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1
Stangel, Anders. "Wannier functions from Bloch orbitals in solids." Thesis, Uppsala universitet, Materialteori, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202140.
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Wannierfunctions are a superposition of the Blochorbitals in a Brillouin zone belonging to a manifold of energy bands. These Wannier functions have several uses regarding the analysis of the crystal on a local level. Since the Bloch orbital has a gauge indeterminacy and the Wannier functions therefore is strongly non-unique, the natural choice is the maximally localized Wannier funcition. These can be calculated from the standard Bloch orbital using unitary transformation by a steepest descent algorithm as proposed by Nicola Marzari and David Vanderbilt. Here the argument for this algorithm is discussed and explained.
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Nacbar, Denis Rafael [UNESP]. "Cálculo de funções de Wannier eletrônicas para aplicações em ciência dos materiais." Universidade Estadual Paulista (UNESP), 2007. http://hdl.handle.net/11449/88467.
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São calculadas e analisadas as funções de Wannier de localização máxima para elétrons em cristais unidimensionais. Essas funções formam uma base apropriada para descrever estados eletrônicos em materiais sólidos. Para cristais com simetria de inversão é utilizado o método desenvolvido por Bruno-Alfonso e Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Cada banda de energia é classificada segundo a simetria das funções de Bloch nos pontos 'gama' e 'qui' da zona de Brillouin. Para cada classe de banda a fase das funções de Bloch é escolhida para que as funções de Wannier tenham localização máxima. A simetria da últimas é determinda pelo tipo de banda. São apresentados resultados analíticos e numéricos para o modelo de Kronig-Penney obtidos através da técnica da matriz de transferência e do método tight binding. Posteriormente, apresenta-se um novo procedimento para calcular funções de Wannier de localização máxima em cristais sem simetria de inversão. Para isso são utilizadas técnicas do Cálculo Variacional. A teoria é aplicada para obter e analisar funções de Wannier de elétrons de condução em duas superredes de materiais semicondutores. Uma dessas estruturas tem simetria de inversão e a outra, não. O comportamento assintótico das funções de Wannier é predito analiticamente e verificado através dos cálculos numéricos. As funções de Wannier de localização máxima mostram um decaimento exponencial multiplicado por um decaimento em lei de potência, ambos isotrópicos. O mesmo acontece com parte das funções que não tem localização máxima. Porém, há outras que que apresentam decaimento exponecial reduzido e anisotropia em seu decaimento em lei de potência. Esses resultados novos são explicados levando em conta pontos de ramificação da continuação analítica das funções de Bloch sobre o plano de vetor de onda complexo.
The maximally localized Wannier functions of electrons in one-dimensional crystals are calculated and analyzed. Those functions form a suitable basis to describe localized states in solid materials. For crystals with inversion symmetry we use the procedure of Bruno-Alfonso and Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Each energy band is classified according to the symmetry of the Bloch functions at the points 'gama' e 'qui' of the Brillouin zone. For each band class, the phase of the Bloch functions in chosen to give the maximally localized Wannier functions. The symmmetry of those functions depends on the band class. Analytical and numerical results are presented for the Kronig-Penney model. Those result are obtained through the tight-binding method or a transfer-matrix technique. A new procedure to calculate the maximally localized Wannier functions in crystals without inversion symmetry is established. This involves techniques of the Variational Calculus. The theory is applied to obtain the Wannier functions of conduction electrons in superlattices of semiconductor materials. One of the superlattices presents inversion symmetry, but the other does not. The asymptotic behavior of the Wannier functions is predicted analytically and verified through numerical calculations. The maximally localized Wannier functions display an isotropic exponetial decal times an isotropic power-law decay. The same applies to a class of non-optimal Wannier functions. However, there is another class of non-optimal Wannier functions with reduced exponential decay and anisotropic power-law decay. Such new results are explained by taking into account branch points in the analytical continuation of the Bloch functions into the plane of complex wave vector.
3
Nacbar, Denis Rafael. "Cálculo de funções de Wannier eletrônicas para aplicações em ciência dos materiais /." Bauru : [s.n.], 2007. http://hdl.handle.net/11449/88467.
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Orientador: Alexys Bruno AlfonsoBanca: Guo-Qiang Hai
Banca: Aguinaldo Robinson de Souza
O Programa de Pós-Graduação em Ciência e Tecnologia de Materiais, PosMat, tem caráter institucional e integra as atividades de pesquisa em materiais de diversos campi da Unesp
Resumo: São calculadas e analisadas as funções de Wannier de localização máxima para elétrons em cristais unidimensionais. Essas funções formam uma base apropriada para descrever estados eletrônicos em materiais sólidos. Para cristais com simetria de inversão é utilizado o método desenvolvido por Bruno-Alfonso e Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Cada banda de energia é classificada segundo a simetria das funções de Bloch nos pontos 'gama' e 'qui' da zona de Brillouin. Para cada classe de banda a fase das funções de Bloch é escolhida para que as funções de Wannier tenham localização máxima. A simetria da últimas é determinda pelo tipo de banda. São apresentados resultados analíticos e numéricos para o modelo de Kronig-Penney obtidos através da técnica da matriz de transferência e do método tight binding. Posteriormente, apresenta-se um novo procedimento para calcular funções de Wannier de localização máxima em cristais sem simetria de inversão. Para isso são utilizadas técnicas do Cálculo Variacional. A teoria é aplicada para obter e analisar funções de Wannier de elétrons de condução em duas superredes de materiais semicondutores. Uma dessas estruturas tem simetria de inversão e a outra, não. O comportamento assintótico das funções de Wannier é predito analiticamente e verificado através dos cálculos numéricos. As funções de Wannier de localização máxima mostram um decaimento exponencial multiplicado por um decaimento em lei de potência, ambos isotrópicos. O mesmo acontece com parte das funções que não tem localização máxima. Porém, há outras que que apresentam decaimento exponecial reduzido e anisotropia em seu decaimento em lei de potência. Esses resultados novos são explicados levando em conta pontos de ramificação da continuação analítica das funções de Bloch sobre o plano de vetor de onda complexo.
Abstract: The maximally localized Wannier functions of electrons in one-dimensional crystals are calculated and analyzed. Those functions form a suitable basis to describe localized states in solid materials. For crystals with inversion symmetry we use the procedure of Bruno-Alfonso and Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Each energy band is classified according to the symmetry of the Bloch functions at the points 'gama' e 'qui' of the Brillouin zone. For each band class, the phase of the Bloch functions in chosen to give the maximally localized Wannier functions. The symmmetry of those functions depends on the band class. Analytical and numerical results are presented for the Kronig-Penney model. Those result are obtained through the tight-binding method or a transfer-matrix technique. A new procedure to calculate the maximally localized Wannier functions in crystals without inversion symmetry is established. This involves techniques of the Variational Calculus. The theory is applied to obtain the Wannier functions of conduction electrons in superlattices of semiconductor materials. One of the superlattices presents inversion symmetry, but the other does not. The asymptotic behavior of the Wannier functions is predicted analytically and verified through numerical calculations. The maximally localized Wannier functions display an isotropic exponetial decal times an isotropic power-law decay. The same applies to a class of non-optimal Wannier functions. However, there is another class of non-optimal Wannier functions with reduced exponential decay and anisotropic power-law decay. Such new results are explained by taking into account branch points in the analytical continuation of the Bloch functions into the plane of complex wave vector.
Mestre
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Eichelhardt, Frank. "Wannier-Function based Scattering-Matrix Formalism for Photonic Crystal Circuitry." [S.l. : s.n.], 2009. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000010434.
