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.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20890号 / 理博第4342号 / 新制||理||1623(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 前野 悦輝, 教授 佐藤 昌利, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This dissertation presents our theoretical study of fundamental topological properties of ferromagnetic and antiferromagnetic systems, including topological magnetic excitations and topological magnetic textures. In the first part, we explored the topological magnonic phases in various systems with Dzyaloshinskii-Moriya interaction using a linear spin-wave theory. We have calculated the magnonic Chern number, topological phase diagram, and magnon thermal Hall conductivity at low temperature with tunable interactions due to the lattice deformation. In particular, we have investigated the topological phase transitions between distinct topological magnonic phases characterized by magnonic Chern numbers. We have also studied the magnon band topology and magnonic edge states in each topological phase. We found a sign reversal of the thermal Hall conductivity during topological phase transitions. We explicitly demonstrated the correspondence of thermal Hall conductivity with the topological edge states and their propagation directions. In the second part, a magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii-Moriya interaction was theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first established magnonic Snell’s law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii-Moriya interactions. Based on magnonic Snell’s law, we found that spin waves can experience total internal reflection. The critical angle of total internal reflection was strongly dependent on the sign and strength of Dzyaloshinskii-Moriya interaction. Furthermore, spin-wave beam fiber and spin-wave lens were designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii-Moriya interactions. In the last part, we studied the impact of spin Hall torque, spin transfer torque, and topological torque on the velocity-current relation of antiferromagnetic skyrmions with the aim of reducing the deformation. Using a combination of micromagnetic simulations and analytical derivations, we demonstrated that the lateral expansion of the antiferromagnetic skyrmion is reminiscent of the well-known Lorentz contraction identified in one-dimensional antiferromagnetic domain walls. We also showed that in the flow regime the lateral expansion is accompanied by a progressive saturation of the skyrmion velocity when driven by spin Hall and topological torques. This saturation occurs at much smaller velocities when driven by the topological torque, while the lateral expansion is reduced, preventing the skyrmion size from diverging at large current densities. Our findings suggested that a compromise must be made between skyrmion velocity and lateral expansion during the device design. In this respect, exploiting the topological torque could lead to better control of the skyrmion velocity in antiferromagnetic racetracks.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22112号 / 理博第4539号 / 新制||理||1652(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 前野 悦輝, 教授 松田 祐司, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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.

Thesis advisor: Ilija Zeljkovic / The splendid world of quantum materials is being unveiled in modern condensed matter physics, thanks to the advanced material synthesis methods, refined experimental probing techniques and deeper theoretical understanding. Unconventional superconductivity and topological phenomena are two of the main themes in this realm. Many outstanding problems are waiting to be solved and there is also a great potential in future technological applications. Among many routes of studying the quantum materials, creating thin film structures provides a special opportunity to learn the physical properties in low dimensions, to explore the effect of substrate and strain and to make novel electronic devices.In this thesis, I will present successful molecular beam epitaxy thin film synthesis of: (1) unconventional superconductor FeSe, (2) topological insulator Bi2Se3 doped with magnetic Fe atoms and (3) kagome structure magnets FeSn and Fe3Sn2. For (1), I will describe the finding of a dislocation network, its impact on the spatially-modulated strain field and its interesting interplay with the spontaneous symmetry-broken nematic phase. This is a new finding in the FeSe/SrTiO3 heterostructure and also provides fresh insights in the understandings of nematicity. For (2), I will show how we cross-check the doping ratio using different characterization techniques. Our observation indicates the possible formation of Fe clusters or impurity phases and sets the foundation for future synthesis of similar structures. For (3), I will demonstrate the novel selective synthesis of FexSny thin films. A plethora of spectral features were found in Fe3Sn2, implying a link with the Weyl physics. The FexSny thin films can potentially be a platform for the exploration of correlated, topological quantum phases in low dimensions. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

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.

