In den letzten Jahren führte die Verbindung zwischen Topologie und kondensierter Materie zur Entdeckung vieler interessanter und exotischer elektronischer Effekte. Während sich die Forschung anfangs auf elektronische Systeme mit einer Bandlücke wie den topologischen Isolator konzentrierte, erhalten in letzter Zeit topologische Halbmetalle viel Aufmerksamkeit. Das bekannteste Beispiel sind Weyl-Halbmetalle, die an beliebigen Punkten in der Brillouin-Zone lineare Kreuzungen von nicht entarteten Bändern aufweist. An diese Punkte ist eine spezielle Quantenzahl namens Chiralität gebunden, die die Existenz von Weyl-Punktpaaren erzwingt. Diese Paare sind topologisch geschützt und wirken als Quellen und Senken der Berry-Krümmung, einem topologischen Feld im reziproken Raum. Diese Berry-Krümmung steht in direktem Zusammenhang mit dem anomalen Hall-Effekt, der die Entstehung einer Querspannung aus einem Längsstrom in einem magnetischen Material beschreibt. Analog existiert auch der anomale Nernst-Effekt, bei dem der longitudinale Strom durch einen thermischen Gradienten ersetzt wird. Dieser Effekt ermöglicht die Umwandlung von Wärme in elektrische Energie und ist zudem stark an die Berry-Krümmung gebunden. In dieser Arbeit werden die anomalen Transporteffekte zunächst in fundamentalen Modellsystemen untersucht. Hier wird eine Kombination aus analytischen und numerischen Methoden verwendet, um Quantisierungen sowohl des Hall- und Nernst- als auch des thermischen Hall-Effekts in zweidimensionalen Systemen mit und ohne externen Magnetfeldern zu zeigen. Eine Erweiterung in drei Dimensionen zeigt eine Quasi-Quantisierung, bei der die Leitfähigkeiten Werte der jeweiligen zweidimensionalen Quanten skaliert durch charakteristische Wellenvektoren annehmen. Im nächsten Schritt werden verschiedene Mechanismen zur Erzeugung starker Berry-Krümmung und damit großer anomaler Hall- und Nernst-Effekte sowohl in Modellsystemen als auch in realen Materialien untersucht. Dies ermöglicht die Identifizierung und Isolierung vielversprechender Effekte in den einfachen Modellen, in denen wichtige Merkmale untersucht werden können. Die Ergebnisse können dann auf die realen Materialien übertragen werden, wo die jeweiligen Effekte erkennbar sind. Hier werden sowohl Weyl-Punkte als auch Knotenlinien in Kombination mit Magnetismus als vielversprechende Eigenschaften identifiziert und Materialrealisierungen in der Klasse der Heusler-Verbindungen vorgeschlagen. Diese Verbindungen sind eine sehr vielseitige Materialklasse, in der unter anderem auch magnetische topologische Metalle zu finden sind. Um ein tieferes Verständnis der anomalen Transporteffekte zu erhalten sowie Faustregeln für Hochleistungsverbindungen abzuleiten, wurde eine High-Throughput-Rechnung von magnetisch-kubischen Voll-Heusler-Verbindungen durchgeführt. Diese Berechnung zeigt die Bedeutung von Spiegelebenen in magnetischen Materialien für große anomale Hall- und Nernst-Effekte und zeigt, dass einige der Heusler-Verbindungen die höchsten bisher berichteten Literaturwerte bei diesen Effekten übertreffen. Auch andere interessante Effekte im Zusammenhang mit Weyl-Punkten werden untersucht. Beim bekannten Weyl-Halbmetall NbP weisen die Weyl-Punkte aufgrund der hohen Symmetrie des Kristalls eine hohe Entartung auf. Die Anwendung von einachsigem Zug reduziert jedoch die Symmetrien und hebt damit die Entartungen auf. Eine theoretische Untersuchung zeigt, dass die Weyl-Punkte bei einachsigem Zug energetisch verschoben werden und, was noch wichtiger ist, dass sie bei realistischen Werten das Fermi-Niveau durchschreiten. Dies macht NbP zu einer vielversprechenden Plattform, um die Weyl-Physik weiter zu untersuchen. Die theoretischen Ergebnisse werden mit experimentellen Messungen von Shubnikov-de-Haas-Oszillationen unter einachsigem Zug kombiniert und es wird eine gute Übereinstimmung mit den theoretischen Ergebnissen gefunden. Als erster Schritt in Richtung neuer Berechnungsmethoden wird die Idee eines Weyl-Halbmetall-basierten Chiralitätsfilters für Elektronen untersucht. An der Grenzfläche zweier Weyl-Halbmetalle kann in Abhängigkeit von den genauen Weyl-Punktparametern nur eine Chiralität übertragen werden. Hier wird ein effektives geometrisches Modell erstellt und zur Untersuchung realer Materialgrenzflächen eingesetzt. Während im Allgemeinen eine Filterwirkung möglich erscheint, zeigten die untersuchten Materialien keine geeignete Kombination. Hier können weitere Studien mit Fokus auf magnetische Weyl-Halbmetalle oder Multifold-Fermion-Materialien durchgeführt werden.:List of publications Preface 1. Theoretical background 1.1. Berry curvature and Weyl semimetals 1.1.1. From the adiabatic evolution to the Berry phase 1.1.2. From the Berry phase