No description available.

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.

Made available in DSpace on 2014-06-11T19:23:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-12-18Bitstream added on 2014-06-13T19:50:17Z : No. of bitstreams: 1 nacbar_dr_me_bauru.pdf: 1169690 bytes, checksum: c7a661675601c87b8e63ac301a1c144c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / 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.

No description available.

Le champ électromagnétique térahertz (THz) se situe dans l'intervalle de fréquence entre l'infrarouge et les micro-ondes, à peu près entre 1 THz à 10 THz. Ce domaine est hautement souhaitable tant pour la recherche fondamentale que pour les applications. Pourtant des sources THz compacts et accordables ne sont pas encore disponibles. Depuis la première proposition en 1970, les superréseaux semiconducteurs, dans lequel deux couches semi-conductrices atomiques avec bande interdite différente sont disposés périodiquement, fournissent de nouvelles possibilités. De nouvelles techniques et de nouveaux dispositifs deviennent réalisables. Dans cette thèse, les oscillations de Bloch dans des mini-bandes électroniques d’un superréseau polarise et la dispersion du gain associée sont utilisées pour réaliser une source THz compacte et accordable : l’oscillateur de Bloch THz. Un premier ensemble de dispositifs utilisent des réseaux dopes spécifiquement conçus pour éviter la formation de domaine d’accumulation de charges. Ces dispositifs utilisent une surface semi-isolante ou deux surfaces métalliques permettant un guidage par plasmon de surface. Cependant, malgré la réalisation de couplage par les bords ou par un réseau diffractant en surface et des mesures directes ou avec un interféromètre a transformation de Fourrier (FTIR), l’électroluminescence a été observée dans le domaine térahertz, avec un gain qui n’a pas pu etre relie aux oscillations de Bloch. Avec des superréseaux non dope, l'émission THz des oscillations de Bloch a été détectée par spectroscopie dans le domaine temporel. La dépendance de la fréquence d’émission avec le champ électrique appliqué constitue une preuve directe des oscillations de Bloch. L’échelle de Wannier Stark des trous sous pompage optique continu a aussi été observe dans les superréseaux non dopes. Avec l’augmentation de la puissance de pompage optique, les pics du photocourant se décalent et leurs formes deviennent asymétriques. L’évolution est attribue a l’accumulation des porteurs photogénérés dans les deux couches encadrant le superréseau. En outre, pour une puissance de pompage élevée, la bistabilité du photocourant a été également observée. / Terahertz (THz) electromagnetic field, which lies in the frequency gap between the infrared and microwave, roughly between 1 THz to 10 THz, is highly desirable for both fundamental research and application. Yet tuneable compact THz sources are still not available. On the other hand, ever since first proposed in 1970, semiconductor superlattice provides new playground for various new technique and devices of tremendous research and application interest. In this thesis, an innovative theme, relying on Bloch oscillations in a dc biased semiconductor superlattice, is explored to realize tunable compact THz source THz Bloch oscillator. For doped superlattice Bloch oscillator, we designed quantum cascade super-superlattice structure to realize Bloch oscillations whilst prohibit electrical domain formation. The designed structures were processed into various waveguide and grating devices for electroluminescence detection using Fourier transform infrared spectroscopy (FTIR). The Bloch gain of semi-insulating surface plasmon waveguide device was also measured using THz time domain spectroscopy. Even though the electroluminescence and gain at THz regime were observed, no direct evidence of Bloch emission was confirmed. For undoped superlattice, the THz emission from Bloch oscillations was observed by time domain spectroscopy. At last, the photocurrent corresponding to heavy hole and Wannier Stark Ladder (WSL) states transitions in undoped superlattice was studied. Under CW laser pumping, the photocurrent as function of the applied voltage showed multiple WSL peaks, which indicated laser induced and controllable negative differential conductance (NDC). With increasing pumping power, the nonlinear NDC regime and bistable states were investigated as well.

Orientador: Alexys Bruno Alfonso / Banca: 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

Submitted by Allan Victor Ribeiro null (allan_vr@fc.unesp.br) on 2017-07-12T19:01:29Z No. of bitstreams: 1 Tese - Allan Victor Ribeiro - Posmat.pdf: 17273743 bytes, checksum: 654df5020a2a453977468f1145d42794 (MD5) / Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-07-14T17:31:10Z (GMT) No. of bitstreams: 1 ribeiro_av_dr_bauru.pdf: 17273743 bytes, checksum: 654df5020a2a453977468f1145d42794 (MD5) / Made available in DSpace on 2017-07-14T17:31:10Z (GMT). No. of bitstreams: 1 ribeiro_av_dr_bauru.pdf: 17273743 bytes, checksum: 654df5020a2a453977468f1145d42794 (MD5) Previous issue date: 2017-04-28 / 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.

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)

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)

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 2D / This 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