Academic literature on the topic 'Thermal Hall effect'

Half-integer thermal quantum Hall conductance has recently been reported for the two-dimensional honeycomb material α-RuCl3. We found that the half-integer thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The measured field-angular variation of the quantized thermal Hall conductance has the same sign structure as the topological Chern number of the pure Kitaev spin liquid. This observation suggests that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in α-RuCl3.

AbstractA key feature of quantum spin liquids is the predicted formation of fractionalized excitations. They are expected to produce changes in the physical response, providing a way to observe the quantum spin liquid state1. In the honeycomb magnet α-RuCl3, a quantum spin liquid has been proposed to explain the behaviour observed on applying an in-plane magnetic field H||. Previous work reported that the thermal Hall conductivity took on a half-integer quantized value and suggested this as a signature of a fractionalized Majorana edge mode predicted to exist in Kitaev quantum spin liquids2. However, the temperature and magnetic-field range of the half-quantized signal2–4 and its association with Majorana edge modes are still under debate5,6. Here we present a comprehensive study of the thermal Hall conductivity in α-RuCl3 showing that approximately half-integer quantization exists in an extended region of the phase diagram, particularly across a plateau-like parameter regime for H|| exceeding 10 T and temperature below 6.5 K. At lower fields, the thermal Hall conductivity exhibits correlations with complex anomalies in the longitudinal thermal conductivity and magnetization, and is suppressed by cooling to low temperatures. Our results can be explained by the existence of a topological state in magnetic fields above 10 T.

We present the first theoretical evidence of zero magnetic field topological (anomalous) thermal Hall effect due to Weyl magnons in stacked noncoplanar frustrated kagomé antiferromagnets. The Weyl magnons in this system result from macroscopically broken time-reversal symmetry by the scalar spin chirality of noncoplanar chiral spin textures. Most importantly, they come from the lowest excitation, therefore they can be easily observed experimentally at low temperatures due to the population effect. Similar to electronic Weyl nodes close to the Fermi energy, Weyl magnon nodes at the lowest excitation are the most important. Indeed, we show that the topological (anomalous) thermal Hall effect in this system arises from nonvanishing Berry curvature due to Weyl magnon nodes at the lowest excitation, and it depends on their distribution (distance) in momentum space. The present result paves the way to directly probe low excitation Weyl magnons and macroscopically broken time-reversal symmetry in three-dimensional frustrated magnets with the anomalous thermal Hall effect.

Abstract The Krypton Large IMpulse Thruster (KLIMT) ESA/PECS project, which has been implemented in the Institute of Plasma Physics and Laser Microfusion (IPPLM) and now is approaching its final phase, was aimed at incremental development of a ~500 W class Hall effect thruster (HET). Xenon, predominantly used as a propellant in the state-of-the-art HETs, is extremely expensive. Krypton has been considered as a cheaper alternative since more than fifteen years; however, to the best knowledge of the authors, there has not been a HET model especially designed for this noble gas. To address this issue, KLIMT has been geared towards operation primarily with krypton. During the project, three subsequent prototype versions of the thruster were designed, manufactured and tested, aimed at gradual improvement of each next exemplar. In the current paper, the heat loads in new engine have been discussed. It has been shown that thermal equilibrium of the thruster is gained within the safety limits of the materials used. Extensive testing with both gases was performed to compare KLIMT’s thermal behaviour when supplied with krypton and xenon propellants.

The past decade has witnessed the rise of the thermal Hall measurement as a sensitive probe of transport properties in solids. Experiments performed on a wide range of materials, such as magnetic insulators, spin ice, kagome spin liquids with both ferromagnetic and antiferromagnetic exchange interactions, a quantum paraelectric, and even high-Tc cuprates, showed the existence of thermal Hall transport phenomena caused by neutral excitations. There is little doubt that an era of electromagnetism without electrons has dawned. This review covers a brief and somewhat personal account of the theory and the experimental developments of the thermal Hall effect as a new discipline of condensed matter physics over the past decade.

Thesis (M.S. in in Aeronautical Engineering)--Air Force Institute of Technology, March 2008.
"Presented to the Faculty, Department of Aeronautics and Astronautics Graduate School of Engineering and Management, Air Force Institute of Technology Air University, Air Education and Training Command in partial fulfillment of the requirements for the Degree of Master of Science in Aeronautical Engineering, March 2008."--P. [ii]. Thesis advisor: Dr. William Hargus. "March 2008." "AFIT/GA/ENY/08-M01." Includes bibliographical references. Also available online in PDF from the DTIC Online Web site.

