This dissertation reports on infrared optical spectroscopic studies of a novel class of materials named Dirac materials, which cover a broad range of materials including Topological Insulators (TI) and Dirac/Nodal-line semimetals. These materials share a similar low-energy Hamiltonian that can be described by massless/massive Dirac fermions. Adding out-of-plane magnetic field generates additional features in the optical spectra that allow us to distinguish Dirac fermions with usual fermions with parabolic bands. I will first demonstrate identifications of surface states (SS) of TI using Faraday rotation spectroscopy, where both the top and bottom SS can be identified and found to host carriers of opposite sign. Secondly, I will generalize the power-law behavior for two-dimensional (2D) and three-dimensional (3D) Dirac semimetals to dispersive nodal-line semimetals. This leads to the discoveries of Dirac nodal-lines in topological semimetal NbAs2. Finally, the optical signatures of electronic correlations are discussed and the unexplored overlapping area between strongly correlated systems and Dirac semimetals are studied. The prominent correlation effects in nodal-line semimetal ZrSiSe uncovered by a combination of optical and magneto-optical spectroscopies will be discussed.

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In this work we exploit the unique characteristics of a Dirac semimetal material to be symmetry-protected, to investigate dierent topological phase transitions provided by chemical dopings, focusing in particular on the electronic, magnetic and topological properties of the doped systems, studied by the mean of rst-principles methods based on density functional theory (DFT) approach. In particular these doped systems, besides being of interest for investigating the role of topology in solid state physics, could have a great potential for practical application since the dierent topological phases that come along with the chemical dopings allow one to exploit the unique properties of topological materials. The starting point for our study will be the material called cadmium-arsenide (Cd3As2), an example of a topological Dirac semimetal, which is chemically stable at ambient conditions. Chapter I presents a general introduction to topology, especially in condensed matter physics, and to the main physical properties of the topological materials we mentioned. Then, in chapter II, we briey present the methods and the computational tools that we used for our study. In chapter III a more detailed introduction to our work is given, along with a schemetic view of the path we followed, together with the results that we obtained for pristine Cd3As2, which we use as bench mark for our computational methods. Finally, in chapter IV and V, the results for the doped systems are presented and discussed, respectevely for the non-magnetic (IV) and magnetic (V) dopings. Our study has enabled us to discern how doping can give rise to see dierent topological phase transitions. Specically our work shows that dierent realizations of non-magnetic doping gives rise to dierent topological phases: the topological Weyl semimetal phase, which is of great interest since it can support a robust quantum spin Hall eect, and a very special mixed Dirac + Weyl phase, where surprisingly both a Dirac and a Weyl phase can coexist in the same system. Furthermore, magnetically doped systems show the emergence of a magnetic Weyl phase, which can support a quantum anomalous Hall eect. Our work can be the starting point for future studies, both theoretical and experimental, in which the unique physical properties we found in the doped Cd3As2 systems can be further investigated, in order to exploit them for practical applications.