to the Berry curvature 1.1.3. Topological phases of condensed matter 1.1.4. Weyl semimetals 1.1.5. Dirac semimetals 1.1.6. Nodal line semimetals 1.2. Density-functional theory 1.2.1. Born-Oppenheimer approximation 1.2.2. Hohenberg-Kohn theorems 1.2.3. Kohn-Sham formalism 1.2.4. Exchange-correlation functional 1.2.5. Pseudopotentials 1.2.6. Basis functions 1.2.7. VASP 1.3. Tight-binding Hamiltonian from Wannier functions 1.3.1. Wannier functions 1.3.2. Constructing Wannier functions from DFT 1.3.3. Generating a Wannier tight-binding Hamiltonian 1.3.4. Necessity of the tight-binding Hamiltonian 1.4. Linear response theory 1.4.1. General introduction to linear response 1.4.2. Anomalous Hall effect 1.4.3. Anomalous Nernst effect 1.4.4. Anomalous thermal Hall effect 1.4.5. Common features of anomalous transport effects 1.4.6. Symmetry considerations for Berry curvature related transport effects 1.4.7. Magneto-optic Kerr effect 1.4.8. About the efficiency of the calculations 2. (Quasi-)Quantization in the Hall, thermal Hall, and Nernst effects 2.1. Quantization with an external magnetic field 2.1.1. Two-dimensional case 2.1.2. Three-dimensional case 2.2. Quantization without an external field 2.2.1. Two-dimensional case 2.2.2. Three-dimensional case . 2.3. A remark on the spin Hall effect 2.4. A remark on the quasi-quantization of the three-dimensional conductivities 2.5. Conclusions 3. Understanding anomalous transport 3.1. Anomalous transport without a net magnetic moment 3.1.1. Toy model 3.1.2. Ti2MnAl and related compounds 3.2. Large Berry curvature enhancement from nodal line gapping 3.2.1. Toy model 3.2.2. Fe2MnP and related compounds 3.2.3. Co2MnGa 3.3. Topological features away from the Fermi level and the anomalous Nernst effect 3.3.1. Toy model . 3.3.2. Co2FeGe and Co2FeSn 3.4. Conclusions 4. Heusler database calculation 4.1. Workflow 4.2. Importance of mirror planes 4.3. The right valence electron count 4.4. Correlation between anomalous Hall and Nernst effects 4.5. Selected special compounds 4.6. Conclusions 5. NbP under uniaxial strain 5.1. NbP and its symmetries 5.2. The influence of strain on the electronic structure 5.2.1. Shifting of the Weyl points 5.2.2. Splitting of the Fermi surfaces 5.3. Comparison with experimental results 5.4. Conclusions 6. A tunable chirality filter 6.1. Concept 6.2. Geometrical simplification and expansion for more Weyl points 6.3. Material selection 6.3.1. Workflow 6.3.2. Results for NbP and TaAs 6.3.3. Results for Ag2Se and Ag2S 6.4. Conclusions and perspective . Summary and outlook A. Numerical tricks A.1. Hamiltonian setup at several k points at once A.2. Precalculating prefactors B. Derivation of the conductivity (quasi-)quanta B.1. Two dimensions B.1.1. General formula and necessary approximations B.1.2. Useful integrals B.1.4. Quantized thermal Hall effect B.1.5. Quantized Nernst effect B.1.6. Flat bands and the Nernst effect B.2. Three dimensions B.2.1. General formula B.2.2. Three-dimensional electron gas B.2.3. Three-dimensional Weyl semimetal C. Heusler database tables D. Details on the NbP strain calculations E. Details on the geometrical matching procedure References List of abbreviations List of Figures List of Tables Acknowledgements Eigenständigkeitserklärung / In recent years, the connection between topology and condensed matter resulted in the discovery of many interesting and exotic electronic effects. While in the beginning, the research was focused on gapped electronic systems like the topological insulator, more recently, topological semimetals are getting a lot of attention. The most well-known example is the Weyl semimetal, which hosts linear crossings of non-degenerate bands at arbitrary points in the Brillouin zone. Tied to these points there is a special quantum number called chirality, which enforces the existence of Weyl point pairs. These pairs are topologically protected and act as sources and sinks of the Berry curvature, a topological field in reciprocal space. This Berry curvature is directly connected to the anomalous Hall effect, which describes the emergence of a transverse voltage from a longitudinal current in a magnetic material. Analogously, there also exists the anomalous Nernst effect, where the longitudinal current is replaced by a thermal gradient. This effect allows for the conversion of heat into electrical energy and is also strongly tied to the Berry curvature. In this work, the anomalous transport effects are at first studied in fundamental model systems. Here, a combination of analytical and numerical methods is used to reveal quantizations in both the Hall, the Nernst, and the thermal Hall effects in two-dimensional systems with and without external magnetic fields. An expansion