Electrical and structural properties of Bismuth thin films were studied simultaneously. Electrical properties of the Bismuth thin films have been characterized by measuring temperature dependent conductivity and Hall effect. Structural analysis were carried out by X-ray diffraction technique and using a room temperature Atomic Force Microscope (RT-AFM).

Many-body physics studies the collective behavior of systems with a large number of microscopic constituents. The interaction between the fundamental particles creates a common behavior within the system with emergent excitations exhibiting uncommon characteristics. In three spatial dimensions it has recently been found that a new kind of particles can exist characterized by a fractionalized mobility, being either immobile or mobile only along sub-dimensional spaces: fractons. In this thesis I explore fracton phases focusing on their topological and thermal properties. Fractons can be explained as a generalization of usual topological particles with some fundamental differences, which make fracton order a new field on its own. Fracton models are studied first from the point of view of exactly solvable lattice spin models, focusing on the similarities and differences with usual topological models. Fracton phases are also described through the use of symmetric tensor gauge theory. This gives a theoretical background which is used to explore some possible phases at finite densities of fractons, like Fermi liquids and quantum Hall states. The thermal properties of such systems are studied in detail through the use of numerical simulations relying on exact-diagonalization. Various correspondences with systems featuring quantum many-body scars are found, in particular with the PXP model. The non-thermal behavior of the models under study is justified by the fragmentation of the Hilbert space in a large number of separated sub-sectors, not related to symmetries of the model. Further, the range of the local Hamiltonian operators is found to be of fundamental relevance in the thermal properties of the system. For certain ranges it is observed that the models are not able to reach the thermal state at long times. Instead, increasing the length of interactions the system becomes ergodic, with the exception of a small number of special eigenstates which remain non-thermal.

La technologie de la microelectronique silicium beneficie aujourd'hui d'investissements massifs et continus. Tout porte a croire que les excellentes proprietes du systeme si/sio#2 assureront la perennite du si pendant encore de nombreuses annees. Le developpement de nouveaux materiaux pouvant ameliorer les performances des dispositifs a base de si est donc encourage. En particulier, l'heterosysteme si/sige apparait comme le meilleur candidat pour le developpement d'une technologie a heterojonction a base de si. De tels materiaux doivent cependant etre compatibles avec les temperatures de recuit utilisees dans la technologie si. Les deux principaux dispositifs electroniques dans lesquels l'utilisation du sige est envisagee sont le transistor bipolaire et le transistor a effet de champ. Dans le cas du transistor a effet de champ, l'interet du sige est d'ameliorer les proprietes de transport parallele au plan des couches. Cette these est consacree a l'etude experimentale de ces proprietes ainsi qu'a l'analyse et a la comprehension du fonctionnement des heteronjonctions si/sige. Nous rappelons tout d'abord les proprietes de structure de bandes des heterosystemes contraints si/sige ainsi que la methode de mesure par effet hall que nous avons utilisee. Une etude de l'evolution thermique des proprietes de transport et de confinement de modulations de dopage si/sige de type p est ensuite presentee. Puis, nous analysons les proprietes de transport electronique des heterostructures si/sige elaborees sur un pseudo-substrat de sige relaxe. Le principe de fonctionnement specifique des dispositifs mos a canal enterre en sige est ensuite mis en evidence experimentalement. Nous constaterons finalement que les caracteristiques electriques des dispositifs mos a base de si peuvent etre ameliorees par l'introduction d'un canal enterre en sige