Thesis advisor: Fazel Tafti / Since the idea of topology was realized in real materials, the hunt is on for new candidates of topological semimetals with novel electromagnetic responses. For example, topological states can be highly conductive due to a topological protection, which can be destroyed in a magnetic field and lead to an extremely high magnetoresistance. In Weyl semimetals, a transverse current that would usually require a magnetic field to emerge, can be generated by intrinsic Berry curvature without a magnetic field -- the celebrated anomalous Hall effect. In this dissertation, both phenomena mentioned above are studied in rare-earth monopnictides and RAlX material family (R=rare-earths, X=Ge/Si), respectively. The monopnictides are ideal for the study of extreme magnetoresistance because of their topological transitions and abundant magnetic phases. In LaAs, we untied the connection between topological states and the extreme magnetoresistance, the origin of which is clarified. In HoBi, we found an unusual onset of extreme magnetoresistance controlled by a magnetic phase dome. On the other hand, RAlX material family is a new class of Weyl semimetals breaking both inversion and time-reversal symmetries. In particular, in PrAlGeₓSi₁₋ₓ (x=0-1), we unveiled the first transition from intrinsic to extrinsic anomalous Hall effect in ferromagnetic Weyl semimetals, and the role of topology is discussed. In CeAlSi, we found that the Fermi level can be tuned as close as 1 meV away from the Weyl nodes; moreover, a novel anomalous Hall response appears only when the Fermi level is tuned to be near the Weyl nodes. Thus, we established a new transport response solely induced by Weyl nodes. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Topology, an important topic in physics since several years, is handled as possible solution to many current-state problems in electronics and energy. It could allow to dramatically shrink computational devices or increase their speed without the current problem of heat dissipation, or topological principles can be used to introduce room temperature high-conduction paths within materials. Unfortunately, while many promising materials have been presented yet, the one breakthrough material is still missing. Current style materials are either consisting of toxical elements, obstructing possible use cases, or their electronic structure is too complex to investigate the interplay of all the facets of the electronic structure present in the mateirals. In this thesis, two very promising materials will be thoroughly introduced, namely TaIrTe4 and GaGeTe. Both materials have the potential, to lift one of the shortcomings mentioned. First, TaIrTe4 will be presented. TaIrTe4 is a simplistic Weyl semimetal in terms of its electronic and topological structure - the simplest yet known material. It hosts four Weyl points, the minimum amount of Weyl nodes possible in a non-centrosymmetric material. Predictions state, that these nodes are well separated throughout the Brillouin zone, and are connected by nearly parallel Fermi arcs. The existance of the topological states is proved in this thesis through angle-resolved photoemission spectroscopy (ARPES) and confirmed by spin polarization measurements on these states. GaGeTe is predicted to be a Bi2Se3-style topological insulator, but ARPES data presented shows, that no direct band gap could be observed. Yet, a topological state is still believed to be present. This makes this material interesting in many ways: its elemental composition is less toxic than bismuth and selenium, as well as it is the first realization of such a specific electronic structure. A full discussion of the electronic states close to the Fermi level including the possible existance of topological states is shown in this thesis.