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Hermann, Daniel. "Wannier-Function based Scattering-Matrix Formalism for Photonic Crystal Circuitry." [S.l. : s.n.], 2008. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000009666.
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Sivadas, Nikhil. "First-Principles and Wannier-Function-Based Study of Two-Dimensional Electronic Systems." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/990.
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One of the goals in making better devices is to achieve the desired functionality in materials that enable a given application. The strong link between the functional behavior and the physical properties of materials is key to making better devices. This thesis focuses on applications of density functional theory (DFT), a powerful computational tool, for understanding the electronic, magnetic, magneto-optic, topological and thermodynamic properties of two-dimensional electronic systems (2DES). Why are 2DES interesting? Firstly, the reduced dimensionality renders these materials with properties which could be absent in the bulk form. Secondly, from a technological point of view, the desired functionality can be easily controlled externally in these 2DES by the application of a gate voltage or strain. The 2DES considered here could be crucial in beyond-CMOS electronic technologies. The materials considered in this thesis can be broadly categorized into two different classes of systems. The first one is the two-dimensional electron gas observed at the complex oxide interfaces. The discussion will go into the details of the formation of 2DEG in oxides resulting both from polar catastrophe and also due to the presence of vacancies. The second class of materials is two-dimensional (2D) atomic crystals, more specifically, 2D magnets. We not only predict a class of compounds, transition metal trichalcogenides (TMTC), that can exhibit magnetism in the 2D limit, but also demonstrate control of these magnetic degrees of freedom. Finally, we also demonstrate both using symmetry based tight-binding models and first-principles calculations a new way to detect magnetism in the 2D limit, which is applicable to compounds other than TMTC as well.
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Hardrat, Björn [Verfasser]. "Ballistic transport in one-dimensional magnetic nanojunctions: A first-principles Wannier function approach / Björn Hardrat." Kiel : Universitätsbibliothek Kiel, 2012. http://d-nb.info/1028798954/34.
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Merchant, Alexander Raymond. "An investigation of carbon nitride." Thesis, The University of Sydney, 2001. http://hdl.handle.net/2123/832.
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This thesis employs experimental and theoretical methods to characterise carbon nitride solids and proposes a generalstructural model for amorphous carbon nitride (a-C:N). It finds that a-C:N deposited by several methods is essentially identical, with similar bonding environments for carbon and nitrogen atoms. Using evidence from several techniques, the saturation of nitrogen in an sp2 carbon matrix is discussed. The experimental studies on a range of carbon nitride solids show no evidence for a crystalline form of carbon nitride. In addition to the experimental characterisation of a-C:N, ab initio molecular dynamics were used to investigate bonding and structure in carbon nitride. These simulations show that the most common form of nitrogen bonding was three-fold sites with a lone pair of electrons. Two-fold nitrogen sites were also found in agreement with experimental findings. An increase of nitrogen in a-C:N decreases the sp3-carbon fraction, but this is not localised on the nitrogen and the effect is most severe at high densities. A simulation of a low density/high nitrogen content network shows that the nitrogen saturation seen experimentally may be due to the formation of N2 dimers and C-N molecules which are easily driven out of the structure. The ab initio simulations also explore the nature of charged nitrogen and carbon sites in a-C:N. An analysis based on Wannier Function centres provided further information about the bonding and allowed for a detailed classification of these sites. The removal of electrons from the networks caused structural changes that could explain the two-state conductivity in ta-C:N memory devices. Finally, a theoretical study of the electron energy-loss near-edge structure (ELNES) calculated using multiple scattering theory is presented. The calculated ELNES of diamond, graphite and boron, silicon and carbon nitride structures compare well to experiment and supports the experimental finding that no crystalline carbon nitride had (or has) been produced. These ELNES calculations will however, provide a means of identifying crystalline beta-C3N4 should it be synthesised.
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Merchant, Alexander Raymond. "An investigation of carbon nitride." University of Sydney. Physics, 2001. http://hdl.handle.net/2123/832.
Full textAbstract:
This thesis employs experimental and theoretical methods to characterise carbon nitride solids and proposes a generalstructural model for amorphous carbon nitride (a-C:N). It finds that a-C:N deposited by several methods is essentially identical, with similar bonding environments for carbon and nitrogen atoms. Using evidence from several techniques, the saturation of nitrogen in an sp2 carbon matrix is discussed. The experimental studies on a range of carbon nitride solids show no evidence for a crystalline form of carbon nitride. In addition to the experimental characterisation of a-C:N, ab initio molecular dynamics were used to investigate bonding and structure in carbon nitride. These simulations show that the most common form of nitrogen bonding was three-fold sites with a lone pair of electrons. Two-fold nitrogen sites were also found in agreement with experimental findings. An increase of nitrogen in a-C:N decreases the sp3-carbon fraction, but this is not localised on the nitrogen and the effect is most severe at high densities. A simulation of a low density/high nitrogen content network shows that the nitrogen saturation seen experimentally may be due to the formation of N2 dimers and C-N molecules which are easily driven out of the structure. The ab initio simulations also explore the nature of charged nitrogen and carbon sites in a-C:N. An analysis based on Wannier Function centres provided further information about the bonding and allowed for a detailed classification of these sites. The removal of electrons from the networks caused structural changes that could explain the two-state conductivity in ta-C:N memory devices. Finally, a theoretical study of the electron energy-loss near-edge structure (ELNES) calculated using multiple scattering theory is presented. The calculated ELNES of diamond, graphite and boron, silicon and carbon nitride structures compare well to experiment and supports the experimental finding that no crystalline carbon nitride had (or has) been produced. These ELNES calculations will however, provide a means of identifying crystalline beta-C3N4 should it be synthesised.
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Bernasconi, Leonardo. "Interpretation of the electronic structure in condensed phase calculatioons." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249511.
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Romano, Maria Cecilia [UNESP]. "Funções de Wannier para cristais fotônicos unidimensionais." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/99679.
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Os cristais fotônicos são novos materiais em que a permissividade dielétrica e a permeabilidade magnética apresentam a periodicidade de uma rede de Bravais. No caso dos sólidos cristalinos, é a energia potencial de cada elétron que apresenta esse tipo de periodicidade. Por conta das semelhanças que existem entre as equações que descrevem os sintomas eletrônicos e fotônicos, muitos dos conceitos e métodos da teoria de estados eletrônicos vêm sendo aplicados na investigação de cristais fotônicos. Dentre esses conceitos, as funções de Wannier apresentam vantagens para o tratamento de estados eletrônicos e modos fotônicos localizados. Este trabalho aborda o caso de cristais fotônicos unidimensionais com simetria de inversão. Primeiramente são calculados e analisadas funções de Wannier bem localizadas. Em seguida são investigados os modos eletromagnéticos localizados produzidos por defeitos em cristais fotônicos, utilizando o método de matriz de transferência e o método da combinação linear das funções de Wannier. Finalmente, é feita a comparação dos resultados obtidos mediante esses métodos e são discutidas as vantagens do uso de funções de Wannier
Photonic crystal are new materials where both the dielectric permittivity and the magnetic permeability present the periodicity of a Bravais lattice. In the case of electronic states, this property is shown by the mono-eletronic potential energy. Due to the similarities between the eletronic and photonic problems, many concepts and methods of theory of electronic states are being applied to investigate photonic crystals. Among such concepts, the Wannier functions are advantageous to deal with either localized photonic modes. This work addresses the case of one-dimensional photonic crystals with inversion symmetry. First, well-localized Wannier functions are calculated and analyzed. Then, the localized modes produced by defects in photonic crystals are investigated by using either transfer matrices or linear combination Wannier functions. Finally, the results obtained by the two methods are compared and the advantages of using Wannier functions are discussed
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Villanova, John William. "Examining Topological Insulators and Topological Semimetals Using First Principles Calculations." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/82959.
