To obtain accurate adsorption energies of molecules on surfaces is a challenging task as the methods with sufficient accuracy are too computationally demanding to be applied to the systems of interest. Embedding theories provide a natural remedy: focus the computation on a small region and incorporate the effects of the environment. In this thesis, embedding schemes and the response of many-electron systems to an adsorbed impurity are investigated. To this end, two approaches are used: tight-binding and ab initio. In the tight-binding method, the Green's function formalism is studied and explicit expressions for Green's functions of various one- and two-dimensional models are obtained. Using this formalism, we study qualitatively the local density of states and adsorption energies. In the second part of this thesis, state-of-the-art ab initio methods are employed to study convergence of the subtractive embedding scheme for adsorption energies of small closed-shell systems on two-dimensional graphene and hexagonal boron nitride. The efficiency and applicability of the scheme are assessed for neon and hydrogen fluoride as adsorbates. We found that the studied embedding method works better for neon compared to hydrogen fluoride, which may be explained by the use of a two-body dispersion correction.

It has been shown recently that high-quality epitaxial graphene (EPG) can be grown on the SiC substrate that exhibits interesting physical properties and has great advantages for varies device applications. In particular, the multilayer graphene films grown on the C-face show rotational disorder. It is expected that the twisted layers exhibit unique new physics that is distinct from that of either single layer graphene or graphite. In this work, by combining density functional and tight-binding model calculations, we investigate the electric field and doping effects on twisted bilayer graphene (TBG), multiple layer effects on twisted triple-layer graphene, and wave packet propagation properties of TBG. Though these studies, we obtain a comprehensive description of the interesting interlayer interaction in this twisted multilayer graphene system.

No description available.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

COSTA, Diego Rabelo da. Transportes e confinamento em monocamada e bicamada de nanoestruturas de grafeno com diferentes bordas, interfaces e potenciais. 2014. 201 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-06-01T22:18:12Z No. of bitstreams: 1 2014_tese_drcosta.pdf: 54910487 bytes, checksum: 82b386bac8259edaa10f6d5ff314bd42 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-06-01T22:19:16Z (GMT) No. of bitstreams: 1 2014_tese_drcosta.pdf: 54910487 bytes, checksum: 82b386bac8259edaa10f6d5ff314bd42 (MD5) / Made available in DSpace on 2015-06-01T22:19:16Z (GMT). No. of bitstreams: 1 2014_tese_drcosta.pdf: 54910487 bytes, checksum: 82b386bac8259edaa10f6d5ff314bd42 (MD5) Previous issue date: 2014 / Graphene, a two-dimensional lattice of carbon atoms, has been widely studied during the past few years. The interest in this material is not only due to its possible future technological applications, but also because it provides the possibility to probe interesting phenomena predicted by quantum field theories, ranging from Klein tunneling and other quasi-relativistic effects to the existence of new types of electron degrees of freedom, namely, the pseudo-spin, and the existence of two inequivalent electronic valleys in the vicinity of the gapless points of its energy spectrum. Several of the exotic properties observed in graphene originate from the fact that within the low energy approximation for the tight-binding Hamiltonian of graphene, electrons behave as massless Dirac fermions, with a linear energy dispersion. Just like in single layer graphene, the low-energy eletronic spectrum in bilayer graphene is gapless, but in this case it is dominated by the parabolic dispersion. Nevertheless, one interesting feature is shared by both monolayer and bilayer graphene: the valley degree of freedom. In this thesis, we theoretically investigate: (i) the dynamic properties in mono and bilayer graphene, performing a systematic study of wave packet scattering in different interface shapes, edges and potentials; and furthermore (ii) the energy levels of confined systems in graphene in the presence or absence of external magnetic and electric fields. In the first part of the work, we use the tight-binding approach to study the scattering of a Gaussian wave packet on monolayer graphene edges (armchair and zigzag) in the presence of real and pseudo (strain induced) magnetic fields and also calculate the transmission