Weyl-Semimetalle haben bemerkenswerte Eigenschaften. Ihr elektrischer Widerstand steigt linear und unsaturiert mit einem angelegten Magnetfeld, diverse Ergebnisse deuten darauf hin, dass sie einen unordnungsinduzierten Metall-Isolator-Phasenübergang aufweisen und ihre Ladungsträger zeigen die chirale Anomalie, d.h., die Nichtkonservierung der chiralen Ladung. Diese Eigenschaften haben ihren Ursprung in der Niedrigenergiephysik der Weyl- Semimetalle, die von Weyl-Punkten, Berührungspunkten zwischen Leitungs- und Valenzband an der Fermi-Energie mit einer linearen Dispersionsrelation, dominiert wird. Diese Berührungspunkte sind topologisch geschützt, d.h., kleine Störung können ihnen nichts anhaben. Weyl-Semimetalle sind daher Beispiele für topologische Semimetalle, Materialien mit geschützten niedrigdimensionalen Berührungenspunkten, -linien, oder -oberflächen an der Fermi-Energie. In dieser Arbeit zeigen wir, wie die Eigenschaften von Weyl-Semimetallen durch Unordnung, Magnetfelder und Deformationen beeinflusst werden. Wir zeigen außerdem eine Querverbindung zwischen Weyl-Semimetallen und nodal line-Semimetallen, topologisch geschützten Semimetallen mit einer eindimensionalen Fermi-Fläche. Durch die Nutzung von Gitter- und Niedrigenergiekontinuumsmodellen können wir Wege aufzeigen, wie man unsere Ergebnisse sowohl aus einer Festkörperphysik- als auch aus einer Hochenergiephysikperspektive verstehen kann. Insbesondere identifizieren wir eine experimentelle Signatur der chiralen Anomalie: die blaue Note, ein charakteristisches Muster in Form einer Note, das mit Hilfe von winkelaufgelöster Photoelektronenspektroskopie gemessen werden kann. Ein weiteres wichtiges Charakteristikum ist der Magnetwiderstand, der in Weyl-Semimetallen vom Winkel zwischen einem angelegten Magnetfeld und der Transportrichtung abhängt. Durch den Einfluss der chiralen Anomalie ist der longitudinale Magnetwiderstand negativ, der transversale Widerstand hingegen wächst linear und grenzenlos mit dem angelegten Magnetfeld. In dieser Dissertation untersuchen wir beide Charakteristiken analytisch und numerisch. Inspiriert durch Experimente, in denen ein scharfes Leitfähigkeitsmaximum für parallele elektrische und Magnetfelder observiert wurde, zeigen wir, dass die Leitfähigkeit vom Winkel zwischen den angelegten Feldern und dem Abstandsvektor der Weyl-Punkte abhängt und dass sie insbesondere für Felder parallel zum Abstandsvektor ein scharfes Maximum aufweist. Dieser Effekt ist besonders ausgeprägt, wenn nur das niedrigste Landau-Niveau zur Leitfähigkeit beiträgt, er bleibt aber auch bei höheren Energien beobachtbar. Für parallelen Magnettransport untersuchen wir starke Unordnung, die außerhalb des von der Störungstheorie abgedeckten Bereichs liegt, numerisch und beobachten einen positiven Magnetwiderstand, qualitativ ähnlich zu experimentellen Daten. Aus Deformationen in Weyl-Semimetallen entstehen sogenannte chirale oder auch axiale Felder, die ähnliche Konsequenzen wie externe elektromagnetische Felder haben, wobei noch viele Details im Verborgenen liegen. Wir untersuchen Deformationen aus zwei verschiedenen Perspektiven: zunächst zeigen wir, wie zwei widersprüchliche Vorhersagen aus der Quantenfeldtheorie, die konsistenten und kovarianten Anomalien, in einem Gittermodell beobachtbar sind. Dann untersuchen wir elektrischen Transport unter Einfluss von axialen Magnetfeldern und zeigen, dass Moden, die sich in unterschiedliche Richtungen bewegen, räumlich getrennt sind. Diese räumliche Trennung hat eine unübliches Wachstums des elektrischen Leitwerts mit der transversalen Systembreite zur Folge. Des weiteren zeigen wir, wie ein nodal line-Semimetall aus einem Weyl-Semimetall entstehen kann, das einer Supergitterstruktur ausgesetzt ist. Wir interpretieren die Oberflächenzustände mit Hilfe der interzellulären Zak-Phase und zeigen zwei verschiedene Mechanismen, die die Bandstruktur vor der Öffnung einer Bandlücke schützen, auf. Um unsere Diskussion abzuschließen, untersuchen wir Transport in nodal line-Semimetallen in Kürze und stellen ihre Quantenfeldtheorie vor. Schließlich wenden wir uns wechselwirkenden Phasen zu und zeigen, welche Konsequenzen die Symmetrieklassifizierung des Sachdev- Ye-Kitaev-Modells hat – ein Modell von Teilchen mit zufälligen Wechselwirkungsstärken, dessen Topologie von der Anzahl der enthaltenen Teilchen bestimmt