Ultrasonic wave transport in strongly scattering, disordered media is investigated via analysis of the multiply-scattered transmitted field. Measurements of transverse confinement, statistics, and correlations of the intensity were performed on an aluminum mesoglass, where aluminum beads were brazed together to form a porous slab sample. Comparison of the transverse confinement measurements with the self-consistent theory of localization was used to identify and locate a mobility edge in the sample at f = 1.1011 MHz, enabling a measurement of the critical exponent nu characterizing the Anderson transition, nu ~ 1.6–2. Infinite-range C0 correlations were observed, and observed to grow dramatically near the mobility edge, along with the C2 and C3 correlations. Measurements of the multifractal exponent Delta_2 were able to confirm the link between C0 correlations and Anderson localization. Experiments using the aluminum mesoglass with ethanol-filled pores showed evidence of two nearly-independent propagating modes, one of which appears to be characterized by a strongly renormalized diffusion coefficient. The density of states and level spacing statistics were investigated using a different mesoglass, constructed by sintering glass beads percolated on a random lattice. Direct measurements of these quantities were obtained by cutting small samples of this mesoglass, allowing individual vibrational modes to be resolved. The density of states showed a plateau extending well into the expected Debye regime, and evidence of a Boson peak was observed at low frequencies. The level spacing statistics indicated that transport in the frequency ranges measured was on the diffusive side of the mobility edge, showing agreement with the predictions of the GOE from random matrix theory. The dynamics of a suspension of bubbles were investigated using phase-based Diffusing Acoustic Wave Spectroscopy, where phase correlations were found to give additional information beyond traditional field- and intensity-based correlation measurements. / October 2015

This work presents a study of the electronic structure of four transition metal oxides (TMOs) using spectroscopic data and a variety of theoretical models. TMOs are a class of materials made from d-block metals in the periodic table, and one or more oxygen atoms. The nature of d-electrons is examined and theoretical models used to treat d-electron systems are tested against experimental data. Background theory of condensed matter physics is outlined. An overview of density functional theory (DFT) as a theoretical model for calculating the electronic structure of materials is presented. A variety of exchange-correlation (XC) functionals used within the DFT framework are outlined and tested for their applicability to the TMO systems in question. X-ray spectroscopy is briefly outlined and used to test the validity of the different XC functionals. All four compounds, AgO, Ag2O, CuO, and Cu2O require a Hubbard U term in the XC functional to most accurately reproduce experimental results. The effects of varying the value of U is examined in depth. The oxygen K-edge X-ray emission spectra (XES) exhibits a“two peak” structure for all compounds; the effect of varying the U value is to change the intensity ratio of the two peaks. The ratio of the two peaks as a function of U shows a linear trend in all compounds. A simple line is fit to the peak ratio vs. U curve. A common line between all compounds would provide an important metric with which to predict the appropriate U value needed in similar materials based on simple experimental data. However, the parameters of the fitted line were not common between the four compounds and any metric derived from this method would be system-dependent and not widely applicable to other systems. There are, however, interesting trends in the data when the U value is varied that provide subjects for future research. A number of fundamental quantities are determined both from experiment and theoretical calculations. Calculated bandgap values are shown to be lower than the experimental values for most functionals tested. This is not unexpected as DFT methods are known to predict much smaller bandgaps than expected. The Heyd-Scuseria-Ernzerhof (HSE) functional used for Ag2O and Cu2O does predict the bandgaps very accurately. The core-hole effect is estimated and proven to be negligible in these systems. Charge transfer and on-site Coulomb repulsion energies, important quantities in the electronic behaviour of TMOs, are determined and compared to previously reported values.

