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Topological insulators and superconductors, which are featured by not only the topological characteristics of their gapped bulk band structure but also the special edge or surface states, have attracted great attention in the past few years. A complete classification of topological insulators and superconductors in terms of symmetry and spatial dimension has been established, while the application of their surface states remains a challenge. The gapless phases which have topologically stable Fermi surfaces could also exhibit peculiar surface states and topological transport phenomena in the bulk. In this thesis, the topological DIII-classs superconducting chains and the application of its Majorana edge states are studied. On the other hand, Weyl semimetals, as the representative example of topological gapless phases, and its exotic transport phenomena are also investigated. Majorana edge states have been a focus of condensed matter research for their potential applications in topological quantum computation, which appear in the topological DIII-class superconducting chains protected by both the particle-hole and time reversal symmetries. We utilize two charge-qubit arrays to explicitly simulate one type of DIII-class superconducting chains and the universal quantum operations performed on the Majorana edge states. It is shown that combined with one braiding operation, universal single-qubit operations on a Majorana-based qubit can be implemented by a controllable inductive coupling between two charge qubits at the ends of the arrays. It is further shown that in a similar way, a controlled-NOT gate for two topological qubits can be simulated in four charge-qubit arrays. Although the current scheme may not truly realize topological quantum operations, we elaborate that the operations in charge-qubit arrays are indeed robust against certain local perturbations. Weyl semimetals possess nontrivial Fermi surface topology in that the pair of Weyl points with opposite topological charges is separated from each other in momentum space. The physical manifestations of this Fermi surface topology are protected surface states and exotic transport phenomena including the anomalous Hall effect as well as the chiral magnetic effect. By studying the path integral measure under the chiral transformation, it is shown that these transport phenomena can be described by the chiral anomaly which appears when the chiral Weyl fermion couples to the topologically nontrivial gauge field. The case of the gauge anomaly for the Weyl fermion coupled to a non-Abelian gauge field is also discussed. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

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archives@tulane.edu / The discovery of topological semimetals has attracted enormous interest since they not only possess many unusual exotic properties, but also offer a fertile ground for searching for new fermions in the low energy spectrum. The first established example of a topological state of matter is the quantum Hall effect, which supports a gapless edge state protected by topological invariance. Later the concept of topology has been extended to describe electronic band structure of solid state materials and this effort leads to discoveries of many new topological quantum states, such as Dirac cone state in graphene, quantum spin Hall insulator states in semiconductor quantum wells, 3D topological insulators, etc. The recently discovered Dirac/Weyl semimetals can be viewed as a 3D analog of graphene. This thesis work aims to discover new Dirac/Weyl semimetals through single crystal synthesis and characterization. This thesis is organized as follows: In chapter 1, I will first briefly review several basic concepts of topological properties and introduce a few prototype topological semimetals related to my thesis work. Since one important part of my thesis work involves single crystal growth of topological semimetals, I will introduce the crystal growth methods used in my research in chapter 2. In chapters 3, 4 and 5, I will present my experimental discoveries of new topological semimetals, including YSn2, CaSn3 and TbPtBi. I will not only show property characterization of these material, but also discuss their underlying physics. For YSn2, my work reveals that its slightly distorted square lattice of Sn generates multiple topologically non-trivial bands, one of which likely hosts nodal line and tunable Weyl semimetal state induced by the Rashba spin-orbit coupling (SOC) and proper external magnetic field. The quasiparticles described as relativistic fermions from these bands are manifested by nearly zero mass, and non-trivial Berry phases probed in de Haas–van Alphen (dHvA) oscillations. The dHvA study also reveals YSn2 has a complex Fermi surface (FS), consisting of several 3D and one 2D pocket. Our first principle calculations show the point-like 3D pocket at Y point on the Brillouin zone boundary hosts the possible Weyl state. Our findings establish YSn2 as a new interesting platform for observing novel topological phases and studying their underlying physics. In the study of CaSn3, we not only found it possesses non-trivial band topology, but also discovered its intrinsic superconductivity at 1.178 K. Its topological fermion properties, including the nearly zero quasi-particle mass and the non-trivial Berry phase accumulated in cyclotron motions, were revealed from the dHvA quantum oscillation studies of this material. Our findings make CaSn3 a promising candidate for exploring new exotic states arising from the interplay between non-trivial band topology and superconductivity, e.g., topological superconductivity. For the Half-Heusler compound TbPtBi, we have studied its field-induced Weyl semimetal state. We have observed remarkable transport signatures of its Weyl state, including the chiral anomaly, intrinsic anomalous Hall effect (AHE), and in-plane Hall effect. Moreover, we found TbPtBi exhibits a much larger AHE than the previously reported field-induced Weyl semimetal state in GdPtBi. The distinct aspect of TbPtBi is that Tb ions carry greater magnetic moments than Gd ions in GdPtBi (9.0B/Tb vs.7.0B/Gd). We find that such a moment increase in TbPtBi drastically enhances its AHE, with its anomalous Hall angle reaching as large as 0.50-0.76 in its antiferromagnetic (AFM) state. This finding not only strongly supports that the Zeeman effect due to the large exchange field from 4f electrons plays a critical role in creating the field-included Weyl state, but also provides clear evidence for the theoretical prediction that the intrinsic anomalous Hall conductivity is proportional to the separation of the Weyl points with opposite chirality. / 1 / Yanglin Zhu