into three dimensions shows a quasi-quantization, where the conductivities take values of the respective two-dimensional quanta scaled by characteristic wavevectors. In the next step, several mechanisms for the generation of strong Berry curvature and thus large anomalous Hall and Nernst effects are studied in both model systems and real materials. This allows for the identification and isolation of promising effects in the simple models, where important features can be studied. The results can then be applied to the real materials, where the respective effects can be recognized. Here, both Weyl points and nodal lines in combination with magnetism are identified as promising features and material realizations are proposed in the class of Heusler compounds. These compounds are a very versatile class of materials, where among others also magnetic topological metals can be found. To get a deeper understanding of the anomalous transport effects as well as to derive guidelines for high-performance compounds, a high-throughput calculation of magnetic cubic full Heusler compounds was carried out. This calculation reveals the importance of mirror planes in magnetic materials for large anomalous Hall and Nernst effects and shows that some of the Heusler compounds outperform the highest so-far reported literature values in these effects. Also other interesting effects related to Weyl points are investigated. In the well-known Weyl semimetal NbP, the Weyl points have a high degeneracy due to the high symmetry of the crystal. However, the application of uniaxial strain reduces the symmetries and therefore lifts the degeneracies. A theoretical investigation shows, that the Weyl points are moved in energy under uniaxial strain and, more importantly, that at reasonable strain values they cross the Fermi level. This renders NbP a promising platform to further study Weyl physics. The theoretical results are combined with experimental measurements of Shubnikov-de Haas oscillations under uniaxial strain and a good agreement with the theoretical results is found. As a first step in the direction of new ways of computation, an idea of a Weyl semimetal based chirality filter for electrons is investigated. At the interface of two Weyl semimetals, depending on the exact Weyl point parameters, it is possible to transmit only one chirality. Here, an effective geometrical model is established and employed for the investigation of real material interfaces. While in general, a filtering effect seems possible, the investigated materials did not show any suitable combination. Here, further studies can be made with the focus on either magnetic Weyl semimetals of multifold-fermion materials.:List of publications Preface 1. Theoretical background 1.1. Berry curvature and Weyl semimetals 1.1.1. From the adiabatic evolution to the Berry phase 1.1.2. From the Berry phase to the Berry curvature 1.1.3. Topological phases of condensed matter 1.1.4. Weyl semimetals 1.1.5. Dirac semimetals 1.1.6. Nodal line semimetals 1.2. Density-functional theory 1.2.1. Born-Oppenheimer approximation 1.2.2. Hohenberg-Kohn theorems 1.2.3. Kohn-Sham formalism 1.2.4. Exchange-correlation functional 1.2.5. Pseudopotentials 1.2.6. Basis functions 1.2.7. VASP 1.3. Tight-binding Hamiltonian from Wannier functions 1.3.1. Wannier functions 1.3.2. Constructing Wannier functions from DFT 1.3.3. Generating a Wannier tight-binding Hamiltonian 1.3.4. Necessity of the tight-binding Hamiltonian 1.4. Linear response theory 1.4.1. General introduction to linear response 1.4.2. Anomalous Hall effect 1.4.3. Anomalous Nernst effect 1.4.4. Anomalous thermal Hall effect 1.4.5. Common features of anomalous transport effects 1.4.6. Symmetry considerations for Berry curvature related transport effects 1.4.7. Magneto-optic Kerr effect 1.4.8. About the efficiency of the calculations 2. (Quasi-)Quantization in the Hall, thermal Hall, and Nernst effects 2.1. Quantization with an external magnetic field 2.1.1. Two-dimensional case 2.1.2. Three-dimensional case 2.2. Quantization without an external field 2.2.1. Two-dimensional case 2.2.2. Three-dimensional case . 2.3. A remark on the spin Hall effect 2.4. A remark on the quasi-quantization of the three-dimensional conductivities 2.5. Conclusions 3. Understanding anomalous transport 3.1. Anomalous transport without a net magnetic moment 3.1.1. Toy model 3.1.2. Ti2MnAl and related compounds 3.2. Large Berry curvature enhancement from nodal line gapping 3.2.1. Toy model 3.2.2. Fe2MnP and related compounds 3.2.3. Co2MnGa 3.3. Topological features away from the Fermi level and the anomalous Nernst effect 3.3.1. Toy model . 