Дисертаційна робота присвячена дослідженню електрофізичних, магніторезистивних, магнітооптичних властивостей та ефекту Холла в плівкових системах на основі металу (Fe) і напівпровідника (Ge) в умовах фазоутворення. У плівкових сплавах, сформованих на основі відпалених до 900−1070 К тришарових плівок Fe(5−10 нм)/Ge(2−25 нм)/Fe(15−50 нм), в залежності від співвідношення концентрацій атомів окремих компонент утворюються магнітні плівки германідів заліза Fe2Ge, FeGe і FeGe2 із середніми розмірами кристалітів 15–30 нм. Порівняння експериментальних величин питомого опору двошарових плівкових систем Ge/Fe/П із розрахунковими на основі моделі, в якій зберігається індивідуальність окремих шарів, свідчать про те, що відміну між цими величинами можна пояснити ефектом утворення екситонів Ваньє−Мотта на основі 4 % електронів провідності. Перехід плівки германіду заліза із аморфного стану в кристалічний відбувається при температурах Та→к = 560−590 К в залежності від товщини плівки. Формування термостабільних (ТКО ~ 10−4 К−1) фаз FeGe і FeGe2 по всьому об’єму зразка приводить до зростання величини МО від 0,02–0,04% у невідпалених системах до 0,30–0,44 % у відпалених до 900 К зразках. Установлено, що у системах на основі плівок Fe і Ge, спостерігається залежність кута Керра від індукції магнітного поля у вигляді прямокутної петлі гістерезису, що свідчить про реалізацію двох магнітних станів і швидкодію чутливих елементів приладів у магнітному полі. Експериментально встановлено, що величина сталої Холла для двошарових плівок на основі Fe і Ge (6–11)·10−9 м3/Кл при зростанні індукції магнітного поля від 0 мТл до 100 мТл. При збільшенні інтервалу термообробки плівкових зразків до 570 К стала Холла зменшується від 11·10−9 м3/Кл до 6·10−9 м3/Кл. Досліджені властивості тонких плівок нітриду вуглецю як захисних покриттів для плівкових чутливих елементів на основі германідів металів.
Диссертация посвящена исследованию электрофизических, магниторезистивных, магнитооптических свойств и эффекта Холла в пленочных системах на основе металла (Fe) и полупроводника (Ge) при фазообразовании. Изучение прoцесов фазообразования в двухкомпонентных пленочных материалах на основе Fe и Ge, сформированных методом послойной конденсации с последующей термообработкой в интервале температур 300–1070 К, позволили устаовить, что в пленочных сплавах, сформированных на основе отожжённых до 900–1070 К трехслойных пленок Fe (5–10 нм)/Ge (2–25 нм)/Fe (15–50 нм), в зависимости от соотношения концентраций атомов отдельных компонент образуются магнитные пленки германидов железа Fe2Ge, FeGe и FeGe2 со средними размерами кристаллитов 15–30 нм. Сравнение экспериментальных величин удельного сопротивления двухслойных плёночных систем Ge/Fe/П с расчетными на основе модели, в которой сохраняется индивидуальность отдельных слоёв, свидетельствует о том, что отличие между этими величинами можно объяснить эффектом образования экситонов Ванье–Мотта на основе 4 % электронов проводимости. Переход пленки германида железа из аморфного состояния в кристаллическое происходит при температурах Та→к = 560–590 К в зависимости от толщины образца. Формирования термостабильных (ТКС ~ 10–4 К–1) фаз FeGe и FeGe2 по всему объему образца приводит к росту величины МО от 0,02–0,04 % в неотожжённых системах до 0,30–0,44 % в отожженных до 900 К образцах. Наблюдается зависимость угла Керра от индукции магнитного поля в виде прямоугольной петли гистерезиса, что свидетельствует о реализации двух магнитных состояний и быстродействии чувствительных элементов устройств в магнитном поле. Получено, что постоянная Холла для двухслойных пленок на основе Fe и Ge имеет величину (6–11) .10-9 м3/Кл при росте индукции магнитного поля от 0 до 100 мТл. При увеличении интервала термообработки пленочных образцов до 570 К постоянная Холла уменьшается от 11·10−9 м3/Кл до 6·10−9 м3/Кл. Исследованы свойства тонких пленок углерода и нитрида углерода как защитных покрытий для пленочных чувствительных элементов. Показано, что плотность пленки CNx/Si (100) уменьшается при снижении температуры подложки и увеличении толщины образца, а максимальная концентрация атомов алмазоподобной структуры наблюдается в области подложки, а при толщине d ≥ 2 нм. Пленка однородная с постоянной плотностью, что свидетельствует о соответствии пленок CNx требованиям к покрытиям, которые могут быть использованы как защитные термостойкие слои для чувствительных элементов сенсорной электроники на основе силицидов и германидов металлов.
The thesis is devoted to systematic research of electrophysical, magnetoresistive, magneto – optical galvanomagnetic properties of film systems on the basis of metal (Fe) and semiconductor (Ge) in the conditions of phase formation. In film alloys formed based on annealed to 900–1070 K three-layer films Fe(5–10 nm)/Ge(2–25 nm)/Fe(15–50 nm), depending on the ratio of the concentrations of atoms of individual components, magnetic films are formed iron germanides Fe2Ge, FeGe and FeGe2 with average crystallite sizes of 15–30 nm. Comparison of resistivity of two-layer Ge/Fe/S (S-substrate) film systems with calculated ones based on the model, which preserves the individuality of individual layers, indicates that the difference between these values can be explained by the effect of Vanier-Mott excitons based on 4 % conduction electrons. The transition of the iron germanide film from the amorphous state to the crystalline state occurs at temperatures Tа→c = 560–590 K depending on the film thickness. The formation of thermostable (TRC ~ 10–4 K–1) phases of FeGe and FeGe2 over the entire volume of the sample leads to an increase in the value of MR from 0.02–0.04 % in non-annealed systems to 0.30–0.44 % in annealed to 900 K samples. It is established that in systems based on Fe and Ge films, the dependence of the angle Θ on the induction of the magnetic field in the form of a "stepped hysteresis loop" is observed, which indicates the realization of two magnetic states and the speed of sensitive elements of functional devices in a magnetic field. It has been experimentally established that the value of the Hall constant for two-layer films based on Fe and Ge (6–11)·10–9 m3/C with increasing magnetic field induction from 0 mT to 100 mT. When increasing the heat treatment interval of film samples to 570 K, the value of the Hall constant decreases from 11·10–9 m3/C to 6·10–9 m3/C. The properties of thin films of carbon and carbon nitride as protective coatings for film sensitive elements have been studied.