wird.:1 Introduction 2 Topological Band Theory 2.1 Geometric Phase and Berry Phase 2.1.1 The Adiabatic Theorem 2.1.2 The Zak Phase 2.2 Tenfold Classification of Topological Insulators and Superconductors 2.3 Topological Semimetals 2.3.1 Weyl Semimetals 2.3.2 Nodal Line Semimetals 2.4 Bulk-boundary Correspondence from the Intercellular Zak Phase 2.4.1 Intra- and Intercellular Zak Phase 2.4.2 Bulk-boundary Correspondence 2.4.3 Conclusion 3 Field Theory Perspective on Topological Phases 3.1 Topological Insulators 3.2 Weyl Fermions and the Chiral Anomaly 3.3 Visualizing the Chiral Anomaly with Photoemission Spectroscopy 3.3.1 The Chiral Anomaly in Condensed Matter Systems 3.3.2 Model and Methods 3.3.3 ARPES Spectra for Weyl and Dirac Semimetals 3.3.4 Experimental Details 3.3.5 Summary and Conclusion 3.4 The Consistent and Covariant Anomalies 3.5 Consistent and Covariant Anomalies on a Lattice 3.5.1 Model and Methods 3.5.2 Lattice Results for Consistent and Covariant Anomalies 3.5.3 Influence of the Mass Term 3.5.4 The Quest for One Third 3.6 The Action of Nodal Line Semimetals 4 Transport in Topological Semimetals 4.1 Longitudinal Magnetoresistance in Weyl Semimetals 4.2 Transversal Magnetoresistance in Weyl Semimetals 4.2.1 Model 4.2.2 Mesoscopic Transport in Clean Samples 4.2.3 Numerical Magnetotransport in the Presence of Disorder 4.2.4 Born-Kubo Analytical Bulk Conductivity 4.2.5 Numerical Results in Disordered Samples 4.2.6 Conclusion 4.3 Transport in the Presence of Axial Magnetic Fields 4.3.1 Model and Methods 4.3.2 Longitudinal Magnetotransport for Axial Fields 4.3.3 Conclusion 4.4 Transport in Nodal Line Semimetals 5 Nodal Line Semimetals from Weyl Superlattices 5.1 Weyl Semimetal on a Superlattice 5.2 Emergent Nodal Phases 5.3 Symmetry Classification of the Nodal Line 5.4 Surface States 5.5 Stability against Wave Vector Mismatch 5.6 Time-reversal Symmetric Weyl Semimetal 5.7 Conclusion 6 Symmetry Classification of the SYK Model 6.1 Model and Topological Classification 6.2 Overlap of Time-reversed Partners 6.2.1 Even Number of Majoranas 6.2.2 Odd Number of Majoranas 6.3 Spectral Function 6.3.1 Zero Temperature 6.3.2 Infinite Temperature 6.4 Symmetry-breaking Terms 6.5 Lattice Model 6.6 Conclusion 7 Conclusion and Outlook Appendix A Zak Phase and Extra Charge Accumulation Appendix B Material-specific Details for ARPES B.1 Relaxation Rates B.2 ARPES in Finite Magnetic Fields B.3 Estimates of the Chiral Chemical Potential Difference Appendix C Weyl Nodes in a Magnetic Field C.1 Scattering between Different Landau Levels C.2 Analytical Born-Kubo Calculation of Transversal Magnetoconductivity C.2.1 Disorder Scattering in Born Approximation C.2.2 Transversal Magnetoconductivity from Kubo Formula Appendix D Transfer Matrix Method D.1 Longitudinal Magnetic Field D.2 Transversal Magnetic Field Bibliography Acknowledgments List of Publications Versicherung / Weyl semimetals have remarkable properties. Their resistance grows linearly and unsaturated with an applied transversal magnetic field, and they are expected to show a disorder-induced metal-insulator transition. Their charge carriers exhibit the chiral anomaly, i.e., the nonconservation of chiral charge. These properties emerge from their low-energy physics, which are dominated by Weyl nodes: zero-dimensional band crossings at the Fermi energy with a linear dispersion. The band crossings are topologically protected, i.e., they cannot be lifted by small perturbations. Thus, Weyl semimetals are examples of topological semimetals, materials with protected lower-dimensional band crossing close to the Fermi surface. In this work, we show how the properties of Weyl semimetals are affected by disorder, magnetic fields, and strain. We further provide a link between Weyl semimetals and nodal line semimetals, topological semimetals with a one-dimensional Fermi surface. By using both lattice and low-energy continuum models, we present ways to understand the results from a condensed-matter and a quantum-field-theory perspective. In particular, we identify an experimental signature of the chiral