probabilities of a Gaussian wave packet through a quantum point contact defined by electrostatic gates in bilayer graphene. These numerical calculations are based on the solution of the time-dependent Schrödinger equation for the tight-binding model Hamiltonian, using the Split-operator technique. Our theory allows us to investigate scattering in reciprocal space, and depending on the type of graphene edge we observe scattering within the same valley, or between different valleys. In the presence of an external magnetic field, the well known skipping orbits are observed. However, our results demonstrate that in the case of a pseudo-magnetic field, induced by non-uniform strain, the scattering by an armchair edge results in a non-propagating edge state. We propose also a very efficient valley filtering through a quantum point contact system defined by electrostatic gates in bilayer graphene. For the suggested bilayer system, we investigate how to improve the efficiency of the system as a valley filter by varying parameters, such as length, width and amplitude of the applied potential. In the second part of the thesis, we present a systematic study of the energy spectra of graphene quantum rings having different geometries and edge types, in the presence of a perpendicular magnetic field. We discuss which features obtained through a simplified Dirac model can be recovered when the eigenstates of graphene quantum rings are compared with the tight-binding results. Furthermore, we also investigate the confined states in two different hybrid monolayer - bilayer systems, identifying dot-localized states and edge states for the suggested bilayer confinement structures, as well as we will study the behavior of the energy levels as a function of dot size and under an applied external magnetic field. Finally, using the four-band continuum Dirac model, we also derive a general expression for the infinite-mass boundary condition in bilayer graphene in order to apply this boundary condition to calculate analytically the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our analytic results exhibit good agreement when compared with the tight-binding ones. / Grafeno, uma rede bidimensional de átomos de carbono, tem sido amplamente estudado durante os últimos anos. O interesse por este material não é apenas devido às suas possíveis aplicações tecnológicas futuras, mas também porque oferece a possibilidade de investigar fenômenos interessantes previstos pelas teorias quânticas de campo, que vão desde o tunelamento de Klein e outros efeitos quasi-relativísticos à existência de novos tipos de graus de liberdade do elétron, ou seja, o pseudo-spin, e a existência de dois vales eletrônicos não-equivalentes na vizinhança dos pontos sem gap do seu espectro de energia. Várias das propriedades exóticas observadas no grafeno originam-se do facto de que dentro da aproximação de baixas energias para o Hamiltoniano tight-binding do grafeno, elétrons se comportam como férmions de Dirac sem massa, com uma dispersão de energia linear. Assim como no caso de uma monocamada de grafeno, o espectro eletrônico de baixas energias para uma bicamada de grafeno é sem gap, mas, neste caso, é dominado pela dispersão parabólica. No entanto, uma característica interessante é compartilhada por ambas monocamada e bicamada de grafeno: o grau de liberdade de vale. Nesta tese, nós investigamos teoricamente: (i) as propriedades dinâmicas em mono e bicamadas de grafeno, realizando um estudo sistemático do espalhamento de pacotes de onda em diferentes formas de interfaces, bordas e potenciais; e, além disso, (ii) os níveis de energia de sistemas confinados no grafeno na presença ou ausência de campos magnéticos e elétricos externos. Na primeira parte do trabalho, nós utilizamos a abordagem tight-binding para estudar o espalhamento de um pacote de onda Gaussiano nas bordas de uma monocamada de grafeno (armchair e zigzag) na presença de campos magnéticos reais e pseudo-magnéticos (induzidos por tensão) e também calculamos as probabilidades de transmissão de um pacote de onda Gaussiano através de um contato de ponto quântico definido por potenciais eletrostáticos em bicamadas de grafeno. Estes cálculos numéricos são baseados na solução da equação de Schrödinger dependente do tempo para o Hamiltoniano do modelo tight-binding, usando a técnica Split-operator. Nossa teoria permite investigar espalhamento no espaço recíproco, e dependendo do tipo de borda do grafeno, nós observamos espalhamento dentro do mesmo vale, ou entre diferentes vales. Na presença de um campo magnético externo, as bem conhecidas órbitas skipping orbits são observadas. No entanto, nossos resultados