3.3.2. Co2FeGe and Co2FeSn 3.4. Conclusions 4. Heusler database calculation 4.1. Workflow 4.2. Importance of mirror planes 4.3. The right valence electron count 4.4. Correlation between anomalous Hall and Nernst effects 4.5. Selected special compounds 4.6. Conclusions 5. NbP under uniaxial strain 5.1. NbP and its symmetries 5.2. The influence of strain on the electronic structure 5.2.1. Shifting of the Weyl points 5.2.2. Splitting of the Fermi surfaces 5.3. Comparison with experimental results 5.4. Conclusions 6. A tunable chirality filter 6.1. Concept 6.2. Geometrical simplification and expansion for more Weyl points 6.3. Material selection 6.3.1. Workflow 6.3.2. Results for NbP and TaAs 6.3.3. Results for Ag2Se and Ag2S 6.4. Conclusions and perspective . Summary and outlook A. Numerical tricks A.1. Hamiltonian setup at several k points at once A.2. Precalculating prefactors B. Derivation of the conductivity (quasi-)quanta B.1. Two dimensions B.1.1. General formula and necessary approximations B.1.2. Useful integrals B.1.4. Quantized thermal Hall effect B.1.5. Quantized Nernst effect B.1.6. Flat bands and the Nernst effect B.2. Three dimensions B.2.1. General formula B.2.2. Three-dimensional electron gas B.2.3. Three-dimensional Weyl semimetal C. Heusler database tables D. Details on the NbP strain calculations E. Details on the geometrical matching procedure References List of abbreviations List of Figures List of Tables Acknowledgements Eigenständigkeitserklärung

A Ilha da Trindade está localizada a aproximadamente 1150 km da costa de Vitória-ES, é uma das ilhas oceânicas brasileiras e está sob o domínio da Marinha do Brasil. Desde o início de sua ocupação sofreu algumas influências antrópicas, como a derrubada de árvores e a introdução de animais (porcos e cabras). Os metais oriundos da costa ou de navios que passam pela região, estão em destaque entre os contaminantes ambientais que podem alterar o ecossistema da ilha. Dessa forma, o objetivo desse trabalho foi quantificar Al, As, Cd, Cu, Fe, Mn, Ni, Pb, Se, Zn e Hg em 300 amostras, compostas por músculo de duas espécies de caranguejo e de fígado e músculo de peixes (duas espécies) e aves (três espécies). Foram verificadas se existiam relações entre parâmetros biológicos (sexo, comprimento, peso), diferenças entre tecidos e entre os períodos de coleta. Nos caranguejos a concentração de Fe em G. lagostoma, e Zn em G. grapsus, foram maiores nos meses mais quentes, nos quais a atividade biológica é maior, sendo uma possível causa para maiores concentrações. Diferentemente dos caranguejos, a espécie M. niger (peixe) apresentou maiores concentrações (Al no músculo e Fe e Zn no Fígado) nos meses mais frios, as concentrações em peixes envolvem muitos fatores além da sazonalidade. Para ambas as espécies de peixes as concentrações de Fe e Zn foram maiores no fígado, assim como para P. arminjoniana (ave) as concentrações de Cu, Fe e Zn também foram maiores no fígado, como era esperado, pois, o fígado é um tecido com grande capacidade de acumular poluentes. Alguns elementos apresentaram correlações com o peso e/ou comprimento, porém todas muito baixas, com exceção do Zn em G. grapsus. Todas as análises de Hg realizada ficaram abaixo do limite de quantificação do método (17,7 µg kg-1). Os metais e semimetais apresentaram resultados semelhantes a estudos desenvolvidos em outras regiões. / The Trindade Island is located approximately 1150 km from the coast of Vitória-ES, is one of Brazilian oceanic islands and is under the control of the Brazilian Navy. At the time the occupation began the island suffered some anthropogenic influences, such as the removal of trees and the animals introduction (pigs and goats). Metals originating from the shore or from ships passing through the region, are highlighting among the environmental contaminants that can change the ecosystem of the island. So the aim of this study was to quantify Al, As, Cd, Cu, Fe, Mn, Ni, Pb, Se, Zn and Hg in three hundred samples of muscle of two species of crab and liver and muscle of fish (two species) and seabirds (three species). The relationships between biological parameters (sex, length, weight), differences between tissues and between sampling periods were checked. The concentration of Fe, G. lagostoma (crab), and the Zn, in G. grapsus (crab), showed higher concentrations in the warmer months, in which biological activity is greater, being a possible cause for higher concentrations. Different from crabs, the species M. niger (fish) presented higher concentrations (Al in the muscle and Fe and Zn in the liver) in the colder months, concentrations in fish involve many factors besides the seasonality. For both species of fish concentrations of Fe and Zn were higher in the liver as well as for P. arminjoniana (seabird) concentrations of Cu, Fe and Zn were higher in the liver, like was expected, because the liver is a tissue with a great capacity to accumulate pollutants. Some elements showed correlations with the weight and/or length, but all very low, with the exception of Zn in G. grapsus. All Hg analyzes performed were below the method quantification limit (17.7 µg kg-1). The metals and semimetals showed similar results to studies conducted in other regions.