anomaly: the blue note, a characteristic note-shaped pattern that can be measured in photoemission spectroscopy. Another important signature is the magnetoresistance. In Weyl semimetals, its behavior depends on the angle between the magnetic field and the transport direction. For parallel transport, a negative longitudinal magnetoresistance as a manifestation of the chiral anomaly is observed; for orthogonal transport, the transversal magnetoresistance shows a linear and unsaturated growth. In this thesis, we investigate both regimes analytically and numerically. Inspired by experiments that show a sharply peaked magnetoresistance for parallel fields, we show that the longitudinal magnetoresistance depends on the angle between applied fields and the Weyl node separation, and that it is sharply peaked for fields parallel to the node separation. This effect is especially strong in the limit where only the lowest Landau level contributes to the magnetoresistance, but it survives at higher chemical potentials. For transversal magnetotransport, we numerically investigate the strong-disorder regime that is beyond the reach of perturbation theory and observe a positive magnetoresistance, qualitatively similar to recent experiments. Strain in Weyl semimetals creates so-called axial fields that result in phenomena similar to the ones driven by electric and magnetic fields, but with some yet unknown consequences. We investigate strain from two perspectives: first, we show how two different predictions from quantum field theory, the consistent and covariant anomalies, manifest on a lattice. Second, we investigate transport in the presence of axial magnetic fields and show that counterpropagating modes are spatially separated, resulting in an unusual scaling of the conductance with the system’s width. We further show how a nodal line semimetal can emerge from a Weyl semimetal on a superlattice. We interpret the presence of surface states in terms of the intercellular Zak phase and show two distinct mechanisms that protect the spectrum from opening a gap. To complete our discussion, transport in nodal line semimetals is briefly discussed, as well as the quantum field theory that describes the low-energy features of these materials. Finally, we conclude this work by showing manifestations of the different symmetry classes that can be realized in the Sachdev-Ye-Kitaev model—a model of randomly interacting particles whose topology is deeply connected to the number of particles.:1 Introduction 2 Topological Band Theory 2.1 Geometric Phase and Berry Phase 2.1.1 The Adiabatic Theorem 2.1.2 The Zak Phase 2.2 Tenfold Classification of Topological Insulators and Superconductors 2.3 Topological Semimetals 2.3.1 Weyl Semimetals 2.3.2 Nodal Line Semimetals 2.4 Bulk-boundary Correspondence from the Intercellular Zak Phase 2.4.1 Intra- and Intercellular Zak Phase 2.4.2 Bulk-boundary Correspondence 2.4.3 Conclusion 3 Field Theory Perspective on Topological Phases 3.1 Topological Insulators 3.2 Weyl Fermions and the Chiral Anomaly 3.3 Visualizing the Chiral Anomaly with Photoemission Spectroscopy 3.3.1 The Chiral Anomaly in Condensed Matter Systems 3.3.2 Model and Methods 3.3.3 ARPES Spectra for Weyl and Dirac Semimetals 3.3.4 Experimental Details 3.3.5 Summary and Conclusion 3.4 The Consistent and Covariant Anomalies 3.5 Consistent and Covariant Anomalies on a Lattice 3.5.1 Model and Methods 3.5.2 Lattice Results for Consistent and Covariant Anomalies 3.5.3 Influence of the Mass Term 3.5.4 The Quest for One Third 3.6 The Action of Nodal Line Semimetals 4 Transport in Topological Semimetals 4.1 Longitudinal Magnetoresistance in Weyl Semimetals 4.2 Transversal Magnetoresistance in Weyl Semimetals 4.2.1 Model 4.2.2 Mesoscopic Transport in Clean Samples 4.2.3 Numerical Magnetotransport in the Presence of Disorder 4.2.4 Born-Kubo Analytical Bulk Conductivity 4.2.5 Numerical Results in Disordered Samples 4.2.6 Conclusion 4.3 Transport in the Presence of Axial Magnetic Fields 4.3.1 Model and Methods 4.3.2 Longitudinal Magnetotransport for Axial Fields 4.3.3 Conclusion 