The electronical and structural properties of TlSe-type chain-like crystals are the main topic of this study. A computational method which is Tight Binding method is introduced and used to obtain the electronic band structure of TlSe and TlInSe2 . For both materials the partial and total density of states are calculated. The results are compared with the other theoretical results.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Desde a descoberta do estado quasicristalino por Daniel Shechtman et al. em 1984 e da fabricação por Roberto Merlin et al. de uma superrede artificial de GaAs/ AlAs em 1985 com características da sequência de Fibonacci, um grande número de trabalhos teóricos e experimentais tem relatado uma variedade de propriedades interessantes no comportamento de sistemas aperiódicos. Do ponto de vista teórico, é bem sabido que a cadeia de Fibonacci em uma dimensão se constitui em um protótipo de sucesso para a descrição do estado quasicristalino de um sólido. Dependendo da regra de inflação, diferentes tipos de estruturas aperiódicas podem ser obtidas. Esta diversidade originou as chamadas regras metálicas e devido à possibilidade de tratamento analítico rigoroso este modelo tem sido amplamente estudado. Neste trabalho, propriedades de localização em uma dimensão são analisadas considerando-se um conjunto de regras metálicas e o modelo de ligações fortes de banda única. Considerando-se o Hamiltoniano de ligações fortes com um orbital por sítio obtemos um conjunto de transformações relativas aos parâmetros de dizimação, o que nos permitiu calcular as densidades de estados (DOS) para todas as configurações estudadas. O estudo detalhado da densidade de estados integrada (IDOS) para estes casos, mostra o surgimento de plateaux na curva do número de ocupação explicitando o aparecimento da chamada escada do diabo" e também o caráter fractal destas estruturas. Estudando o comportamento da variação da energia em função da variação da energia de hopping, construímos padrões do tipo borboletas de Hofstadter, que simulam o efeito de um campo magnético atuando sobre o sistema. A natureza eletrônica dos auto estados é analisada a partir do expoente de Lyapunov (γ), que está relacionado com a evolução da função de onda eletrônica ao longo da cadeia unidimensional. O expoente de Lyapunov está relacionado com o inverso do comprimento de localização (ξ= 1 /γ), sendo nulo para os estados estendidos e positivo para estados localizados. Isto define claramente as posições dos principais gaps de energia do sistema. Desta forma, foi possível analisar o comportamento autossimilar de cadeias com diferentes regras de formação. Analisando-se o espectro de energia em função do número de geração de cadeias que seguem as regras de ouro e prata foi feito, obtemos conjuntos do tipo-Cantor, que nos permitiu estudar o perfil do calor específico de uma cadeia e Fibonacci unidimensional para diversas gerações / Since the discovery of a quasicrystalline state by Daniel Shechtman et al. in 1984 and the growth of artificial GaAs/AlAs superlattices on nonperiodic Fibonacci sequence by Roberto Merlin et al., a number of theoretical and experimental works have reported a variety of interesting physical properties of aperiodic systems. Theoretically, it is well known that in one dimension, the Fibonacci chain is a successful prototype to describe a quasicrystalline state. Depending on the in ation rule, different kinds of aperiodic structures can be obtained. This diversity originates the called metallic means, and due to the possibility of analytical and rigorous mathematical treatments the Fibonacci model has been applied by several authors. In this work, electronic localization properties are studied, taking into account a set of metallic means in one dimension. Considering a single band tight-binding Hamiltonian, a set of decimation transformations is obtained allowing the calculation of the Density of States (DOS) for all configurations. The detailed study of the Integrated Density of States (IDOS), shows the appearance of plateaux in the occupation number curve exhibiting the so-called "devil's staircase"indicating the fractal nature of the structures. Studying the behavior of the energy as a function of the hopping we derive Hofstadter butter y type patters, which simulate the effect of a magnetic field acting on the system. The electronic nature of the eigenstate is analyzed by looking at the Lyapunov exponent which is related to the evolution of the electronic wave unction along the one dimensional chain. Since it is zero for an extended state and positive for a localized one, defining the main gaps positions, it is related to the inverse of the localization length. Through a careful analysis of the Lyapunov curves it was also possible to obtain the perfect self-similarity structures for all chains. In particular,for the chains that follow the golden and silver rules, the study of the energy behavior was done by analyzing the energy spectrum as a function of the generation number of each one of the chains. The results yield Cantor-like sets, which allowed us to calculate the specific heat profile for several generations of the one-dimensional Fibonacci chain.

Orientador: Prof. Dr Gustavo Michel Mendoza La Torre / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2014. / Classical billiards are versatile models for detecting efects of the billiard table over dynamical properties of Hamiltonian systems. Similarly, quantum billiards are ultra-small versions of the same table but now their properties are re ected on eigenvalues of the stationary Schrodinger equation for certain boundary conditions. Integrable and chaotic signatures must distinguish systems at any scale in order to ensure quantum-classical correspondence in the limit ~ ! 0. We demonstrate the classical properties that characterize system dynamics. Also, two intermediate cases are added to debate - mixed and pseudointegrable - for the understanding of possible transitions between dierent dynamics. To do so, the role of action-angle variables in Hamiltonian maps must be discussed. In the quantum context, we seek for ngerprints of classical properties through a systematic study on Local Density of States (LDOS) generated by Green's function numerical methods applied to a lattice representing a Tight-Binding Hamiltonian. We analyze scatisticically the distributions of LDOS from ground state to suciently high levels of energy, trying to identify new characteristics of these systems. This study aims to stimulate experimental measures on LDOS capable to map these signatures through an AFM tip (Atomic Force Microscopy).

