Orientador: Alexys Bruno Alfonso / Banca: Jeverson Teodoro Arantes Junior / Banca: Augusto Batagin Neto / Resumo: 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 dens... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: 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 ... (Complete abstract click electronic access below) / Doutor

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We report here the results of a de Haas-van Alphen (dHvA) investigation of the coupled orbit system in magnesium. The data were taken for magnetic fields extending to 52 kG and temperatures down to 0.29° K. The experimental data are interpreted in the light of coupled orbit system theories of Pippard and of Falicov and Stachowiak; these are each reviewed in some detail. The data are found to disagree qualitatively with the predictions of Falicov and Stachowiak. Since this theory has been assumed, for more than a decade, to be equivalent to Pippard's theory, a detailed comparison of these was made. Full spectrum Fourier analysis of Pippard's band structure density of states shows that the two models disagree qualitatively and, therefore, that they are not equivalent. These experimental results, which do not appear to disagree with Pippard's theory, are interpreted to mean that it is fnally possible to obtain crystals of sufficient purity and perfection to make it necessary to use a band structure description of the delocalized electrons on the couple network. Evidence is presented for the existence of a new type of dHvA frequency corresponding to the ΓKM plane cross-section of the Brillouin zone. A proposed explanation for this dHvA frequency involves the field dependent modulation of the zero frequency component of the Fourier transform of the coupled orbit system density of states. Also included are discussions of crystal preparation and handling, cryogenic apparatus, analogue detection apparatus, digital data acquisition and processing hardware based on a microcomputer, and a new software system ideally suited to small computer research environments.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1973. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1974. / Transcript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.