4.4 Transport in Nodal Line Semimetals 5 Nodal Line Semimetals from Weyl Superlattices 5.1 Weyl Semimetal on a Superlattice 5.2 Emergent Nodal Phases 5.3 Symmetry Classification of the Nodal Line 5.4 Surface States 5.5 Stability against Wave Vector Mismatch 5.6 Time-reversal Symmetric Weyl Semimetal 5.7 Conclusion 6 Symmetry Classification of the SYK Model 6.1 Model and Topological Classification 6.2 Overlap of Time-reversed Partners 6.2.1 Even Number of Majoranas 6.2.2 Odd Number of Majoranas 6.3 Spectral Function 6.3.1 Zero Temperature 6.3.2 Infinite Temperature 6.4 Symmetry-breaking Terms 6.5 Lattice Model 6.6 Conclusion 7 Conclusion and Outlook Appendix A Zak Phase and Extra Charge Accumulation Appendix B Material-specific Details for ARPES B.1 Relaxation Rates B.2 ARPES in Finite Magnetic Fields B.3 Estimates of the Chiral Chemical Potential Difference Appendix C Weyl Nodes in a Magnetic Field C.1 Scattering between Different Landau Levels C.2 Analytical Born-Kubo Calculation of Transversal Magnetoconductivity C.2.1 Disorder Scattering in Born Approximation C.2.2 Transversal Magnetoconductivity from Kubo Formula Appendix D Transfer Matrix Method D.1 Longitudinal Magnetic Field D.2 Transversal Magnetic Field Bibliography Acknowledgments List of Publications Versicherung

Numerous advancements and benefits of the digital age have been made possible by the advent of quantum computers, which is the result of a countless effort of researchers. The rate at which tasks are completed has significantly picked up, while at the same time, the size of these devices is continuing shrinking. When it became clear that even the silicon industry would soon reach its point of saturation, those in the research community became aware of the need to look for an alternative solution. And if we are talking about boosting the speed of computers and reducing the amount of storage space they occupy, there is yet another significant obstacle to overcome in terms of the conservation of energy. Researchers should be working on a solution right now because we are in the midst of a significant energy crisis, and this would be the best time for them to do so. It would be in their best interest to look into ways to reduce their energy consumption, given that we are already aware of how vital it is to pursue such avenues of inquiry. We are certain that the investigation of topological materials can make a contribution to the solution of a good deal of these issues, and we are very optimistic about this prospect (Figure 1.1). It is anticipated that perhaps up to 24 % of all materials will have some topological features [2]. As a consequence of this, the range of possible applications can be increased due to the wide variety of materials that are available. Over the course of the last decade, the expansion of the field of research that focuses on condensed matter physics has directly caused a sea change in the field as a direct result of the growth of materials [3]. These topological materials have the potential to bring scientists one step closer to discovering practical applications for unusual phases. Some of these applications include having the potential to revolutionize electronics and catalysis. These topological materials provide researchers with additional hope to find a solution for the energy crisis. Additionally, prior to the development of applications, it is necessary to identify materials that are suitable for these applications and to study the physical phenomena that are associated with these materials. There are a variety of topological materials that are currently being reexamined for use in improved thermoelectric devices, improved catalytic processes, and various spintronic devices. At the same time, researchers are also looking into new materials which can be used for technical applications in these fields. With this motivation of PhD thesis, several topological semimetals were synthesized to investigate their electronic and magnetic response, and the search for new topological materials with intriguing physical properties were also sought.