demonstram que, no caso de um campo pseudo-magnético induzido por uma tensão não-uniforme, o espalhamento por uma borba armchair resulta em um estado de borda não-propagante. Nós também propomos um sistema de filtragem de vales muito eficiente através de um sistema de contato de ponto quântico definido por portas eletrostáticas em uma bicamada de grafeno. Para o sistema de bicamadas sugerido, nós investigamos a forma de melhorar a eficiência do sistema como um filtro de vales por diferentes parâmetros, como comprimento, largura e amplitude do potencial aplicado. Na segunda parte da tese, nós apresentamos um estudo sistemático dos espectros de energia de anéis quânticos de grafeno com diferentes geometrias e tipos de borda, na presença de um campo magnético perpendicular. Nós discutimos quais características obtidas por meio de um modelo simplificado de Dirac podem ser recuperadas quando os auto-estados de anéis quânticos de grafeno são comparados com os resultados do modelo tight-binding. Além disso, nós também investigamos os estados confinados em dois sistemas híbridos diferentes de monocamada - bicamada, identificando estados localizados dentro do ponto e estados de borda para as estruturas de confinamento em bicamadas sugeridas, assim como vamos estudar o comportamento dos níveis de energia em função do tamanho do ponto e sob um campo magnético externo aplicado. Finalmente, usando o modelo contínuo de Dirac de quatro bandas, nós também derivamos uma expressão geral para a condição de contorno de massa infinita em bicamada de grafeno, a fim de aplicar essa condição de contorno para calcular analiticamente os estados confinados e as correspondentes funções de onda em um ponto quântico em uma bicamada de grafeno na ausência e na presença de um campo magnético perpendicular. Nossos resultados analíticos apresentam boa concordância quando comparados com os resultados tight-binding.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Grafeno, uma rede bidimensional de Ãtomos de carbono, tem sido amplamente estudado durante os Ãltimos anos. O interesse por este material nÃo à apenas devido Ãs suas possÃveis aplicaÃÃes tecnolÃgicas futuras, mas tambÃm porque oferece a possibilidade de investigar fenÃmenos interessantes previstos pelas teorias quÃnticas de campo, que vÃo desde o tunelamento de Klein e outros efeitos quasi-relativÃsticos à existÃncia de novos tipos de graus de liberdade do elÃtron, ou seja, o pseudo-spin, e a existÃncia de dois vales eletrÃnicos nÃo-equivalentes na vizinhanÃa dos pontos sem gap do seu espectro de energia. VÃrias das propriedades exÃticas observadas no grafeno originam-se do facto de que dentro da aproximaÃÃo de baixas energias para o Hamiltoniano tight-binding do grafeno, elÃtrons se comportam como fÃrmions de Dirac sem massa, com uma dispersÃo de energia linear. Assim como no caso de uma monocamada de grafeno, o espectro eletrÃnico de baixas energias para uma bicamada de grafeno à sem gap, mas, neste caso, à dominado pela dispersÃo parabÃlica. No entanto, uma caracterÃstica interessante à compartilhada por ambas monocamada e bicamada de grafeno: o grau de liberdade de vale. Nesta tese, nÃs investigamos teoricamente: (i) as propriedades dinÃmicas em mono e bicamadas de grafeno, realizando um estudo sistemÃtico do espalhamento de pacotes de onda em diferentes formas de interfaces, bordas e potenciais; e, alÃm disso, (ii) os nÃveis de energia de sistemas confinados no grafeno na presenÃa ou ausÃncia de campos magnÃticos e elÃtricos externos. Na primeira parte do trabalho, nÃs utilizamos a abordagem tight-binding para estudar o espalhamento de um pacote de onda Gaussiano nas bordas de uma monocamada de grafeno (armchair e zigzag) na presenÃa de campos magnÃticos reais e pseudo-magnÃticos (induzidos por tensÃo) e tambÃm calculamos as probabilidades de transmissÃo de um pacote de onda Gaussiano atravÃs de um contato de ponto quÃntico definido por potenciais eletrostÃticos em bicamadas de grafeno. Estes cÃlculos numÃricos sÃo baseados na soluÃÃo da equaÃÃo de SchrÃdinger dependente do tempo para o Hamiltoniano do modelo tight-binding, usando a tÃcnica Split-operator. Nossa teoria permite investigar espalhamento no espaÃo recÃproco, e dependendo do tipo de borda do grafeno, nÃs observamos espalhamento dentro do mesmo vale, ou entre diferentes vales. Na presenÃa de um campo magnÃtico externo, as bem conhecidas Ãrbitas skipping orbits sÃo observadas. No entanto, nossos resultados demonstram que, no caso de um campo pseudo-magnÃtico induzido por uma tensÃo nÃo-uniforme, o espalhamento por uma borba armchair resulta em um estado de borda nÃo-propagante. NÃs tambÃm propomos um sistema de filtragem de vales