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The importance and promise that topological materials hold has been recently underscored by the award of the Nobel Prize in Physics in 2016 ``for theoretical discoveries of topological phase transitions and topological phases of matter." This dissertation explores the novel qualities and useful topologically protected surface states of topological insulators and semimetals.
Topological materials have protected qualities which are not removed by weak perturbations. The manifestations of these qualities in topological insulators are spin-momentum-locked surface states, and in Weyl and Dirac semimetals they are unconventional open surface states (Fermi arcs) with anomalous electrical transport properties. There is great promise in utilizing the topologically protected surface states in electronics of the future, including spintronics, quantum computers, and highly sensitive devices. Physicists and chemists are also interested in the fundamental physics and exotic fermions exhibited in topological materials and in heterostructures including them.
Chapter 1 provides an introduction to the concepts and methods of topological band theory. Chapter 2 investigates the spin and spin-orbital texture and electronic structures of the surface states at side surfaces of a topological insulator, Bi2Se3, by using slab models within density functional theory. Two representative, experimentally achieved surfaces are examined, and it is shown that careful consideration of the crystal symmetry is necessary to understand the physics of the surface state Dirac cones at these surfaces. This advances the existing literature by properly taking into account surface relaxation and symmetry beyond what is contained in effective bulk model Hamiltonians.
Chapter 3 examines the Fermi arcs of a topological Dirac semimetal (DSM) in the presence of asymmetric charge transfer, of the kind which would be present in heterostructures. Asymmetric charge transfer allows one to accurately identify the projections of Dirac nodes despite the existence of a band gap and to engineer the properties of the Fermi arcs, including spin texture. Chapter 4 investigates the effect of an external magnetic field applied to a DSM. The breaking of time reversal symmetry splits the Dirac nodes into topologically charged Weyl nodes which exhibit Fermi arcs as well as conventionally-closed surface states as one varies the chemical potential.Ph. D.
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Romano, Maria Cecilia. "Funções de Wannier para cristais fotônicos unidimensionais /." Bauru : [s.n.], 2011. http://hdl.handle.net/11449/99679.
Full textAbstract:
Orientador: Alexys Bruno AlfonsoBanca: Ernesto Reyes Gómez
Banca: Fabio de Jesus Ribeiro
O programa de Pós graduação em Ciência e Tecnologia de Materiais, PosMat, tem carater institucional e integra as atividades de pesquisa em materiais de diversos campi da UNESP
Resumo: Os cristais fotônicos são novos materiais em que a permissividade dielétrica e a permeabilidade magnética apresentam a periodicidade de uma rede de Bravais. No caso dos sólidos cristalinos, é a energia potencial de cada elétron que apresenta esse tipo de periodicidade. Por conta das semelhanças que existem entre as equações que descrevem os sintomas eletrônicos e fotônicos, muitos dos conceitos e métodos da teoria de estados eletrônicos vêm sendo aplicados na investigação de cristais fotônicos. Dentre esses conceitos, as funções de Wannier apresentam vantagens para o tratamento de estados eletrônicos e modos fotônicos localizados. Este trabalho aborda o caso de cristais fotônicos unidimensionais com simetria de inversão. Primeiramente são calculados e analisadas funções de Wannier bem localizadas. Em seguida são investigados os modos eletromagnéticos localizados produzidos por defeitos em cristais fotônicos, utilizando o método de matriz de transferência e o método da combinação linear das funções de Wannier. Finalmente, é feita a comparação dos resultados obtidos mediante esses métodos e são discutidas as vantagens do uso de funções de Wannier
Abstract: Photonic crystal are new materials where both the dielectric permittivity and the magnetic permeability present the periodicity of a Bravais lattice. In the case of electronic states, this property is shown by the mono-eletronic potential energy. Due to the similarities between the eletronic and photonic problems, many concepts and methods of theory of electronic states are being applied to investigate photonic crystals. Among such concepts, the Wannier functions are advantageous to deal with either localized photonic modes. This work addresses the case of one-dimensional photonic crystals with inversion symmetry. First, well-localized Wannier functions are calculated and analyzed. Then, the localized modes produced by defects in photonic crystals are investigated by using either transfer matrices or linear combination Wannier functions. Finally, the results obtained by the two methods are compared and the advantages of using Wannier functions are discussed
Mestre
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Dragoni, Alberto. "Corrélations multi-corps dans les simulations ab initio du transport électronique quantique : une application aux dispositifs OxRAM de nouvelle génération." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAY039.
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Les mémoires résistives non volatiles basées sur les oxydes (OxRAM) acquièrent récemment un grand intérêt pour leurs performances, ce qui en fait des candidats prometteurs comme mémoire de stockage pour remplacer la technologie flash, et comme mémoires intégrées pour les applications réseau de neurones. Néanmoins, les dispositifs OxRAM émergents présentent encore certains inconvénients, comme la non-uniformité des paramètres de commutation et les défaillances de commutation. Surmonter ces inconvénients exige une compréhension plus profonde des principes de fonctionnement de l’OxRAM, jusqu’à présent pas complètement compris. Ceci peut être réalisé au moyen de simulations textit{ab initio}. Ce travail présente donc une étude approfondie de HfO₂, qui fait partie des matériaux les plus prometteurs pour la construction de dispositifs OxRAM, au moyen de calculs précis des états de quasi-particules (QP). Une étude des propriétés du transport électronique dans les dispositifs OxRAM est également de première importance. Toutefois, cela nécessite un cadre théorique solide et fiable afin de calculer la conductance des jonctions métal/isolant. L’approche standard, basée sur la théorie fonctionnelle de la densité, le formalisme de la fonction de Green et la formule de Landauer, a quelques limites et soucis de fiabilité. Ce travail propose une approche plus fiable basée sur les calculs QP, qui fournissent une structure électronique plus précise pour calculer la conductance, et teste en grande partie cette nouvelle méthode sur différentes jonctions imitant les dispositifs OxRAMResistive non-volatile memories based on oxides (OxRAM) are recently acquiring a wide interest for their performances, which make them promising candidates as storage memories to replace flash technology, and as embedded memories for neural network applications. Nevertheless, emerging OxRAM devices still present some drawbacks, like non-uniformity of switching parameters and switching failures. Overcoming these drawbacks requires a deeper comprehension of the OxRAM working principles, so far not completely understood. This can be achieved by means of textit{ab initio} simulations. Hence this work presents a careful characterization of HfO₂, which is within the most promising materials to build OxRAM devices, by means of accurate quasi-particle (QP) calculations. A study of the electronic transport properties in OxRAM devices is also of primary importance. However, this requires a robust and reliable theoretical framework to compute the conductance of bulk metal/insulator junctions. The standard approach, based on density functional theory, Green function formalism, and Landauer formula, has some limitations and reliability issues. This work proposes a more reliable approach based on QP calculations, which provide a more accurate electronic structure to compute the conductance, and largely tests this new method on different junctions mimicking OxRAM devices
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Nacbar, Denis Rafael [UNESP]. "Funções de Wannier generalizadas para aplicações em Ciência dos Materiais." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/106639.