THESIS ORGANISATION This thesis is organised into nine chapters that include seven international and national publications (six accepted and one submitted for publication). The initial overview chapter outlines the justification and direction for this thesis. With the exception of chapter 8 (accepted for publication on the 1st May 2005); all chapters are exact duplicates of published articles in international and national refereed journals (chapters 2 to 7). The initial chapters (2 and 3) presents research findings using a marine fish species, mullet (Mugil cephalus), to measure trace metal bioavailability in Lake Macquarie, NSW Australia. While subsequent chapters (4 to 8) are presenting research under taken to improve the understanding of arsenic cycling in marine and estuarine environments. The final chapter (chapter 9) is a synopsis of the major findings presented in this thesis. Due to the publication nature of this thesis, an unavoidable degree of replication exists within chapters (publications).

Cette thèse porte sur l’étude des cristaux appelés semi-métaux relativistes dans lesquels les électrons se comportent comme des particules relativistes sans masse.Le premier exemple historique d’un tel matériau est le graphène.Dans cet assemblage planaire d’atomes de carbone, les bandes électroniques de valence et de conduction se touchent en deux points distincts du réseau réciproque: il s'agit d'un conducteur de gap nul, un semi-métal.Les électrons proches du niveau de Fermi ont une dynamique relativiste décrite par une équation de Dirac,bien que leur vitesse soit cent fois inférieure à celle de la lumière dans le vide. Des semi-métaux analogues ont récemment été identifiés :les semi-métaux de Weyl et de Dirac à 3D, et des phases plus exotiques décrites par des croisements à plus de deux bandes.Cette diversité de matériaux relativistes pose la question de leurs propriétés communes. Une première partie de la thèse présente les travaux reliés à l’étude de la stabilité de ces phases, c’est à dire du croisement de bandes électroniques. Nous avons étudié cette stabilité d’abord en la reliant à des propriétés topologiques, puis en évaluant l’effet du désordre, tel que des impuretés dans le matériau. Dans la deuxième partie, nous nous intéressons à la manifestation dans le transport de la nature relativiste de ces électrons. Dans une première étude, nous étudions la condition d’existence d’une conductivité finie exactement au croisement des bandes, due à une contribution d’états évanescents. Une deuxième étude porte sur le transport anormal sous champ magnétique dans les semi-métaux de Weyl, comme manifestation de l’anomalie chirale, propriété unique de fermions relativistes. / This thesis adresses the study of crystals called relativistic semi-metals, in which electrons behave like massless relativistic particles.The first historical example of such a material is graphene.In this planar arrangement of carbon atoms, electronic valence and conduction bands touch at two distincts points in the reciprocal lattice. Thus, graphene is a zero-gap semiconductor, a semi-metal.The dynamics of electrons close to the Fermi level is relativistic, described by a Dirac equation, although their velocity is a hunder times lower than the velocity of light in vacuum. Analogous semi-metallic phases have recently been identified: 3D Weyl and Dirac semimetals, as well as more exotic phases described by crossings with more than two bands. This variety of relativistic materials raises the question of their common properties. A first part of this thesis presents work related to the study of the stability of these phases, i.e. of the electronic band crossing. We have investigated this stability first by relating it to topological properties, then by evaluating the effect of disorder, such as the presence of impurities in the material. In the second part, we focus on the manifestation of the relativistic nature of these electrons in transport. In a first study, we examine the condition of existence of a finite conductivity exactly at the band crossing, due to the contribution of evanescent states. A second study concerns the anomalous transport under a magnetic field in Weyl semi-metals, as a manifestation of the chiral anomaly, a unique property of massless relativistic fermions.