muito eficiente atravÃs de um sistema de contato de ponto quÃntico definido por portas eletrostÃticas em uma bicamada de grafeno. Para o sistema de bicamadas sugerido, nÃs investigamos a forma de melhorar a eficiÃncia do sistema como um filtro de vales por diferentes parÃmetros, como comprimento, largura e amplitude do potencial aplicado. Na segunda parte da tese, nÃs apresentamos um estudo sistemÃtico dos espectros de energia de anÃis quÃnticos de grafeno com diferentes geometrias e tipos de borda, na presenÃa de um campo magnÃtico perpendicular. NÃs discutimos quais caracterÃsticas obtidas por meio de um modelo simplificado de Dirac podem ser recuperadas quando os auto-estados de anÃis quÃnticos de grafeno sÃo comparados com os resultados do modelo tight-binding. AlÃm disso, nÃs tambÃm investigamos os estados confinados em dois sistemas hÃbridos diferentes de monocamada - bicamada, identificando estados localizados dentro do ponto e estados de borda para as estruturas de confinamento em bicamadas sugeridas, assim como vamos estudar o comportamento dos nÃveis de energia em funÃÃo do tamanho do ponto e sob um campo magnÃtico externo aplicado. Finalmente, usando o modelo contÃnuo de Dirac de quatro bandas, nÃs tambÃm derivamos uma expressÃo geral para a condiÃÃo de contorno de massa infinita em bicamada de grafeno, a fim de aplicar essa condiÃÃo de contorno para calcular analiticamente os estados confinados e as correspondentes funÃÃes de onda em um ponto quÃntico em uma bicamada de grafeno na ausÃncia e na presenÃa de um campo magnÃtico perpendicular. Nossos resultados analÃticos apresentam boa concordÃncia quando comparados com os resultados tight-binding. / Graphene, a two-dimensional lattice of carbon atoms, has been widely studied during the past few years. The interest in this material is not only due to its possible future technological applications, but also because it provides the possibility to probe interesting phenomena predicted by quantum field theories, ranging from Klein tunneling and other quasi-relativistic effects to the existence of new types of electron degrees of freedom, namely, the pseudo-spin, and the existence of two inequivalent electronic valleys in the vicinity of the gapless points of its energy spectrum. Several of the exotic properties observed in graphene originate from the fact that within the low energy approximation for the tight-binding Hamiltonian of graphene, electrons behave as massless Dirac fermions, with a linear energy dispersion. Just like in single layer graphene, the low-energy eletronic spectrum in bilayer graphene is gapless, but in this case it is dominated by the parabolic dispersion. Nevertheless, one interesting feature is shared by both monolayer and bilayer graphene: the valley degree of freedom. In this thesis, we theoretically investigate: (i) the dynamic properties in mono and bilayer graphene, performing a systematic study of wave packet scattering in different interface shapes, edges and potentials; and furthermore (ii) the energy levels of confined systems in graphene in the presence or absence of external magnetic and electric fields. In the first part of the work, we use the tight-binding approach to study the scattering of a Gaussian wave packet on monolayer graphene edges (armchair and zigzag) in the presence of real and pseudo (strain induced) magnetic fields and also calculate the transmission probabilities of a Gaussian wave packet through a quantum point contact defined by electrostatic gates in bilayer graphene. These numerical calculations are based on the solution of the time-dependent SchrÃdinger equation for the tight-binding model Hamiltonian, using the Split-operator technique. Our theory allows us to investigate scattering in reciprocal space, and depending on the type of graphene edge we observe scattering within the same valley, or between different valleys. In the presence of an external magnetic field, the well known skipping orbits are observed. However, our results demonstrate that in the case of a pseudo-magnetic field, induced by non-uniform strain, the scattering by an armchair edge results in a non-propagating edge state. We propose also a very efficient valley filtering through a quantum point contact system defined by electrostatic gates in bilayer graphene. For the suggested bilayer system, we investigate how to improve the efficiency of the system as a valley filter by varying parameters, such as length, width and amplitude of the applied potential. In the second part of the thesis, we present a systematic study of the energy spectra of graphene quantum rings having different geometries and edge types, in the presence of a