<p>The capability of manipulation of the flow of mechanical energy in the form of mechanical waves (including acoustic and elastic waves) has always been a challenge and a critical part in various areas of engineering. The recent advances in topological acoustic/elastic metamaterials certainly open a new pathway to the manipulation of mechanical waves, especially for the novel scattering-immune wave-guiding capability, even in the presence of defects, disorders or sharp bends along the waveguide. In this Dissertation, the theoretical background and experimental evidence of various types of elastic-wave topological metamaterials including analogues to 2D quantum valley Hall effect (QVHE) materials, 2D quantum spin Hall effect (QSHE) topological insulators are presented. First, the formulation the elastic-wave analogue to QVHE materials in a general continuous elastic phononic structure (not limited to local resonant lattices, filling the gap in the literature) is proposed, and a strategy using pressurized cells to actively control the phononic lattice is presented. By finite prestrain and geometric nonlinear effect, the space inversion symmetry of the original hexagonal lattice is broken, resulting in distinct QVHE phases (characterized by valley Chern numbers) in lattice domains with opposite pressurization. With such mechanism, the edge-state path, i.e., the domain wall connecting lattices with distinct QVHE phases, can be real-time configured. Further more, edge states with tunable frequency-wavenumber dispersion can be created at the external boundaries of the lattice by appropriate pressurization of the outermost cells. An aluminum reticular sheet built with water-jet cutting is machined in the pre-deformed pattern with a Z-shape domain wall at the center, which spatially divides the sheet into two domains with opposite QVHE phases. Using piezoelectric transducers and laser Doppler vibrometry, the measured harmonic and transient responses confirm the back-scattering-immunity of the topological edge states, and the frequency-wavenumber dispersion matches the numerical prediction. A strategy is proposed for unidirectionally generating edge states along the domain wall using two off-phase transducers, which is also experimentally demonstrated. For elastic-wave analogue to QSHE topological insulators, we focus on the ``zone-folding'' method and propose a honeycomb 2D elastic beam network with periodically altered thickness with a generalized Kekule distortion pattern. Such framework provides a parametric space with exhaustive control in the topological phase diagram of waves in the lattice compared to earlier works in the literature. The effective Hamiltonian as well as the characterized topological phase are gauge dependent, particularly they change with different reference frames. This lead to ambiguity in the topological phase of such phononic crystal. Based on this argument, it is predicted that edge states could exist at a dislocation interface connecting two piece of phononic structures of the same pattern with relative displacement. Following the same idea, but considering the available fabrication options, a phononic plate with honeycomb groove pattern engraved on both sides is built, which the depth varied according to the Kekule pattern. With proper tuning of the parameters, it realizes an analogue to the QSHE topological insulator. With <em>ab initio</em> calculation of the Berry curvature (without involving any approximations such as the perturbative approach), a new topological invariant <em>local topological charge</em> is defined and evaluated as the counterpart of the Z₂ invariant in the classical-wave-zone-folding analogue. The local topological charge has intrinsic ambiguity and its value depends on the selected reference frame. However, its <em>change </em>according to changes in the parameters, under a consistent reference frame, is well-defined. Given the fact that shifting the reference frame by certain fractions of a lattice constant was equivalent to changing one of the parameters by a certain amount, it also lead to a well-defined change in the local topological charge, which indicates topological phase transition, and one can predict the existence of edge states at the displacement-dislocation interface between two neighboring lattices having the same pattern up to a rigid-body shifting. The phononic plate is machined by a CNC mill, and the experiment is carried out using piezoelectric transducers and laser Doppler vibrometry, which confirms the existence and robustness of the topological edge states at such dislocation interface connecting identical pattern, which was unprecedented in both quantum and classical systems. The final part of this Dissertation focuses on creating classical mechanical analogues to the 1D Kitaev superconducting model and Majorana-like bound states aimed at future acoustic-wave based computation.</p>

<div>Over the last decade, Dirac matter has become one of the most prominent fields of research in contemporary material science due to the incredibly rich physics of the Dirac equation. Notable examples are the Dirac cones in graphene, Weyl points in TaAs, and gapless edge states in Bi₂Te₃. These unique phases of matter are intimately related to the topological structure of Dirac fermions. However, it remains an open question if the topological structure of Maxwell's equations predicts yet new phases of matter. This thesis will conclusively answer this question.</div><div><br></div><div>Topological electrodynamics is concerned with the geometry of electromagnetic waves in condensed matter. At the microscopic level, photons couple to the dipole-carrying excitations of a material, such as plasmons and excitons, which hybridize to form new normal modes of the system. The interaction between these bosonic oscillators is the origin of temporal and spatial dispersion in optical response functions like the conductivity tensor. Our main achievement is motivating a global interpretation of these response functions, over all frequencies and wavevectors. This theory led us to the conclusion that there are topological invariants associated with the conductivity tensor itself. In this thesis, we show exactly how to calculate these electromagnetic invariants, in both continuum and lattice theories, to identify unique Maxwellian phases of matter. Magnetohydrodynamic electron fluids in strongly-correlated 2D materials like graphene are the first candidates of this new class of topological phase. The fundamental physical mechanism that gives rise to a topological electromagnetic classification is Hall viscosity which adds a nonlocal component to the Hall conductivity. To study the topological electrodynamics, we propose viscous Maxwell-Chern-Simons theory -- a Lagrangian framework that naturally generates the equations of motion, nonlocal Hall response and the boundary conditions. We demonstrate that nonlocal Hall conductivity is the spin-1 photonic equivalent of dispersive mass and induces precession of bulk photonic skyrmions. Nontrivial photonic skyrmions are associated with Dirac monopoles in the bulk momentum space and a singular Berry gauge. A singular gauge occurs when the photonic mass changes sign. Remarkably, the boundary of this medium supports gapless chiral edge states that are spin-1 helically-quantized and satisfy open boundary conditions.</div>

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