The purpose of this master thesis is to investigate theoretically the influence of a nanomagnet on the Josephson effect displayed by phase biased point contacts consisting of topological superconductors. The device is modeled using the nonequilibrium Keldysh Green’s function technique. First, the Gor’kov Green’s functions are calculated. From these Green’s functions, the quasi-classical ones, relevant for energies around the Fermi energy, are obtained. Transport properties such as charge currents are calculated and analyzed in terms of the junction’s density of states displaying Andreev and Majorana states. The combination of the nanomagnet coupling and the spin-momentum locking of the topological superconductors generates a magneto-electric effect causing the supercurrent to depend strongly on the nanomagnet’s direction.

Submitted by YURI POLICEI MARQUES null (yurimarques111@gmail.com) on 2016-03-16T13:32:59Z No. of bitstreams: 1 Thesis_Yuri.pdf: 5717547 bytes, checksum: 01fcb3125bd18e6cdbca67bc795b6088 (MD5) / Approved for entry into archive by Sandra Manzano de Almeida (smanzano@marilia.unesp.br) on 2016-03-16T18:19:59Z (GMT) No. of bitstreams: 1 marques_yp_me_ilha.pdf: 5717547 bytes, checksum: 01fcb3125bd18e6cdbca67bc795b6088 (MD5) / Made available in DSpace on 2016-03-16T18:19:59Z (GMT). No. of bitstreams: 1 marques_yp_me_ilha.pdf: 5717547 bytes, checksum: 01fcb3125bd18e6cdbca67bc795b6088 (MD5) Previous issue date: 2016-02-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Exploramos teoricamente a emergência de estados ligados no contínuo (BICs: bound states in the continuum) em um sistema formado por duas impurezas situadas em lados opostos da folha de grafeno e colineares com o centro da célula hexagonal, onde ambas impurezas estão acopladas aos seis carbonos desta mesma célula, ou ainda acopladas a apenas um átomo fantasma, localizado no centro da célula, que simula os seis carbonos. Verificamos que nesta configuração a densidade local de estados, perto dos pontos de Dirac, exibe aspectos característicos: i) uma densidade de estados com dependência cúbica na energia em vez da dependência linear do grafeno puro, assim como encontrado no New J. Phys. 16, 013045 (2014) e ii) a formação de BICs como consequência de uma interferência Fano destrutiva assistida por uma correlação de Coulomb nas impurezas. Para a geometria em que as impurezas estão colineares com um átomo de carbono, observamos ausência de BICs. / We explore theoretically the formation of bound states in the continuum (BICs) in graphene hosting two collinear adatoms situated at different sides of the sheet and at the center of the hexagonal cell, where a phantom atom of a fictitious lattice emulates the six carbons of the cell. We verify that in this configuration the local density of states (LDOS) near the Dirac points exhibits two characteristic features: i) the cubic dependence on energy instead of the linear one for graphene as found in New J. Phys. 16, 013045 (2014) and ii) formation of BICs as aftermath of a Fano destructive interference assisted by the Coulomb correlations in the adatoms. For the geometry where adatoms are collinear to carbon atoms, we report absence of BICs.