Topological insulators(TIs) constitute a novel state of quantum matter which possesses non-trivial topological properties. Although discovered only in the recent few years, TIs have attracted intensive interest among the community of condensed matter physics and material science. TIs are insulating in the bulk but have conductive gapless edge or surface states on the boundaries, which have their origin in the nontrivial bulk band topology that is induced by the strong spin-orbital interactions in the materials. Existing in all dimensions, TIs exhibit a variety of exotic physics such as quantum spin Hall effect, momentum-spin locked surface states, Dirac fermion transport, quantized anomalous Hall effect, Majorana fermions, etc. In this thesis, I study the transport properties of 2D and 3D TIs by numerical approaches. As an introduction, a brief review of TIs is given. A detailed description of the numerical methods is also presented. The results can be summarized in four aspects. First, disorder is found be able to induce a non-trivial TI from an originally trivial band insulator, where the conductance of a two terminal device drops to nearly zero and then rises to form an anomalous plateau as disorder strength is increased, and finally all the states become localized. The real space Chern number calculation as well as the effective medium theory suggests that disorder is fundamentally responsible for the emerging of the extended helical edge states in this system. We also present a levitation and pair annihilation picture of the extended states for this model. Second, by making the 2D TIs into singly connected quantum point contacts(QPCs), I show a coherent and fast Aharonov-Bohm oscillation of conductance caused by the quantum interference of the helical edge states. This oscillation not only happens against weak magnetic field but also against the gate voltage in the zero-field condition. This results in a giant edge magnetoresistance of the device in weak magnetic fields. The amplitude of the magnetoresistance is controllable by adjusting either the QPCs' slit width or the interference loop size in the device. The oscillation is found robust against disorder. Third, by applying a uniform spin-splitting Zeeman field in the bulk of the 3D TI whose surface states can be viewed as massless Dirac fermions, I find chiral edge states on the gapped surfaces of the 3D TI, which can be considered as interface states between domains of massive and massless Dirac fermions. Effectively these states are result of splitting of a perfect interface conducting channel. This picture is confirmed by the Landauer-B?ttiker calculations in four-terminal Hall bars. Finally, I propose the concept of topological semi-metals. By calculating the local density of states on the surfaces, I demonstrate that surface states and the gapless Dirac cone already exist in the system although the bulk is not gapped. We show how the uni-axial strain induces an insulating band gap and turn the semi-metal into true TI. We predict existence of quantum spin Hall effect in the thin films made of these materials, which can be significantly enhanced by disorders. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

