studierten Vanadiumverbindungen, wurden drei physikalisch zum ersten Mal nachgeforscht (Sr2VO(PO4)2, BaZnVO(PO4)2 und SrZnVO(PO4)2). Zwei hatten bisher nur einleitendes, und falsch gedeutet, magnetische Susceptibilitaet Messungen, die in der Literatur berichtet wurden (Sr2V3O9 und Ba2V3O9) während die restlichen zwei (Li2VOSiO4 und Li2VOGeO4) vorher in irgendeinem Detail aber in der Deutung der Daten waren umstritten nachgeforscht wurden. Wir forschten die magnetischen Eigenschaften dieser Materialien mittels der magnetischen Susceptibilitaet und der spezifischen Waerme (Cp(T)) nach (sowie ESR-Messungen des einzelnen Kristalles im Fall von Sr2V3O9). Wir synthetisierten die Proben, die für unsere körperlichen Studien notwendig sind. Das erforderte eine Suche der optimalen Synthesezustände für das Erreichen der reinen, hohen Qualität, polykristalline Proben. Einzelne Kristalle von Sr2V3O9 und von Pb2VO(PO4)2 wurden auch erfolgreich gewachsen. Pb2VO(PO4)2, BaZnVO(PO4)2, SrZnVO(PO4)2, Li2VOSiO4 und Li2VOGeO4 werden gefunden, um experimentelle Beispiele der frustrierten Quadrat-Gittersysteme zu sein, die durch das J1-j2 model. Wir fanden daß posses Li2VOSiO4 und Li2VOGeO4 ein schwach frustriertes antiferromagnetische quadratisches Gitter, während Pb2VO(PO4)2, BaZnVO(PO4)2 und SrZnVO(PO4)2 ein stärker frustriertes ferromagnetisches quadratisches Gitter bilden. Pb2V5O12 strukturell und zusammenhängt kreativ mit den zweidimensionalen vanadates A2+V4+nO2n+1 beschrieben werden. Seine Struktur besteht aus den Schichten, die durch Rand und Ecke-geteilte quadratische Pyramiden VO5 gebildet werden. Die grundlegenden strukturellen Maßeinheiten sind die plaquettes, die aus sechs Ecke-geteilten Pyramiden bestehen, die in die gleiche Richtung zeigen, die ein Drehbeschleunigunggitter von Romangeometrie bilden.

The field of low-dimensional quantum magnets has received lot of attention owing to the possibility of studying phenomena associated with the quantum nature of matter. Many materials that realize low-dimensional spin arrangements in their structure have been synthesized in the past twenty years due to the emergence and development of crystal growth techniques. These materials have been studied using various experiments in order to explore the wide range of interesting properties predicted theoretically for low-dimensional systems. In this pursuit, novel properties have been observed and many open questions have been raised. One such property that is typically observed in many low-dimensional quantum magnets is heat transport via magnetic excitations. Large magnitudes of magnetic heat conductivity has been found experimentally in materials belonging to this class in addition to the conventionally known phononic heat conduction, and interesting theoretical predictions like the divergence of heat conductivity in certain spin models exist, that have stimulated research in this field. This experimental work mainly deals with the crystal growth and heat transport properties of low-dimensional quantum magnets that include one-dimensional (1D) spin chain systems Sr$_2$CuO$_3$ and SrCuO$_2$, two-dimensional (2D) Heisenberg antiferromagnet La$_2$CuO$_4$, and a five-leg spin ladder La$_8$Cu$_7$O$_{19}$, with a view to understand propagating low-energy magnetic excitations and their interaction amongst themselves, other quasiparticles and impurities present in the systems. These interactions result in scattering processes that govern the magnitude and temperature dependence of heat conductivity. In spite of considerable theoretical and experimental work in the field of heat transport, a complete understanding of the scattering mechanisms is lacking. The work tries to add to the experimental knowledge about magnetic heat transport in such systems and presents cases which motivate the need for theoretical understanding of aspects of heat transport. The focus of this work was twofold. One part focusses on the single crystal growth using the travelling-solvent floating zone (TFSZ) method of materials which realize low-dimensional spin systems in their structure. The TFSZ method is indispensable for growing large single crystals of extraordinary purity, which can be used for investigations using neutrons and other techniques like heat conductivity measurements that probe anisotropic properties. The other part deals with the experimental results on heat transport and other thermodynamic properties of these materials. In order to study the behaviour of the magnetic heat conductivity at high temperatures, and the effect of small amount of magnetic and non-magnetic impurities on the heat transport of 2D Heisenberg antiferromagnet La$_2$CuO$_4$, single crystals of pure La$_2$CuO$_4$, and Ni- and Zn-doped versions, La$_2$Cu$_x$Ni$_{1-x}$O$_4$ and La$_2$Cu$_x$Zn$_{1-x}$O$_4$ for $x$ = 0.001 and 0.003, were grown using the TFSZ method. Heat transport in the pure compound was experimentally investigated for the first time up to very high temperatures of 813 K using two methods, namely the steady state method for low temperatures and the dynamic flash method for measuring high temperature conductivity. Analysis of the magnon mean-free path using empirical models based on semi-classical theories, and qualitative comparison to theoretical calculations seems to suggest that scattering between magnons might play an important role in addition to scattering of magnons with phonons and defects, and that the spin-spin correlation length could be crucial in limiting the mean free path of magnons at high temperatures. These experimental results and indications of probable scattering mechanisms based on non-rigorous analyses and comparisons, strongly motivate the need for theoretical studies. Heat conductivity measurements on the Ni- and Zn- doped versions of La$_2$CuO$_4$ are still incomplete and inconclusive, and hence have not been reported in this work. Heat transport experiments on Ni- and Ca-doped Sr$_2$CuO$_3$ were performed, with a motivation to investigate the role of disorder induced by impurities lying within the spin chains (Ni) and those lying outside the spin chains (Ca), on the heat transport in this system. In