A Ilha da Trindade está localizada a aproximadamente 1150 km da costa de Vitória-ES, é uma das ilhas oceânicas brasileiras e está sob o domínio da Marinha do Brasil. Desde o início de sua ocupação sofreu algumas influências antrópicas, como a derrubada de árvores e a introdução de animais (porcos e cabras). Os metais oriundos da costa ou de navios que passam pela região, estão em destaque entre os contaminantes ambientais que podem alterar o ecossistema da ilha. Dessa forma, o objetivo desse trabalho foi quantificar Al, As, Cd, Cu, Fe, Mn, Ni, Pb, Se, Zn e Hg em 300 amostras, compostas por músculo de duas espécies de caranguejo e de fígado e músculo de peixes (duas espécies) e aves (três espécies). Foram verificadas se existiam relações entre parâmetros biológicos (sexo, comprimento, peso), diferenças entre tecidos e entre os períodos de coleta. Nos caranguejos a concentração de Fe em G. lagostoma, e Zn em G. grapsus, foram maiores nos meses mais quentes, nos quais a atividade biológica é maior, sendo uma possível causa para maiores concentrações. Diferentemente dos caranguejos, a espécie M. niger (peixe) apresentou maiores concentrações (Al no músculo e Fe e Zn no Fígado) nos meses mais frios, as concentrações em peixes envolvem muitos fatores além da sazonalidade. Para ambas as espécies de peixes as concentrações de Fe e Zn foram maiores no fígado, assim como para P. arminjoniana (ave) as concentrações de Cu, Fe e Zn também foram maiores no fígado, como era esperado, pois, o fígado é um tecido com grande capacidade de acumular poluentes. Alguns elementos apresentaram correlações com o peso e/ou comprimento, porém todas muito baixas, com exceção do Zn em G. grapsus. Todas as análises de Hg realizada ficaram abaixo do limite de quantificação do método (17,7 µg kg-1). Os metais e semimetais apresentaram resultados semelhantes a estudos desenvolvidos em outras regiões. / The Trindade Island is located approximately 1150 km from the coast of Vitória-ES, is one of Brazilian oceanic islands and is under the control of the Brazilian Navy. At the time the occupation began the island suffered some anthropogenic influences, such as the removal of trees and the animals introduction (pigs and goats). Metals originating from the shore or from ships passing through the region, are highlighting among the environmental contaminants that can change the ecosystem of the island. So the aim of this study was to quantify Al, As, Cd, Cu, Fe, Mn, Ni, Pb, Se, Zn and Hg in three hundred samples of muscle of two species of crab and liver and muscle of fish (two species) and seabirds (three species). The relationships between biological parameters (sex, length, weight), differences between tissues and between sampling periods were checked. The concentration of Fe, G. lagostoma (crab), and the Zn, in G. grapsus (crab), showed higher concentrations in the warmer months, in which biological activity is greater, being a possible cause for higher concentrations. Different from crabs, the species M. niger (fish) presented higher concentrations (Al in the muscle and Fe and Zn in the liver) in the colder months, concentrations in fish involve many factors besides the seasonality. For both species of fish concentrations of Fe and Zn were higher in the liver as well as for P. arminjoniana (seabird) concentrations of Cu, Fe and Zn were higher in the liver, like was expected, because the liver is a tissue with a great capacity to accumulate pollutants. Some elements showed correlations with the weight and/or length, but all very low, with the exception of Zn in G. grapsus. All Hg analyzes performed were below the method quantification limit (17.7 µg kg-1). The metals and semimetals showed similar results to studies conducted in other regions.