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São calculadas e analisadas funções de Wannier de elétrons num potencial periódico com ênfase nas funções de Wannier generalizadas de máxima localização. A máxima localização das funções calculadas é a sua propriedade mais relevente para as aplicações em Ciência dos Materiais. Inicialmente, é apresentado um procedimento analítico para calcular funções de Wannier generalizadas de localização máxima de cristais unidimensionais com simetria de inversão. O método consiste em combinar linearmente as funções de Bloch de duas bandas consecutivas com o intuito de se obter quase funções de Bloch. As funções de Wannier generalizadas são obtidas através do valor médio das quase funções de Bloch sobre a primeira zona de Brillouin. São apresentados resultados analíticos e numéricos para um modelo diatômico do tipo Kroning-Penney. A fim de verificar os resultados analíticos, são apresentados também os resultados numéricos conseguidos através do operador de posição projetado nas bandas consideradas. Posteriormente, funções de Wannier de localização máxima de super-redes diatômicas com simetria de inversão são calculadas e analisadas e analisadas. As funções de Wannier de cada banda são obtidas mediante a classificação das bandas de energia segundo a simetria das funções de Bloch nos pontos de simetria do cristal. Investiga-se também como a largura de uma das camadas da super-rede na classificação das bandas de energia e na escolha apropriada da fase das funções de Bloch. As funções de Wannier de bandas simples são comparadas com as funções de Wannier generalizadas, e suas relações com orbitais moleculares e atômicos são discutidas. Finalmente, são apresentadas expressões concisas e gerais que permitem obter funções de Wannier de localização máxima de elétrons em sistemas com...
The Wannier functions of an electron in a periodic potential are investigated, with emphasis on the generalized Wannier functions of maximal localization. The maximal localization of the calculated functions is their most important property for applications in Materials Science. We first present and analytical procedure to calculate maximally localized generalized Wannier functions in one-dimensional crystals with inversion symmetry. The method consists in linearly combiniting of Bloch functions of two consecutive bands, in order to obtain quasi-Bloch functions. The generalized Wannier functions are obtained by the mean value of quasi-Bloch functions over the first brillouim zone. We present analytical and numerical results for the a diatomic Kroning-Penney model. In order to verify the analytical results, we also present numerical results obtained using the method of the band-projected position operator. Then, maximally localized Wannier functions of diatomic superlattices with inversion symmetry are calculated and analyzed. Wannier functions of each band are obtained by classifying the energy bands according to the symmetry of the Bloch functions at the symmetry points of the crystal. It is also investigated how the width of one of the layers of the superlattice influences the energy-band classification and the appropriate phase choise for the Bloch functions. We compare the Wannier functions of simple bands with generalized Wannier functions, and discuss their relations with molecular-like and atomic-like orbitals. Finally, we present concise and general expressions for the calculation of maximally localized Wannier functions in systems presenting different types of dimensionality and periodicity. For the cases... (Complete abstract click electronic access below)
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Nacbar, Denis Rafael. "Funções de Wannier generalizadas para aplicações em Ciência dos Materiais /." Bauru : [s.n.], 2012. http://hdl.handle.net/11449/106639.
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Orientador: Alexys Bruno AlfonsoBanca: Ricardo Wagner Nunes
Banca: Jeverson Teodoro Arantes Junior
Banca: Julio Ricardo Sambrano
Banca: Andre Luiz Malvezzi
Resumo: São calculadas e analisadas funções de Wannier de elétrons num potencial periódico com ênfase nas funções de Wannier generalizadas de máxima localização. A máxima localização das funções calculadas é a sua propriedade mais relevente para as aplicações em Ciência dos Materiais. Inicialmente, é apresentado um procedimento analítico para calcular funções de Wannier generalizadas de localização máxima de cristais unidimensionais com simetria de inversão. O método consiste em combinar linearmente as funções de Bloch de duas bandas consecutivas com o intuito de se obter quase funções de Bloch. As funções de Wannier generalizadas são obtidas através do valor médio das quase funções de Bloch sobre a primeira zona de Brillouin. São apresentados resultados analíticos e numéricos para um modelo diatômico do tipo Kroning-Penney. A fim de verificar os resultados analíticos, são apresentados também os resultados numéricos conseguidos através do operador de posição projetado nas bandas consideradas. Posteriormente, funções de Wannier de localização máxima de super-redes diatômicas com simetria de inversão são calculadas e analisadas e analisadas. As funções de Wannier de cada banda são obtidas mediante a classificação das bandas de energia segundo a simetria das funções de Bloch nos pontos de simetria do cristal. Investiga-se também como a largura de uma das camadas da super-rede na classificação das bandas de energia e na escolha apropriada da fase das funções de Bloch. As funções de Wannier de bandas simples são comparadas com as funções de Wannier generalizadas, e suas relações com orbitais moleculares e atômicos são discutidas. Finalmente, são apresentadas expressões concisas e gerais que permitem obter funções de Wannier de localização máxima de elétrons em sistemas com... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The Wannier functions of an electron in a periodic potential are investigated, with emphasis on the generalized Wannier functions of maximal localization. The maximal localization of the calculated functions is their most important property for applications in Materials Science. We first present and analytical procedure to calculate maximally localized generalized Wannier functions in one-dimensional crystals with inversion symmetry. The method consists in linearly combiniting of Bloch functions of two consecutive bands, in order to obtain quasi-Bloch functions. The generalized Wannier functions are obtained by the mean value of quasi-Bloch functions over the first brillouim zone. We present analytical and numerical results for the a diatomic Kroning-Penney model. In order to verify the analytical results, we also present numerical results obtained using the method of the band-projected position operator. Then, maximally localized Wannier functions of diatomic superlattices with inversion symmetry are calculated and analyzed. Wannier functions of each band are obtained by classifying the energy bands according to the symmetry of the Bloch functions at the symmetry points of the crystal. It is also investigated how the width of one of the layers of the superlattice influences the energy-band classification and the appropriate phase choise for the Bloch functions. We compare the Wannier functions of simple bands with generalized Wannier functions, and discuss their relations with molecular-like and atomic-like orbitals. Finally, we present concise and general expressions for the calculation of maximally localized Wannier functions in systems presenting different types of dimensionality and periodicity. For the cases... (Complete abstract click electronic access below)
Doutor
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Swartz, Charles W. "First Principles Calculations for Liquids and Solids Using Maximally Localized Wannier Functions." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/274283.
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PhysicsPh.D.