both the cases, the magnetic heat transport is observed to be strongly suppressed upon doping. Empirical analysis of the data seems to suggest that in the temperature regime of 100-300 K, the temperature dependence of the mean-free path of magnetic excitations for the Ni- and Ca-doped samples can be described by scattering with defects (Ni and Ca impurities) and phonons alone. However, surprisingly, a strong increase of phononic conductivity is observed perpendicular and parallel to the spin chains of the Ni-doped compounds compared to the pure compounds, whose explanation seems to lie in the existence of an additional dissipative scattering mechanism present in the pure compounds that is lifted upon doping, possibly due to the presence of a spin gap in the doped compounds. The effect of Ni on the Sr$_2$CuO$_3$ and SrCuO$_2$ was also investigated by studying the low energy regime of the spin excitation spectrum using other microscopic probes like nuclear magnetic resonance (NMR) and inelastic neutron scattering (INS). Large single crystals of SrCu$_x$Ni$_{1-x}$O$_2$, with $x$ = 0.01 were grown and used in these experiments that observed the presence of a spin gap in the Ni-doped sample. Further theoretical investigations are however required to understand the possible role of the spin gap in influencing the spin-phonon scattering mechanism, and its relevance to the observed enhancement in phononic conduction. Although we observe that in the case of both 1D and 2D systems, a semi-classical kinetic model for heat transport along with empirical models of scattering processes describe the temperature dependence of the measured heat conductivity surprisingly well in the temperature regime up to 300 K and 800 K respectively, interpretations based on these analyses must be treated as only preliminary, and as a step towards understanding microscopically the scattering mechanisms involved in low-dimensional systems such as the ones discussed in this work. In the direction of exploratory research towards synthesis of novel low-dimensional materials, two cuprate compounds were synthesized in the form of single crystals using the floating zone method for the first time, namely, a five leg $S=tfrac{1}{2}$ antiferromagnetic spin ladder compound La$_8$Cu$_7$O$_{19}$ and an insulating delafossite LaCuO$_{2}$. A bulk 3D antiferromagnetic ordering is observed in La$_8$Cu$_7$O$_{19}$. Heat conductivity of La$_8$Cu$_7$O$_{19}$ is observed to be purely phononic and no contribution from magnetic excitations seem to exist, although the measurements indicates that there is a large anisotropy in heat transport. However, detailed diffraction experiments using x-rays and neutrons indicate that both the crystal and magnetic structures are complicated, and that the details of the structure prevent La$_8$Cu$_7$O$_{19}$ from being a perfect realization of a five-leg spin ladder.

The research in low-dimensional (low-D) quantum spin systems has become an arduous challenge for the condensed matter physics community during the last years. In systems with low dimensional magnetic interactions the exchange coupling is restricted to dimensions lower than the full three-D exhibited by the bulk real material. The remarkable interest in this field is fueled by a continuous stream of striking discoveries like superconductivity, quantum liquid and spin gap states, chiral phases, etc, derived from the strong effect of quantum fluctuations on the macroscopic properties of the system and the competition between electronic and magnetic degrees of freedom. The main goal of the current studies is to reach a broad understanding of the mechanisms that participate in the formation of those novel ground states as well as the characteristic dependence with respect to relevant physical parameters. In this thesis we present the results of an Electron Spin Resonance (ESR)-based study on different quasi-1D spin systems, exemplifying the realization of 1D-magnetic spin-chains typically containing transition metal oxides such as Cu2+ or V4+. The local sensitivity of the ESR technique has been considered useful in exploring magnetic excitation energies, dominant mechanisms of exchange interactions, spin fluctuations and the dimensionality of the electron spin system, among others. Aside from ESR other experimental results, e.g., magnetization and nuclear magnetic resonance besides some theoretical approaches were especially helpful in achieving a proper understanding and modeling of those low-D spin systems. This thesis is organized into two parts: The first three chapters are devoted to the basic knowledge of the subject. The first chapter is about magnetic exchange interactions between spin moments and the effect of the crystal field potential and the external magnetic field. The second chapter is a short introduction on exchange interactions in a 1D-spin chain, and the third chapter is devoted to ESR basics and the elucidation of dynamic magnetic properties from the absorption spectrum parameters. The second part deals with the experimental results. In the fourth chapter we start with the magnetization results from the zero-dimensional endohedral fullerene Dy3N@C80. This system is seemingly ESR “silent” at the frequency of X-band experiments. The fifth chapter shows an unexpected temperature dependence of the anisotropy in the homometallic ferrimagnet Na2Cu5Si4O14 containing alternating dimer-trimer units in the zig-zag Cu-O chains. In the sixth chapter different magnetic species in the layer structure of vanadium oxide nanotubes (VOx-NT) have been identified, confirming earlier magnetization measurements. Moreover the superparamagnetic-like nature of the Li-doped VOx-NT samples was found to justify its ferromagnetic character at particular Li concentration on the room temperature scale. In the seventh chapter the Li2ZrCuO4 system is presented as a unique model to study the influence of additional interactions on frustrated magnetism. The eighth chapter highlights the magnetic properties of the pyrocompound Cu2As2O7. The results suggest significant spin fluctuations below TN. The thesis closes with the summary and the list of references.