This thesis focuses on the development of nonlinear optical techniques and the measurement of topological properties of the Weyl semimetals. The first portion of this thesis describes technical developments of the nonlinear optical spectroscopic probes rotational anisotropy second harmonic generation (RA-SHG) and transient grating. In our work on SHG, we describe a fast-reflective optic-based rotational anisotropy nonlinear harmonic generation spectrometer built upon synchronization of stepper motors and a voice-coil fast turning motor with data recorded by a data acquisition card. This device enables fast accumulation of significantly more data points than traditional SHG spectrometers and further allows spectral measurement over a broad wavelength range to be performed without optical realignment. We then describe the Fourier domain RA-SHG, allows direct measurements of the RA-SHG signal components of Cn symmetry. This method is based on the fast scanning RA-SHG device described above and operates by recording the nth harmonics of the fast scanning signal using a lock-in amplifier. Finally, we describe a novel method of performing transient grating measurements based on low power laser diodes, a laser diode pulser, a digital delay generator, and a data acquisition card. The RA-SHG technique was applied to the chiral Weyl semimetal RhSi, where a spectrum of the sole SHG tensor element χ(2) i jk was measured over the unprecedented 0.275-1.5 eV incoming photon energy range. Our data shows evidence of a strong surface state response and are detailed enough to reveal the second order corrections to the linear band structure as well as the Pauli blocking condition which was observed to occur at ∼630 meV. We also describe measurements of the linear photogalvanic effect (LPGE) and circular photogalvanic effect (CPGE) in RhSi deriving from topological Fermi arc states. While the magnitude of the CPGE response broadly matched theoretical predictions, the data also exhibit an inexplicably high degree of symmetry in the response as a function of incoming polarization in both CPGE and LPGE channels. Collaborative work on the SHG spectrum from TaAs is also described, from which we attribute the origin of the SHG response peak to the third cumulant of the Bloch wavefunction. Further collaborative studies of the CPGE in RhSi (111) revealed a response that was likely due to the topological band structure, but that also shows that the theoretically predicted quantized CPGE was not observed due to impurities and from contributions from sources other than the Weyl nodes. Finally, we briefly summarized how the crystal structure of PrAlGe1-xSix was revealed to be non-centrosymmetric using the RA-SHG technique. Transition from intrinsic to extrinsic anomalous Hall effect by tuning the dopant concentration x was studied in this ferromagnetic Weyl semimetal. / Physics

<p>In this thesis, we present the results for the finite frequency response of a variety of materials. These materials all share the common theme that their low energy excitations are Dirac-like. This coincidence was not by design, and highlights the now-ubiquitous nature of Dirac-quasiparticles in condensed matter physics. We present results for graphene, the high temperature superconducting cuprates, and Weyl semi metals. For graphene, our calculations revolve around a new experimental technique: Near field infrared spectroscopy. Conventionally it is ok to use the $\vec{q}\rightarrow 0$ limit when calculating the low energy optical response. This new technique is able to directly probe the finite $\vec{q}$ response by using an atomic force microscope tip as an antenna. We computed the optical conductivity of graphene at finite wavevector and studied how the quasiparticle peak is altered by disorder and the electron-phonon interaction. The calculations on the high $T_c$ cuprates use a model of the pseudogap phase known as the Yang, Rice and Zhang (YRZ) model. We employed the model to study the resistivity in the pseudogap regime, both in-plane and along the c-axis. We used a coherent tunneling matrix element to describe transport along the c-axis. We found that the model was able to reproduce the metaliclike behavior in the plane while being resistive out of plane. We then extended the model to the finite frequency response, as well as the superconducting phase. We found a pseduogap feature at finite frequency that was previously explained through an interlayer collective mode. We also found that microwave spectroscopy puts strong limits on the form of the scattering rate. Finally, we computed the optical response of Weyl semimetals subjected to an applied magnetic field. Weyl semimetals are a topological phase of matter that have yet to be observed. The form of the conductivity contains a series of asymmetric peaks, whose spacing is a signature of the underlying relativistic dispersion. These peaks remain robust, even with moderate disorder.</p> / Doctor of Philosophy (PhD)

No description available.