The field of condensed matter computational physics has seen an explosion of applicability over the last 50+ years. Since the very first calculations with ENIAC and MANIAC the field has continued to pushed the boundaries of what is possible; from the first large-scale molecular dynamics simulation, to the implementation of Density Functional Theory and large scale Car-Parrinello molecular dynamics, to million-core turbulence calculations by Standford. These milestones represent not only technological advances but theoretical breakthroughs and algorithmic improvements as well. The work in this thesis was completed in the hopes of furthering such advancement, even by a small fraction. Here we will focus mainly on the calculation of electronic and structural properties of solids and liquids, where we shall implement a wide range of novel approaches that are both computational efficient and physically enlightening. To this end we routinely will work with maximally localized Wannier functions (MLWFs) which have recently seen a revival in mainstream scientific literature. MLWFs present us with interesting opportunity to calculate a localized orbital within the planewave formalism of atomistic simulations. Such a localization will prove to be invaluable in the construction of layer-based superlattice models, linear scaling hybrid functional schemes and model quasiparticle calculations. In the first application of MLWF we will look at modeling functional piezoelectricity in superlattices. Based on the locality principle of insulating superlattices, we apply the method of Wu et al to the piezoelectric strains of individual layers under iifixed displacement field. For a superlattice of arbitrary stacking sequence an accurate model is acquired for predicting piezoelectricity. By applying the model in the superlattices where ferroelectric and antiferrodistortive modes are in competition, functional piezoelectricity can be achieved. A strong nonlinear effect is observed and can be further engineered in the PbTiO 3 /SrTiO 3 superlattice and an interface enhancement of piezoelectricity is found in the BaTiO 3 /CaTiO 3 superlattice. The second project will look at The ionization potential distributions of hydrated hydroxide and hydronium which are computed within a many-body approach for electron excitations using configurations generated by ab initio molecular dynamics. The experimental features are well reproduced and found to be closely related to the molecular excitations. In the stable configurations, the ionization potential is mainly perturbed by solvent water molecules within the first solvation shell. On the other hand, electron excitation is delocalized on both proton receiving and donating complex during proton transfer, which shifts the excitation energies and broadens the spectra for both hydrated ions. The third project represents a work in progress, where we also make use of the previous electron excitation theory applied to ab initio x-ray emission spectroscopy. In this case we make use of a novel method to include the ultrafast core-hole electron dynamics present in such situations. At present we have shown only strong qualitative agreement with experiment.
Temple University--Theses
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Ribeiro, Allan Victor [UNESP]. "Cálculo de funções de Wannier para nanomateriais: cumuleno e grafeno." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/151099.
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Gregory H. Wannier, em 1937, introduziu uma representação dos orbitais eletrônicos cristalinos em termos de funções ortogonais localizadas relacionadas com os orbitais atômicos. Posteriormente, tais funções foram denominadas de funções de Wannier. Nos últimos 30 anos, estudos têm apontado um crescente interesse da comunidade científica por estas funções, as quais se apresentam como uma poderosa ferramenta para a investigação de propriedades eletrônicas dos materiais. No presente trabalho, calculamos as funções de Wannier de sistemas nanométricos uni e bidimensionais. Inicialmente abordamos o cumuleno, que consiste em uma cadeia de átomos de carbono equidistantes. As funções de Bloch são obtidas por meio de uma aproximação tight binding e as funções de Wannier, usuais e generalizadas, são calculadas a partir delas. São discutidas as relações entre as funções de Wannier generalizadas obtidas por meio da aproximação tight binding e os orbitais híbridos sp. Isto é explicado mediante um cálculo alternativo das funções de Wannier, com a resolução de um problema de autovalores generalizado. As funções de Wannier das bandas pz do grafeno também são calculadas a partir das funções de Bloch obtidas por meio de uma aproximação tight binding. Elas assemelham-se a um par ligante-antiligante de orbitais moleculares, e suas propriedades de simetria e localização são discutidas. Finalmente, por meio de uma combinação dos pacotes PWscf (baseado em ondas planas e na teoria do funcional da densidade) e wannier90, são calculadas as funções de Bloch e as funções de Wannier de máxima localização para arranjos atômicos com periodicidade em uma (cumuleno) e duas (grafeno) dimensões. Há boa concordância qualitativa entre os resultados da aproximação tight binding e da teoria do funcional da densidade. Deve-se ressaltar que a primeira abordagem não usa réplicas dos sistemas nanométricos e permite aprofundar o entendimento das propriedades e do significado físico das funções de Wannier.
Gregory H. Wannier, in 1937, introduced a representation of crystalline electronic orbitals in terms of localized orthogonal functions related to the atomic orbitals. Subsequently, these functions were called as Wannier functions. Over the past 30 years, studies have shown a growing interest of the scientific community on these functions, which are presented as a powerful tool to investigate the electronic properties of materials. In this work, we calculate the Wannier functions of one and two-dimensional nanometric systems. Initially, we deal with cumulene, which consists of a chain of equidistant carbon atoms. The Bloch functions are obtained by means of a tight binding approximation, and the standard and the generalized Wannier functions are derived from them. The relations between the generalized Wannier functions and the sp hybrid orbitals is discussed. This is explained through an alternative calculation of the Wannier functions, solving a generalized eigenvalue problem. The pz Wannier functions of graphene are also calculated from the Bloch functions obtained by means of a tight binding approximation. They resemble a bonding-antibonding pair of molecular orbitals, and their symmetry and localization properties are discussed. Finally, by combining the computational codes PWscf (based on plane waves and the Density-functional Theory) and wannier90, the Bloch functions and the maximally localized Wannier functions are calculated for atomic arrangements which are periodic in one (cumulene) and two (graphene) dimensions. There is a good qualitative agreement between the results of the tight binding and density-functional approaches. It should be noted that the former does not involve replicas of the nanometric systems and allows a deeper understanding of the properties and the physical meaning of the Wannier functions.
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Yuvanc, Mustafa. "Numerical calculation of the Wannier Functions GaAs/Al(0.25)Ga(0.75)As superlattice structure." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1999. http://handle.dtic.mil/100.2/ADA365370.
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Thesis (M.S. in Physics) Naval Postgraduate School, June 1999."June 1999". Thesis advisor(s): James H.. Luscombe, Robert L. Armstead. Includes bibliographical references (p. 37-38). Also available online.
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Schillinger, Matthias. "Maximally localized photonic Wannier functions for the highly efficient description of integrated Photonic Crystal circuits." [S.l. : s.n.], 2006. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000007183.
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Wanner, Veronika [Verfasser], and Walter [Akademischer Betreuer] Gubler. "Subharmonic functions and real-valued differential forms on non-archimedean curves / Veronika Wanner ; Betreuer: Walter Gubler." Regensburg : Universitätsbibliothek Regensburg, 2019. http://d-nb.info/1190888386/34.
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Bakhta, Athmane. "Modèles mathématiques et simulation numérique de dispositifs photovoltaïques." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1046/document.