Topological materials have discovered ultrahigh magnetoresistance, chiral anomalies, the inherent anomalous Hall effect, and unique Fermi arc surface states. Topological materials now include insulators, metals, and semimetals. Weyl semimetals (WSM) are topological materials that show linear dispersion with crossings in their band structure which creates the pair of Weyl nodes of opposite chirality. WSMs have topological Fermi arc surface states connecting opposing chirality Weyl nodes. Spin-orbit coupling can result in the band opening in Dirac nodal rings, and creating the pair of Weyl nodes either by breaking the time-reversal or spatial inversion symmetry (but not both) 1-3. The chirality of a Weyl node is set by the Berry flux through a closed surface in reciprocal space around it. The purpose of this thesis was to characterize and investigate the thermodynamic stability of WSM. To accomplish these goals, quantum mechanical modeling at the level of density functional theory (DFT) was used. WloopPHI, a Python module, integrates the characterization of WSMs into WIEN2k, a full-potential all-electron density functional theory package. It calculates the chirality of the Weyl node (monopole charge) with an enhanced Wilson loop method and Berry phase approach. First, TaAs, a well-characterized Weyl semimetal, validates the code theoretically. We then used the approach to characterize the newly discovered WSM YRh6Ge4, and we found a set of Weyl points into it. Further, we study the stability of the kagome-based materials A3Sn2S2, where A is Co, Rh, or Ru, in the context of the ternary phase diagrams and competing binary compounds using DFT. We demonstrated that Co3Sn2S2 and Rh3Sn2S2 are stable compounds by examining the convex hull and ternary phase diagrams. It is feasible to synthesize Co3Sn2S2 by a chemical reaction between SnS, CoSn and Co9S8. Moreover, Rh3Sn2S2 can be produced by SnS, RhSn and Rh3S4. On the other hand, we found that Ru3Sn2S2 is a thermodynamically unstable material with respect to RuS2, Ru3S7 and Ru. Our work provides some insights for confirming materials using the DFT approach. 1. S. M. Young et al. Dirac Semimetal in Three Dimensions. Physical Review Letters108(14) (2012), 140405. 2. J. Liu and D. Vanderbilt. Weyl semimetals from noncentrosymmetric topological insulators. Physical Review B 90(15) (2014), 155316. 3. H. Weng et al. Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides. Physical Review X 5(1) (2015), 011029. / Thesis / Master of Applied Science (MASc)

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Materialien mit einer geringen, aber endlichen Zahl an beweglichen Ladungsträgern bieten eine interessante Plattform für die experimentelle Erforschung von niederenergetischen elektronischen Anregungen. Derartige Halbmetalle und Halbleiter mit geringer Bandlücke zeigen starke Effekte in Magnetfeldern, wie z. B. Quantenoszillationen und Magnetwiderstandseffekte, welche ein hilfreiches Werkzeug zur Untersuchung der elektronischen Eigenschaften darstellen. In Kombination mit verschiedenen experimentellen Techniken wie elektrischen und thermischen Transportmessungen, der Anwendung uniaxialer Spannung, und Ultraschallmessungen, kann man umfassende Informationen über die Wechselwirkungen und Symmetriebeziehungen in solch einem Material gewinnen. In letzter Zeit sind vor allem die topologischen Eigenschaften der elektronischen Bänder in den Fokus der Festkörperphysik gerückt, deren Beitrag zu den Transporteigenschaften insbesondere in Halbmetallen und Halbleitern mit geringer Bandlücke zu klären ist. In der vorliegenden Dissertation wurden drei solcher Materialien hinsichtlich ihrer außergewöhnlichen elektronischen Eigenschaften untersucht. In NbP, einem Halbmetall mit komplex geformter, anisotroper Fermi-Fläche, welche aus mehreren räumlich entarteten Taschen besteht, wurden die Effekte der Gitterdeformation untersucht. Die Anwendung uniaxialer Spannung führt zur Brechung der Kristallsymmetrie und damit zur Aufhebung der räumlichen Entartung der Fermi-Taschen, was mittels Analyse der Shubnikov-de Haas-Oszillationen im Magnetwiderstand nachgewiesen werden konnte. Weiterhin konnte durch Messung der im Ultraschall