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Thesis advisor: Kenneth S. Burch / Since their first experimental realizations in the 2000s, bulk electronic topological materials have been one of the most actively studied areas of condensed matter physics. Among the more recently discovered classes of topological materials are the Weyl semimetals whose low energy excitations behave like massless, relativistic particles with well-defined chirality. These material systems display exotic behavior such as surface Fermi arc states, and the chiral anomaly in which parallel magnetic and electric fields lead to an imbalance of left- and right-handed particles. Much of the research into these materials has focused on the electronic properties, but relatively little has been directed towards understanding the vibrational properties of these systems, or of the interplay between the electronic and vibrational degrees of freedom. Further, the technological potential of these materials is still underdeveloped, with the search for physical properties enhanced by the topological nature of these materials being sought after. In this dissertation we address both of these issues. In Chapters III and IV we present temperature dependent Raman investigations of the the Weyl semimetals WP2, NbAs, and TaAs. Measurements of the optical phonon linewidths are used to identify the available phonon decay paths, with ab-initio calculations and group theory used to aid the interpretation of these results. We find that some phonons display linewidths indicative of dominant decay into electron-hole pairs near the Fermi surface, rather than decay into acoustic phonons. In light of these results we discuss the role of phonon-electron coupling in the transport properties of these Weyl semimetals. In Chapter V, we discuss the construction of our "PVIC" setup for the measurement of nonlinear photocurrents. We discuss the experimental capabilities that the system was designed to possess, the operating principles behind key components of the system, and give examples of the operating procedures for using the setup. The penultimate chapter, Chapter VI, presents the results of photocurrent measurements using this setup on the Weyl semimetal TaAs. Through careful analysis of the photocurrent polarization dependence, we identify a colossal bulk photovoltaic effect in this material which exceeds the response displayed by previously studied materials by an order of magnitude. Calculations of the second-order optical conductivity tensor show that this result is consistent with the divergent Berry connection of the Weyl nodes in TaAs. In addition to these topics, Chapter II addresses the results of Raman measurements on thin film heterostructures of the topological insulator Bi2Se3 and the magnetic semiconductor EuS. By investigating the paramagnetic Raman signal in films with different compositions of EuS and Bi2Se3 we provide indirect evidence of charge transfer between the two layers. We also track the evolution of phonon energies with varying film thicknesses on multiple substrates which provides insight into the interfacial strain between layers. We conclude the dissertation in Chapter VII with a summary of the main results from each preceding chapter, and give suggestions for future experiments that further investigate these topics. / Thesis (PhD) — Boston College, 2020. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

The importance and promise that topological materials hold has been recently underscored by the award of the Nobel Prize in Physics in 2016 ``for theoretical discoveries of topological phase transitions and topological phases of matter." This dissertation explores the novel qualities and useful topologically protected surface states of topological insulators and semimetals. Topological materials have protected qualities which are not removed by weak perturbations. The manifestations of these qualities in topological insulators are spin-momentum-locked surface states, and in Weyl and Dirac semimetals they are unconventional open surface states (Fermi arcs) with anomalous electrical transport properties. There is great promise in utilizing the topologically protected surface states in electronics of the future, including spintronics, quantum computers, and highly sensitive devices. Physicists and chemists are also interested in the fundamental physics and exotic fermions exhibited in topological materials and in heterostructures including them. Chapter 1 provides an introduction to the concepts and methods of topological band theory. Chapter 2 investigates the spin and spin-orbital texture and electronic structures of the surface states at side surfaces of a topological insulator, Bi2Se3, by using slab models within density functional theory. Two representative, experimentally achieved surfaces are examined, and it is shown that careful consideration of the crystal symmetry is necessary to understand the physics of the surface state Dirac cones at these surfaces. This advances the existing literature by properly taking into account surface relaxation and symmetry beyond what is contained in effective bulk model Hamiltonians. Chapter 3 examines the Fermi arcs of a topological Dirac semimetal (DSM) in the presence of asymmetric charge transfer, of the kind which would be present in heterostructures. Asymmetric charge transfer allows one to accurately identify the projections of Dirac nodes despite the existence of a band gap and to engineer the properties of the Fermi arcs, including spin texture. Chapter 4 investigates the effect of an external magnetic field applied to a DSM. The breaking of time reversal symmetry splits the Dirac nodes into topologically charged Weyl nodes which exhibit Fermi arcs as well as conventionally-closed surface states as one varies the chemical potential. / Ph. D.

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This diploma thesis deals with an optimization technique for the determination of semimetals in selected samples of food, which consists of sample digestion, preconcentration and detection of the elements. Preconcentration is usually chosen because these elements are contained in foods only in trace amounts, which are undetectable for some techniques. This work also made characteristics of semimetals, in terms of their functions in the body, of the occurrence in food and the consequences for the organism on their surplus or shortage. The chosen technique of preconcentration in this work was the preconcentration of titanium dioxide. When optimizing the techniques, however, was unlike the results published in literature, obtained low yield of elements sorbed on titanium dioxide, therefore the samples were measured by inductively coupled plasma mass spectrometry directly after their mineralization, wet digestion with low temperature. The results of this work indicate that the elements arsenic, boron and selenium are given technique detectable without preconcentration, whilst set germanium content in all samples failed, due to very low concentrations and therefore in these cases would be required preconcentration.