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Cette thèse comporte deux volets indépendants mais tous deux motivés par la modélisation mathématique et la simulation numérique de procédés photovoltaïques. La Partie I traite de systèmes d’équations aux dérivées partielles de diffusion croisée, modélisant l’évolution de concentrations ou de fractions volumiques de plusieurs espèces chimiques ou biologiques. Nous présentons dans le chapitre 1 une introduction succincte aux résultats mathématiques connus sur ces systèmes lorsqu’ils sont définis sur des domaines fixes. Nous présentons dans le chapitre 2 un système unidimensionnel que nous avons introduit pour modéliser l’évolution des fractions volumiques des différentes espèces chimiques intervenant dans le procédé de déposition physique en phase vapeur (PVD) utilisé pour la fabrication de cellules solaires à couches minces. Dans ce procédé, un échantillon est introduit dans un four à très haute température où sont injectées les différentes espèces chimiques sous forme gazeuse, si bien que des atomes se déposent petit à petit sur l’échantillon, formant une couche mince qui grandit au fur et à mesure du procédé. Dans ce modèle sont pris en compte à la fois l’évolution de la surface du film solide au cours du procédé et l’évolution des fractions volumiques locales au sein de ce film, ce qui aboutit à un système de diffusion croisée défini sur un domaine dépendant du temps. En utilisant une méthode récente basée sur l’entropie, nous montrons l’existence de solutions faibles à ce système et nous étudions leur comportement asymptotique dans le cas où les flux extérieurs imposés à la surface du film sont supposés constants. De plus, nous prouvons l’existence d’une solution à un problème d’optimisation sur les flux extérieurs. Nous présentons dans le chapitre 3comment ce modèle a été adapté et calibré sur des données expérimentales. La Partie II est consacrée à des questions reliées au calcul de la structure électronique de matériaux cristallins. Nous rappelons dans le chapitre 4 certains résultats classiques relatifs à la décomposition spectrale d’opérateurs de Schrödinger périodiques. Dans le chapitre 5, nous tentons de répondre à la question suivante : est-il possible de déterminer un potentiel périodique tel que les premières bandes d’énergie de l’opérateur de Schrödinger associé soient aussi proches que possible de certaines fonctions cibles ?Nous montrons théoriquement que la réponse à cette question est positive lorsque l’on considère la première bande de l’opérateur et des potentiels unidimensionnels appartenant à un espace de mesures périodiques bornées inférieurement en un certain sens. Nous proposons également une méthode adaptative pour accélérer la procédure numérique de résolution du problème d’optimisation. Enfin, le chapitre 6 traite d’un algorithme glouton pour la compression de fonctions de Wannier en exploitant leurs symétries. Cette compression permet, entre autres, d’obtenir des expressions analytiques pour certains coefficients de tight-binding intervenant dans la modélisation de matériaux 2DThis thesis includes two independent parts, both motivated by mathematical modeling and numerical simulation of photovoltaic devices. Part I deals with cross-diffusion systems of partial differential equations, modeling the evolution of concentrations or volume fractions of several chemical or biological species. We present in Chapter 1 a succinct introduction to the existing mathematical results about these systems when they are defined on fixed domains. We present in Chapter 2 a one-dimensional system that we introduced to model the evolution of the volume fractions of the different chemical species involved in the physical vapor deposition process (PVD) used in the production of thin film solar cells. In this process, a sample is introduced into a very high temperature oven where the different chemical species are injected in gaseous form, so that atoms are gradually deposited on the sample, forming a growing thin film. In this model, both the evolution of the film surface during the process and the evolution of the local volume fractions within this film are taken into account, resulting in a cross-diffusion system defined on a time dependent domain. Using a recent method based on entropy estimates, we show the existence of weak solutions to this system and study their asymptotic behavior when the external fluxes are assumed to be constant. Moreover, we prove the existence of a solution to an optimization problem set on the external fluxes. We present in Chapter3 how was this model adapted and calibrated on experimental data. Part II is devoted to some issues related to the calculation of the electronic structure of crystalline materials. We recall in Chapter 4 some classical results about the spectral decomposition of periodic Schrödinger operators. In text of Chapter 5, we try to answer the following question: is it possible to determine a periodic potential such that the first energy bands of the associated periodic Schrödinger operator are as close as possible to certain target functions? We theoretically show that the answer to this question is positive when we consider the first energy band of the operator and one-dimensional potentials belonging to a space of periodic measures that are lower bounded in certain ness. We also propose an adaptive method to accelerate the numerical optimization procedure. Finally, Chapter 6 deals with a greedy algorithm for the compression of Wannier functions into Gaussian-polynomial functions exploiting their symmetries. This compression allows, among other things, to obtain closed expressions for certain tight-binding coefficients involved in the modeling of 2D materials
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Voloshina, Elena, Denis Usvyat, Martin Schütz, Yuriy Dedkov, and Beate Paulus. "On the physisorption of water on graphene: a CCSD(T) study." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-138776.
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The electronic structure of the zero-gap two-dimensional graphene has a charge neutrality point exactly at the Fermi level that limits the practical application of this material. There are several ways to modify the Fermi-level-region of graphene, e.g. adsorption of graphene on different substrates or different molecules on its surface. In all cases the so-called dispersion or van der Waals interactions can play a crucial role in the mechanism, which describes the modification of electronic structure of graphene. The adsorption of water on graphene is not very accurately reproduced in the standard density functional theory (DFT) calculations and highly-accurate quantum-chemical treatments are required. A possibility to apply wavefunction-based methods to extended systems is the use of local correlation schemes. The adsorption energies obtained in the present work by means of CCSD(T) are much higher in magnitude than the values calculated with standard DFT functional although they agree that physisorption is observed. The obtained results are compared with the values available in the literature for binding of water on the graphene-like substratesDieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich
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Voloshina, Elena, Denis Usvyat, Martin Schütz, Yuriy Dedkov, and Beate Paulus. "On the physisorption of water on graphene: a CCSD(T) study." Royal Society of Chemistry, 2011. https://tud.qucosa.de/id/qucosa%3A27779.
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The electronic structure of the zero-gap two-dimensional graphene has a charge neutrality point exactly at the Fermi level that limits the practical application of this material. There are several ways to modify the Fermi-level-region of graphene, e.g. adsorption of graphene on different substrates or different molecules on its surface. In all cases the so-called dispersion or van der Waals interactions can play a crucial role in the mechanism, which describes the modification of electronic structure of graphene. The adsorption of water on graphene is not very accurately reproduced in the standard density functional theory (DFT) calculations and highly-accurate quantum-chemical treatments are required. A possibility to apply wavefunction-based methods to extended systems is the use of local correlation schemes. The adsorption energies obtained in the present work by means of CCSD(T) are much higher in magnitude than the values calculated with standard DFT functional although they agree that physisorption is observed. The obtained results are compared with the values available in the literature for binding of water on the graphene-like substrates.Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
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Thorpe, Adam. "High Harmonic Generation in a Kronig-Penney Model Solid." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/41572.
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In 2010 high harmonic generation (HHG) in solids was first observed where high order harmonics of a strong laser field's frequency were observed. HHG in solids is now a rapidly developing field that allows for exciting applications like fully solid state attosecond XUV sources and new ultrafast resolution imaging techniques for quantum dynamics in solids.
HHG in solids has been explained by two mechanisms: an interband mechanism, due to polarization associated with separate energy bands, and an intraband mechanism that results from nonlinearities and population changes associated with each individual band. While interband HHG has been seen in wide bandwidth semiconductors, intraband HHG has been observed in narrow bandwidth dielectrics. There has not yet been an explanation of the alternation of mechanisms with material differences. The main goal of this thesis is to attempt to provide a better understanding of the most important mechanisms and where they prevail. Although numerical modelling of HHG requires consideration of multiple energy bands, a two-band model consisting only of a valence band and a single conduction band can explain the most important mechanisms. This model requires a given material's band gap between its valence and conduction bands as well as dipole matrix elements between the bands. In this thesis we follow the Kronig-Penney model to develop a 1D delta-function potential model of solids to obtain these properties required of the two-band model. We implement this in a Wannier quasi-classical (WQC) model of interband HHG in semiconductors that explains the dominant dynamics leading to such through quasi-classical real space electron-hole pair trajectories. Although HHG in solids can be explained to be the result of a resonant process in which an electron-hole pair is generated in the first step, there are also virtual transition processes that lack consideration. These processes do not conserve energy and correspond to transitions to conduction bands resulting from field induced distortions of the ground state. We use methodology introduced by Keldysh for optical field ionization of atoms and solids along with the 1D delta-function potential model to quantify how both resonant and virtual transitions lead to HHG in solids for wide and low bandwidth solids.