auftretenden Quantenoszillationen eine genaue Untersuchung der Anisotropie der Elektron-Phonon-Wechselwirkung durchgeführt werden. ZrTe5 ist ein aus zweidimensionalen Schichten bestehender Halbleiter mit geringer Bandlücke, welcher kürzlich aufgrund seiner besonderen Niedrigtemperatur-Magnetotransporteigenschaften größere Aufmerksamkeit erfahren hat. So weist ZrTe5 plateau-ähnliche Features im Hall-Widerstand, sowie einen ungewöhnlichen Magnet- und Hall-Widerstand im Quanten-Limit auf. Im Rahmen dieser Arbeit wurde der Effekt uniaxialer Spannung auf diese Transportphänomene untersucht, was dazu beitragen kann, deren bislang umstrittene Ursache aufzuklären. Schließlich wurden die elektrischen und thermischen Magnetotransporteigenschaften von GdPtBi untersucht, einem Halbleiter mit geschlossener Bandlücke, welcher sich durch das Vorliegen starker, lokalisierter magnetischer Momente ausgehend von den 4f-Elektronen des Gd auszeichnet. Es konnte gezeigt werden, dass das Auftreten von Anomalien im elektrischen Magnetotransport, welche ursprünglich den topologischen Eigenschaften der im Magnetfeld gekreuzten elektronischen Bänder zugeschrieben wurden, auch durch magnetische Wechselwirkungen zu erklären ist. Desweiteren konnte durch die Messung magnetfeldabhängiger thermischer Transporteigenschaften das Auftreten von Wechselwirkungen zwischen Phononen und magnetischen Momenten, sowie möglicherweise auch magnetischen Spinwellen, nachgewiesen werden. / Materials with a low, but finite density of charge carriers offer an interesting experimental platform for the investigation of electronic low-energy excitations. Such semimetals and narrow-gap semiconductors exhibit large magnetic-field responses, e.g., quantum oscillations (QOs) and magnetoresistance (MR) effects, that can be used as a powerful tool to study the electronic properties. In combination with experimental techniques such as electrical- and thermal-transport measurements, uniaxial-stress application, and measurement of the ultrasound velocity, a lot can be learned about the interactions and symmetry dependences in the materials. Recently, the topological properties of electronic bands became an important research field in condensed matter physics. Especially in semimetals and narrow-gap semiconductors, it is to be clarified to what extent exotic transport phenomena are related to topological effects. In this thesis, three such materials with intriguing electronic properties have been investigated. In NbP, a semimetal with a complex, anisotropic Fermi surface, consisting of spatially degenerate pockets whose degeneracy is tied to the symmetry of the crystal lattice, the effects of lattice deformation have been studied. Application of uniaxial stress breaks the crystalline symmetries and, thereby, lifts the degeneracy of the Fermi-surface pockets, which could be traced via analyzing Shubnikov-de Haas oscillations in the MR. Furthermore, the measurement of QOs in the ultrasound allowed for a detailed analysis of the anisotropy of the electron-phonon interaction in NbP. ZrTe5 is a layered narrow-gap semiconductor that recently attracted a lot of attention due to its remarkable low-temperature magnetotransport, namely plateau-like features in the Hall resistance as well as unconventionalMRand Hall resistance in the quantum limit. Here, the uniaxial-stress response of those features was investigated as a contribution to clarify their origin, which, to date, remains under discussion. Lastly, the electrical and thermal magnetotransport properties of GdPtBi were studied. GdPtBi is a zero-gap semiconductor that features the presence of large localized magnetic moments stemming from Gd’s 4 𝑓 -electron shell. The occurrence of anomalous features in the electrical MR was previously attributed to the topological properties of magnetic-field induced crossings of the electronic bands. However, in the course of this thesis it could be shown that those features can also be explained by magnetic interactions. Further, the presence of interactions between phonons and magnetic moments, and potentially also between phonons and magnetic spin waves, was demonstrated via measurement of a magnetic-field-dependent thermal resistance.