Orientador: Antonio Carlos Ferreira Seridonio / Resumo: Exploramos teoricamente a emergência de estados ligados no contínuo (BICs: bound states in the continuum) em um sistema formado por duas impurezas situadas em lados opostos da folha de grafeno e colineares com o centro da célula hexagonal, onde ambas impurezas estão acopladas aos seis carbonos desta mesma célula, ou ainda acopladas a apenas um átomo fantasma, localizado no centro da célula, que simula os seis carbonos. Verificamos que nesta configuração a densidade local de estados, perto dos pontos de Dirac, exibe aspectos característicos: i) uma densidade de estados com dependência cúbica na energia em vez da dependência linear do grafeno puro, assim como encontrado no New J. Phys. 16, 013045 (2014) e ii) a formação de BICs como consequência de uma interferência Fano destrutiva assistida por uma correlação de Coulomb nas impurezas. Para a geometria em que as impurezas estão colineares com um átomo de carbono, observamos ausência de BICs. / Abstract: We explore theoretically the formation of bound states in the continuum (BICs) in graphene hosting two collinear adatoms situated at different sides of the sheet and at the center of the hexagonal cell, where a phantom atom of a fictitious lattice emulates the six carbons of the cell. We verify that in this configuration the local density of states(LDOS) near the Dirac points exhibits two characteristic features: i) the cubic dependence on energy instead of the linear one for graphene as found in New J. Phys. 16, 013045 (2014) and ii) formation of BICs as aftermath of a Fano destructive interference assisted by the Coulomb correlations in the adatoms. For the geometry where adatoms are collinear to carbon atoms, we report absence of BICs. / Mestre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Desde a descoberta do estado quasicristalino por Daniel Shechtman et al. em 1984 e da fabricação por Roberto Merlin et al. de uma superrede artificial de GaAs/ AlAs em 1985 com características da sequência de Fibonacci, um grande número de trabalhos teóricos e experimentais tem relatado uma variedade de propriedades interessantes no comportamento de sistemas aperiódicos. Do ponto de vista teórico, é bem sabido que a cadeia de Fibonacci em uma dimensão se constitui em um protótipo de sucesso para a descrição do estado quasicristalino de um sólido. Dependendo da regra de inflação, diferentes tipos de estruturas aperiódicas podem ser obtidas. Esta diversidade originou as chamadas regras metálicas e devido à possibilidade de tratamento analítico rigoroso este modelo tem sido amplamente estudado. Neste trabalho, propriedades de localização em uma dimensão são analisadas considerando-se um conjunto de regras metálicas e o modelo de ligações fortes de banda única. Considerando-se o Hamiltoniano de ligações fortes com um orbital por sítio obtemos um conjunto de transformações relativas aos parâmetros de dizimação, o que nos permitiu calcular as densidades de estados (DOS) para todas as configurações estudadas. O estudo detalhado da densidade de estados integrada (IDOS) para estes casos, mostra o surgimento de plateaux na curva do número de ocupação explicitando o aparecimento da chamada escada do diabo" e também o caráter fractal destas estruturas. Estudando o comportamento da variação da energia em função da variação da energia de hopping, construímos padrões do tipo borboletas de Hofstadter, que simulam o efeito de um campo magnético atuando sobre o sistema. A natureza eletrônica dos auto estados é analisada a partir do expoente de Lyapunov (γ), que está relacionado com a evolução da função de onda eletrônica ao longo da cadeia unidimensional. O expoente de Lyapunov está relacionado com o inverso do comprimento de localização (ξ= 1 /γ), sendo nulo para os estados estendidos e positivo para estados localizados. Isto define claramente as posições dos principais gaps de energia do sistema. Desta forma, foi possível analisar o comportamento autossimilar de cadeias com diferentes regras de formação. Analisando-se o espectro de energia em função do número de geração de cadeias que seguem as regras de ouro e prata foi feito, obtemos conjuntos do tipo-Cantor, que nos permitiu estudar o perfil do calor específico de uma cadeia e Fibonacci unidimensional para diversas gerações / Since the discovery of a quasicrystalline state by Daniel Shechtman et al. in 1984 and the growth of artificial GaAs/AlAs superlattices on nonperiodic Fibonacci sequence by Roberto Merlin et al., a number of theoretical and experimental works have reported a variety of interesting physical properties of aperiodic systems. Theoretically, it is well known that in one dimension, the Fibonacci chain is a successful prototype to describe a quasicrystalline state. Depending on the in ation rule, different kinds of aperiodic structures can be obtained. This diversity originates the called metallic means, and due to the possibility of analytical and rigorous mathematical treatments the Fibonacci model has been applied by several authors. In this work, electronic localization properties are studied, taking into account a set of metallic means in one dimension. Considering a single band tight-binding Hamiltonian, a set of decimation transformations is obtained allowing the calculation of the Density of States (DOS) for all configurations. The detailed study of the Integrated Density of States (IDOS), shows the appearance of plateaux in the occupation number curve exhibiting the so-called "devil's staircase"indicating the fractal nature of the structures. Studying the behavior of the energy as a function of the hopping we derive Hofstadter butter y type patters, which simulate the effect of a magnetic field acting on the system. The electronic nature of the eigenstate is analyzed by looking at the Lyapunov exponent which is related to the evolution of the electronic wave unction along the one dimensional chain. Since it is zero for an extended state and positive for a localized one, defining the main gaps positions, it is related to the inverse of the localization length. Through a careful analysis of the Lyapunov curves it was also possible to obtain the perfect self-similarity structures for all chains. In particular,for the chains that follow the golden and silver rules, the study of the energy behavior was done by analyzing the energy spectrum as a function of the generation number of each one of the chains. The results yield Cantor-like sets, which allowed us to calculate the specific heat profile for several generations of the one-dimensional Fibonacci chain.

The first part of this work gives an introduction into aperiodic order in general and the lines of research pursued. The second part consists of eight manuscripts.