perpendicular magnetic field. We discuss which features obtained through a simplified Dirac model can be recovered when the eigenstates of graphene quantum rings are compared with the tight-binding results. Furthermore, we also investigate the confined states in two different hybrid monolayer - bilayer systems, identifying dot-localized states and edge states for the suggested bilayer confinement structures, as well as we will study the behavior of the energy levels as a function of dot size and under an applied external magnetic field. Finally, using the four-band continuum Dirac model, we also derive a general expression for the infinite-mass boundary condition in bilayer graphene in order to apply this boundary condition to calculate analytically the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our analytic results exhibit good agreement when compared with the tight-binding ones.

Dans cette thèse, nous construisons un modèle de liaisons fortes tridimensionnel minimal pour les cuprates supraconducteurs monocouches à base de lanthane. Celui-ci prend en compte huit orbitales, dont deux d'entre elles impliquent les ions oxygène apicaux. L'optimisation des paramètres microscopiques permet de reproduire presque parfaitement la bande de conduction tridimensionnelle telle qu'elle a été obtenue à partir des calculs DFT. Nous discutons la façon dont chacun des paramètres entrant en jeu dans ce modèle multi-bandes influence la bande de conduction, et nous montrons que la forme particulière de sa dispersion contraint les valeurs des paramètres. Nous mettons alors en évidence que la détermination standard d'un modèle effectif à une bande au travers d'un traitement perturbatif converge lentement en raison de la valeur relativement faible du gap de transfert de charges. A ce stade, cela nous permet, en revanche, de lever le voile sur l'origine microscopique des amplitudes de saut des électrons au sein des plans et en-dehors des plans. Une approche alternative au calcul des paramètres microscopiques de saut du modèle effectif de liaisons fortes est présentée et mise à contribution. Il en résulte que l'accord avec la DFT est préservé à condition que les amplitudes de saut de plus longue portée soient conservées. Une comparaison avec les modèles existants est également effectuée. La surface de Fermi, mettant en exergue des domaines décalés qui alternent en taille et en forme, est comparée à l'expérience. De plus, la densité d'états du modèle est aussi calculée. Une analyse plus approfondie du modèle est réalisée au travers d'une étude en couplage faible des instabilités magnétiques. Les calculs sont effectués sur de grandes cellules et nous avons trouvé une compétition parmi plusieurs instabilités magnétiques tridimensionnelles dans la région d’intérêt du dopage en trous accessible expérimentalement. Bien qu'à notre connaissance cela ne semble pas avoir été évoqué expérimentalement, nous montrons à l'issue de notre étude, que la tendance du modèle à former des ondes de densité de spin incommensurables tridimensionnelles est la plus forte à proximité du dopage 1/8. / In this thesis, we construct a minimal three-dimensional tight-binding model for single-layer La-based cuprate superconductors. It entails eight orbitals, two of them involving apical oxygen ions. Parameter optimization allows to almost perfectly reproduce the three-dimensional conduction band as obtained from DFT. We discuss how each parameter entering this multiband model influences it, and show that the peculiar form of its dispersion severely constraints the parameter values. We then evidence that standard perturbative derivation of an effective one-band model is poorly converging because of the comparatively small value of the charge transfer gap. Yet, this allows us to unravel the microscopical origin of the in-plane and out-of-plane hopping amplitudes. An alternative approach to the computation of the tight-binding parameters of the effective model is presented and worked out. It results that the agreement with DFT is preserved provided longer-ranged hopping amplitudes are retained. A comparison with existing models is performed, too. The Fermi surface, showing staggered pieces alternating in size and shape, is compared to experiment. The density of states is calculated as well. The model is further analyzed through a weak coupling study of magnetic instabilities. It is performed on large clusters and competition between several three-dimensional magnetic instabilities in the hole-doping region of experimental interest is found. We show that the tendency to form a three-dimensional incommensurate spin density wave is strongest in the vicinity of 1/8 doping.