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

The Lorentz force that a magnetic field exerts on a moving charge carrier is perpendicular to the direction of motion and to the magnetic field. Since both electric and thermal currents are carried by mobile electrons and ions, a wide range of galvanomagnetic and thermomagnetic effects result. The effects that occur in an isotropic polycrystalline metal are illustrated in Fig. 20.1. As to be expected, many more cross-coupled effects occur in less symmetric solids. The galvanomagnetic experiments involve electric field, electric current, and magnetic field as variables. The Hall Effect, transverse magnetoresistance, and longitudinal magnetoresistance all describe the effects of magnetic fields on electrical resistance. Analogous experiments on thermal conductivity are referred to as thermomagnetic effects. In this case the variables are heat flow, temperature gradient, and magnetic field. The Righi–Leduc Effect is the thermal Hall Effect in which magnetic fields deflect heat flow rather than electric current. The transverse thermal magnetoresistance (the Maggi–Righi–Leduc Effect) and the longitudinal thermal magnetoresistance are analogous to the two galvanomagnetic magnetoresistance effects. Additional interaction phenomena related to the thermoelectric and piezoresistance effects will be discussed in the next two chapters. In tensor form Ohm’s Law is . . .Ei = ρijJj , . . . where Ei is electrical field, Jj electric current density, and ρij the electrical resistivity in Ωm. In describing the effect of magnetic field on electrical resistance, we expand the resistivity in a power series in magnetic flux density B. B is used rather than the magnetic field H because the Lorentz force acting on the charge carriers depends on B not H.

This chapter discusses the statics and dynamics of particle ensemble evolution under multiple stimuli—electrical, magnetic and thermal, particularly (thermoelectromagnetic interaction)—by developing the evolution of the distribution function in a generalized form from its thermal equilibrium form. In the presence of electrical and magnetic fields, this shows the Hall effect, magnetoresistance, et cetera. Add thermal gradients, and one can elaborate additional consequences that can be calculated in terms of momentum relaxation times and the nature of impulse interaction, since momentum and energies carried by the ensemble are accounted for. So, parameters such as thermal conductivity due to the carriers can be determined, thermoelectric, thermomagnetic and thermoelectromagnetic interactions can be quantified and the Ettinghausen effect, the Nernst effect, the Righi-Leduc effect, the Ettinghausen-Nernst effect, the Seebeck effect, the Peltier effect and the Thompson coefficient understood. The dynamics also makes it possible to determine the frequency dependence of the phenomena.

Electron energy bands in solids are introduced. Free electron theory for metals is presented: the Fermi gas, Fermi energy and temperature. Electrical and thermal conductivity are interpreted, including the Wiedermann–Franz law. The Hall effect and information it brings about charge carriers is discussed. Plasma oscillations of conduction electrons and the optical properties of metals are examined. Formation of quasi-particles of an electron and its screening cloud are discussed. Electron-electron and electron-phonon scattering and how they affect the mean free path are treated. Then the analysis of crystalline materials using electron Bloch waves is presented. Tight and weak binding cases are examined. Electron band structure is explained including Brillouin zones, electron kinematics and effective mass. Fermi surfaces in crystals are treated. The ARPES technique for exploring dispersion relations is explained.