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Gomes, Arianne Vellasco. "Estrutura eletrônica de cristais : generalização mediante o cálculo fracionário /." Universidade Estadual Paulista (UNESP), 2018. http://hdl.handle.net/11449/154280.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Tópicos fundamentais da estrutura eletrônica de materiais cristalinos, são investigados de forma generalizada mediante o Cálculo Fracionário. São calculadas as bandas de energia, as funções de Bloch e as funções de Wannier, para a equação de Schrödinger fracionária com derivada de Riesz. É apresentado um estudo detalhado do caráter não local desse tipo de derivada fracionária. Resolve-se a equação de Schrödinger fracionária para o modelo de Kronig-Penney e estuda-se os efeitos da ordem da derivada e da intensidade do potencial. Verificou-se que, ao passar da derivada de segunda ordem para derivadas fracionárias, o comportamento assintótico das funções de Wannier muda apreciavelmente. Elas perdem o decaimento exponencial, e exibem um decaimento acentuado em forma de potência. Fórmulas simples foram dadas para as caudas das funções de Wannier. A banda de energia mais baixa mostrou-se estar relacionada ao estado ligado de um único poço quântico. Sua função de onda também apresentou decaimento em lei de potência. As bandas de energia superiores mudam de comportamento em função da intensidade do potencial. No caso inteiro, a largura de cada uma dessas bandas diminui. No caso fracionário, diminui inicialmente e depois volta a aumentar, aproximando-se de um valor infinito à medida que a intensidade do potencial tende ao infinito. O grau de localização das funções de Wannier, expresso pelo desvio padrão da posição, mostra um comportamento similar ao da largura das bandas de energia. Além dos cristais perfeitos a Ciência de Materiais estuda cristais com defeito. Os defeitos são responsáveis por muitas propriedades de interesse tecnológico e podem induzir estados localizados. Neste trabalho, calculado o estado localizado de menor energia no modelo de Kronig-Penney fracionário com defeito, mediante método das transformadas de Fourier e das funções de Wannier. Verificou-se que este estado também decai em forma de lei de potência.
Basics topics on the electronic structure of crystalline materials are investigated in a generalized fashion through Fractional Calculus. The energy bands, the Bloch and Wannier functions for the fractional Schr odinger equation with Riesz derivative are calculated. The non-locality of the Riesz fractional derivative is analyzed. The fractional Schr odinger equation is solved for the Kronig-Penney model and the e ects of the derivative order and the potential intensity are studied. It was shown that moving from the integer to the fractional order strongly a ects the asymptotic behavior of the Wannier functions. They lose the exponential decay, gaining a strong power-law decay. Simple formulas have been given for the tails of the Wannier functions. A close relatim between the lowest energy band and the bound state of a single quantum well was found. The wavefunction of the latter decays as a power law. Higher energy bands change their behavior as the periodic potential gets stronger. In the integer case, the width of each one of those bands decreases. In the fractional case, it initially decreases and then increases. The width approaching a nite value as the strength tends to in nity. The degree of localization of the Wannier functions, as expressed by the position standard deviation, behaves similarly to the width of the energy bands. In addition to perfect crystals, Materials Science studies defective crystals. Defects are responsible for many properties of technological interest and can induce localized states. In this work, the localized state of lowest energy in the fractional Kronig-Penney model with defect is calculated through of the Fourier transform method and the Wannier functions. It was shown that is decays as a power law.
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Hermann, Daniel [Verfasser]. "Wannier-function based scattering-matrix formalism for photonic crystal circuitry / von Daniel Hermann." 2008. http://d-nb.info/991925408/34.
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Mack, Patrick [Verfasser]. "2D H-polarized auxiliary basis functions for the extension of the photonic Wannier function expansion for photonic crystal circuitry / von Patrick Mack." 2011. http://d-nb.info/1012674371/34.
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(8082827), Kuang-Chung Wang. "METHOD DEVELOPMENT IN THE NEGF FRAMEWORK: MAXIMALLY LOCALIZED WANNIER FUNCTION AND BÜTTIKER PROBE FOR MULTI-PARTICLE INTERACTION." Thesis, 2019.
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The work involves two new method implementation and application in the Quantum transport community for nano-scale electronic devices.
First method: Ab-initio Tight-Binding(TB)
As the surfacing of novel 2D materials, layers can be stacked freely on top of each other bound by Van der Waals force with atomic precision. New devices created with unique characteristics will need the theoretical guidance. The empirical tight-binding method is known to have difficulty accurately representing Hamiltonian of the 2D materials. Maximally localized Wannier function(MLWF) constructed directly from ab-initio calculation is an efficient and accurate method for basis construction. Together with NEGF, device calculation can be conducted. The implementation of MLWF in NEMO5 and the application on 2D MOS structure to demystify interlayer coupling are addressed.
Second method: Büttiker-probe Recombination/Generation(RG) method:
The non-equilibrium Green function (NEGF) method is capable of nanodevice performance predictions including coherent and incoherent effects. To treat incoherent scattering, carrier generation and recombination is computationally very expensive. In this work, the numerically efficient Büttiker-probe model is expanded to cover recombination and generation effects in addition to various incoherent scattering processes. The capability of the new method to predict nanodevices is exemplified with quantum well III-N light-emitting diodes and photo-detector. Comparison is made with the state of art drift-diffusion method. Agreements are found to justify the method and disagreements are identified attributing to quantum effects.
The two menthod are individually developed and utilized together to study BP/MoS2 interface. In this vertical 2D device, anti-ambipolar(AAP) IV curve has been identified experimentally with different explanation in the current literature. An atomistic simulation is performed with basis generated from density functional theory. Recombination process is included and is able to explain the experiment findings and to provide insights into 2D interface devices.
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Moscolari, Massimo. "On the localization dichotomy for gapped quantum systems." Doctoral thesis, 2019. http://hdl.handle.net/11573/1471195.
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Since their introduction by G. Wannier in 1937, Wannier functions have been extensively used in solid state physics to analyze and understand the physical properties of perfect crystalline quantum systems. In 2016, D. Monaco, G. Panati, A. Pisante and S. Teufel proved a localization dichotomy result for periodic Schrödinger operators, namely that the localization properties of Wannier functions are deeply connected to the topological properties of the quantum system. The original results presented in this thesis concern the possibility of extending such localization dichotomy to generic gapped quantum systems. First of all, by reviewing and analyzing the different few existing results about generalized Wannier functions, we give a precise definition of generalized Wannier functions for generic gapped quantum systems. Moreover, we prove the existence of Parseval frames of exponentially localized generalized Wannier functions for a large class of magnetic systems, as a byproduct we show the existence of a generalized Wannier basis for magnetic Hamiltonians. Furthermore, we analyze the Chern number in position space, namely the Chern character, by proving a gap labelling theorem for Bloch-Landau Hamiltonians using gauge covariant magnetic perturbation theory and investigating the validity of the gap labelling theorem in a non-covariant setting. We also explicitly show how to connect the Chern character to the Středa formula. Finally, we show that an ultra generalized type of Wannier basis is not capable to encode the physical properties of the systems and we prove that the existence of a well-localized localized generalized Wannier basis implies the vanishing of the Chern character.
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Chen, Yu-Chang, and 陳昱璋. "Wannier functions of magnetic atoms in nanojunctions and bulk materials." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/hms6r2.
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碩士國立交通大學
電子物理系所
102
In this thesis, we have applied the maximally localized Wannier function approach[Wannier90] to a density function theory based first principle code[Quantum espresso]. In order to understand the behavior of magnetic atom in different environment, we calculate three different systems which are isolated atom system, CuCoCu nanojunction system and Co doped in Cu bulk system. We found that magnetic properties, PDOS and Maximally localized Wannier functions will be varied depends on the symmetry between the magnetic d orbital and nearest atoms around it. We also found spreads of MLWF will be changed depending on distance between MLWF and nearest atoms around it and spreads also depends on spin if it is a spin polarized case.