When a nanostructure is coupled between two leads, the electron transmission probability as a function of energy, E, is used in the Landauer formula to obtain the electrical conductance of the nanodevice. The electron transmission probability as a function of energy, T (E), is calculated from the appropriate solution of the time independent Schrödinger equation. Recently, a large class of nanostructures called quantum dragons has been discovered. Quantum dragons are nanodevices with correlated disorder but still can have electron transmission probability unity for all energies when connected to appropriate (idealized) leads. Hence for a single channel setup, the electrical conductivity is quantized. Thus quantum dragons have the minimum electrical conductance allowed by quantum mechanics. These quantum dragons have potential applications in nanoelectronics. It is shown that for dimerized leads coupled to a simple two-slice (l = 2, m = 1) device, the matrix method gives the same expression for the electron transmission probability as renormalization group methods and as the well known Green's function method. If a nanodevice has m atoms per slice, with l slices to calculate the electron transmission probability as a function of energy via the matrix method requires the solution of the inverse of a (2 + ml) (2 + ml) matrix. This matrix to invert is of large dimensions for large m and l. Taking the inverse of such a matrix could be done numerically, but getting an exact solution may not be possible. By using the mapping technique, this reduces this large matrix to invert into a simple (l + 2) (l + 2) matrix to invert, which is easier to handle but has the same solution. By using the map-and-tune approach, quantum dragon solutions are shown to exist for single-layer planar rectangular crystals with different boundary conditions. Each chapter provides two different ways on how to find quantum dragons. This work has experimental relevance, since this could pave the way for planar rectangular nanodevices with zero electrical resistance to be found. In the presence of randomness of the single-band tight-binding parameters in the nanodevice, an interesting quantum mechanical phenomenon called Fano resonance of the electron transmission probability is shown to be observed.

<p>Parkinson’s disease is a neurodegenerative disorder characterized by a loss of dopaminergic neurons, where mitochondrial dysfunction and neuroinflammation are implicated in this process. However, the exact mechanisms of mitochondrial dysfunction, oxidative stress and neuroinflammation leading to the onset and development of Parkinson’s disease are not well understood. There is a lack of tools necessary to dissect these mechanisms, therefore we engineered genetically encoded fluorescent biosensors to monitor redox status and an inflammatory signal peptide with high spatiotemporal resolution. To measure intracellular redox dynamics, we developed red-shifted redox sensors and demonstrated their application in dual compartment imaging to study cross compartmental redox dynamics in live cells. To monitor extracellular inflammatory events, we developed a family of spectrally diverse genetically encoded fluorescent biosensors for the inflammatory mediator peptide, bradykinin. At the organismal level, we characterized the locomotor effects of mitochondrial toxicant-induced dopaminergic disruption in a zebrafish animal model and evaluated a behavioral assay as a method to screen for dopaminergic dysfunction. Pairing our intracellular redox sensors and our extracellular bradykinin sensors in a Parkinson’s disease animal model, such as a zebrafish toxicant-induced model will prove useful for dissecting the role of mitochondrial dysfunction and inflammation in Parkinson’s disease. </p>