Nesse trabalho foram realizados estudos para o fracionamento e especiação de Cu, Fe, Mn, Se e Zn em castanha-do-pará (Bertholletia excelsa H. B. K), polpa de coco (Cocos nucifera L.) e semente de cupuaçu (Theobroma grandiflorum). A extração seqüencial sólido-líquido combinada com GF AAS foi utilizada para o fracionamento e determinação dos elementos associados às frações proteicas. As concentrações de proteínas encontradas nos extratos de castanha-do-pará (6 a 76 mg g-1) foram maiores do que aquelas encontradas nos extratos de semente de cupuaçu (2 a 27 mg g-1) e de polpa de coco (1 a 12 mg g-1). A preliminar relação de Cu, Fe, Mn, Se e Zn associado a diferentes grupos de proteínas foi observada, indicando a possível interação desses elementos com albuminas, globulinas, prolaminas e glutelínas. O acoplamento on-line SEC-UV e off-line SEC-UV GFAAS foi aplicado com sucesso para a identificação das espécies de Cu, Fe, Mn, Se e Zn nos extratos de água, NaCl e NaOH de castanha-do-pará, polpa de coco e semente de cupuaçu. Em geral, os elementos de interesse encontram-se associados a espécies de pesos moleculares inferiores a 13 kDa nos extratos de água e NaCl e a 28 kDa nos extratos de NaOH. A combinação das informações obtidas desse acoplamento com os espectros de massas do MALDI-TOF da castanha-do-pará confirmam a associação de Cu, Fe, Mn, Se e Zn com duas espécies presentes no extrato de água de 6 kDa (Fe, Mn and Zn) e 11 kDa (Cu, Mn and Se). / In this work, studies were done for the fractionation and speciation of Cu, Fe, Mn, Se and Zn in Brazil-nut (Bertholletia excelsa H.B.K.), cupuassu (Theobroma grandiflorum) seeds and coconut (Cocos nucifera L.) pulp. The sequential solid-liquid extraction combined with GF AAS was used to fractionation and determination of elements associated to proteins fractions. The determined protein concentrations in extractants of Brazil-nut (6 a 76 mg g-1) are higher than those observed for extractants of cupuassu seeds (2 a 27 mg g-1) and coconut pulp (1 a 12 mg g-1). The preliminary relationship of Cu, Fe, Mn, Se and Zn associated to different proteins groups was observed, indicating a possible interation of these elements with albumins, globulins, prolamins and glutelins. The on-line SEC-UV and off-line SEC-UV GFAAS hyphenation was applied with sucess for the identification of Cu, Fe, Mn, Se and Zn species in the water, NaCl and NaOH extractants of Brazil-nut, cupuassu seeds and coconut pulp. In general, the interest elements were found associated to species of molecular weights lower than 13 kDa for water and NaCl extractants and 28 kDa for NaOH extractants. The combination of the informations of this hyphenation with MALDI-TOF mass spectra of the Brazil-nut gave confirmation of the association of the Cu, Fe, Mn, Se and Zn with two water-soluble species of 6 kDa (Fe, Mn and Zn) and 11 kDa (Cu, Mn and Se).

Abstract After the discovery of topological insulators (TIs), it has come to be widely recognized that topological states of matter can actually be widespread. In this sense, TIs have established a new paradigm about topological materials. Recent years have seen a surge of interest in topological semimetals, which embody two different ways of generalizing the effectively massless electrons to bulk materials. Dirac and, particularly, Weyl semimetals should support several transport and optical phenomena that are still being sought in experiments. A number of promising experimental results indicate superconductivity in members of half-Hesuler semimetals which realize the mixing singlet and triplet pairing symmetry. We now turn to results we got through the work on topological semimetals. This work presents quantum high field transports on Dirac and Weyl topological semimetals including Sr1-yMn1-zSb2 (y, z < 0.1), YbMnBi2 and TaP. In case of Sr1-yMn1-zSb2 (y, z < 0.1), massless relativistic fermion was reported with m* = 0.04-0.05m0. This material presented a ferromagnetic order for in 304 K < T < 565 K, but a canted antiferromagnetic order with a net ferromagnetic component for T < 304 K. These are considered striking features of Dirac fermions For YbMnBi2, we reported the unusual interlayer quantum transport behavior in magnetoresistivity, resulting from the zeroth LL mode observed in this time reversal symmetry breaking type II Weyl semimetal. Also, for Weyl semimetal TaP the measurements probed multiple Fermi pockets, from which nontrivial π Berry phase and Zeeman splitting were extracted. Our ultra-low penetration depth measurements on half-Heuslers YPdBi and TbPdBi revealed a power- law behavior with n= 2.76 ± 0.04 for YPdBi samples and n=2.6 ± 0.3 for TbPdBi sample. We may conclude the exponent n > 2 implies nodless superconducting gap in our samples. Also, we found that despite the increase in magnetic correlations from YPdBi to TbPdBi, superconductivity remains robust in both systems which indicates that AF fluctuations do not play a major role in superconducting mechanism.