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Lin, Wei-Cheng, and 林緯政. "Application of Wannier Functions on the dynamics of strongly bounded excitons." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/91906417603560189269.
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碩士淡江大學
物理學系碩士班
98
A first-principles Wannier-function method is proposed to explore the propagation of the strongly bound Frenkel exciton in Alkali Halides ( LiF, LiCl, LiBr, NaF, NaCl, and NaBr). This study find strongly angular dependence of the excitons by means of a direct product of the Fourier transform of the local particle-hole wave functions. This result can straightforward explain the angular resolved inelastic x-ray scattering experiment. Furthermore, in order to solve response function of strongly interacting system within the linear response scheme more effectively, a new approach is proposed by formulating the “effective two-particle kinetic kernel (T) ” which contains all the mobility information of excitons.
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Marzari, Nicola. "Ballistic Transport in Nanostructures from First-Principles Simulations." 2003. http://hdl.handle.net/1721.1/3655.
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We developed and implemented a first-principles based theory of the Landauer ballistic conductance, to determine the transport properties of nanostructures and molecular-electronics devices. Our approach starts from a quantum-mechanical description of the electronic structure of the system under consideration, performed at the density-functional theory level and using finite-temperature molecular dynamics simulations to obtain an ensemble of the most likely microscopic configurations. The extended Bloch states are then converted into maximally-localized Wannier functions to allow us to construct the Green’s function of the conductor, from which we obtain the density of states (confirming the reliability of our microscopic calculations) and the Landauer conductance. A first application is presented to the case of carbon nanotubes.Singapore-MIT Alliance (SMA)
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Bulovyatova, Tatiana [Verfasser]. "Numerical methods of localization of Wannier functions in modeling of photonic cCrystals / von Tatiana Bulovyatova." 2011. http://d-nb.info/1011236206/34.
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Lee, Young-Su, Marco Buongiorno Nardelli, and Nicola Marzari. "Ballistic Transport in Carbon Nanotubes from First-Principles Molecular Dynamics Simulations." 2003. http://hdl.handle.net/1721.1/3796.
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We determined the Landauer ballistic conductance of pristine nanotubes at finite temperature via a novel scheme that combines ab-initio molecular dynamics, maximally-localized Wannier functions, and a tight-binding formulation of electronic transport in nanostructures. Large-scale ab-initio molecular dynamics simulations are used to obtain efficiently accurate trajectories in phase space. The extended Bloch orbitals for states along these trajectories are converted into maximally-localized orbitals, providing an exact mapping of the ground-state electronic structure onto a short-ranged Hamiltonian. Green's functions, self-energies, and ballistic conductance can then be obtained for any given configuration, and averaged over the appropriate statistical ensemble.Singapore-MIT Alliance (SMA)
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Ziletti, Angelo. "First-principles modelling of materials: from polythiophene to phosphorene." Thesis, 2015. https://hdl.handle.net/2144/14535.
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As a result of the computing power provided by the current technology, computational methods now play an important role in modeling and designing materials at the nanoscale.
The focus of this dissertation is two-fold: first, new computational methods to model nanoscale transport are introduced, then state-of-the-art tools based on density functional theory are employed to explore the properties of phosphorene, a novel low dimensional material with great potential for applications in nanotechnology.
A Wannier function description of the electron density is combined with a generalized Slater-Koster interpolation technique, enabling the introduction of a new computational method for constructing first-principles model Hamiltonians for electron and hole transport that maintain the density functional theory accuracy at a fraction of the computational cost. As a proof of concept, this new approach is applied to model polythiophene, a polymer ubiquitous in organic photovoltaic devices.
A new low dimensional material, phosphorene - a single layer of black phosphorous - the phosphorous analogue of graphene was first isolated in early 2014 and has attracted considerable attention. It is a semiconductor with a sizable band gap, which makes it a perfect candidate for ultrathin transistors. Multi-layer phosphorene transistors have already achieved the highest hole mobility of any two-dimensional material apart from graphene.
Phosphorene is prone to oxidation, which can lead to degradation of electrical properties, and eventually structural breakdown. The calculations reported here are some of the first to explore this oxidation and reveal that different types of oxygen defects are readily introduced in the phosphorene lattice, creating electron traps in some situations. These traps are responsible for the non-ambipolar behavior observed by experimental collaborators in air-exposed few-layer black phosphorus devices.
Calculation results predict that air exposure of phosphorene creates a new family of two-dimensional oxides, which has been later confirmed by X-ray photoemission measurements. These oxides can form protective coatings for phosphorene and have interesting tunable electronic properties.
Finally, Wannier function interpolation has been used to demonstrate that a saddle-point van Hove singularity is present near the phosphorene Fermi energy, as observed in some layered cuprate high temperature superconductors; this leads to an intriguing strain-induced ferromagnetic instability.
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Schillinger, Matthias Hubertus [Verfasser]. "Maximally localized photonic Wannier functions for the highly efficient description of integrated photonic crystal circuits / von Matthias Hubertus Schillinger." 2007. http://d-nb.info/986419222/34.
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Schnell, Ilan [Verfasser]. "Ab-initio Wannier functions, Coulomb matrix elements, Hartree (-Fock) and LSDA calculations for the 3d transition metals Fe, Co, Ni and Cu / von Ilan Schnell." 2002. http://d-nb.info/965575349/34.
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(11203593), Timothy Sean Wolfe. "ELECTRONIC AND OPTICAL PROPERTIES OF FIRST-ROW TRANSITION METALS IN 4H-SIC FOR PHOTOCONDUCTIVE SWITCHING." Thesis, 2021.
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Photoconductive Semiconductor Switches (PCSS) are metal-semiconductor-metal devices used to switch an electrical signal through photoconduction. Rapidly switched PCSS under high bias voltages have shown remarkable potential for high power electronic and electromagnetic wave generation, but are dependent on precise optoelectronic material parameters such as defect ionization energy and optical absorption. These properties can be measured but are difficult to attribute definitively to specific defects and materials without the aid of high-accuracy, predictive modeling and simulation. This work combines well-established methods for first principles electronic structure calculations such as Density Functional Theory (DFT) with novel modern approaches such as Local Moment Counter Charge (LMCC) boundary conditions to adequately describe charge states and Maximally Localized Wannier Functions (MLWF) to render the summation of optical excitation paths as computationally tractable. This approach is demonstrated to overcome previous barriers to obtaining reliable qualitative or quantitative results, such as DFT band gap narrowing and the prohibitive computational cost of coupled electron-phonon processes. This work contributes electronic structure calculations of 4H-SiC doped with first-row transition metals (V through Ni) that are consistent with prior published work where applicable and add new possibilities for prospective semi-insulating metal-semiconductor systems where investigating new dopant possibilities. The results indicate a spectrum of highly localized, mid-gap, spin-dependent defect energy levels which suggest a wider range of potential amphoteric dopants suitable for producing semi-insulating material. Additionally, this work contributes MLWF-based calculations of phonon-resolved optical properties in 3C and 4H-SiC, indirect gap semiconductors, which accurately produce the expected onset of optical absorption informed by experiment. These results were further expanded upon with small V-doped cells of 4H-SiC, which while not fully converged in terms of cell size still provided a qualitative point of comparison to the ground state results for determining the true optical excitation energy required for substantial photoconductivity. The subsequent speculative analysis suggests the importance of anisotropic absorption and alternative metal defects for optimizing high current optoelectronic devices such as PCSS.