The work presented in this thesis investigates the behaviour of the Rashba semi-conductor BiTeI and of the topological insulator $\text{Bi}_2\text{Te}_3\,$ under pressure. Using Shubnikov-de Haas quantum oscillation measurements, the evolution of the Fermi surface of both materials was tracked as a function of pressure. At ambient pressure, two distinct quantum oscillation frequencies in BiTeI, corresponding to inner and outer Fermi surface orbits as a result of spin-splitting caused by the Rashba effect, were observed. Using a model Hamiltonian with a Rashba interaction term to model this system, experimental results were fitted to determine model parameters. Based on this model, carrier densities for the samples were calculated and there was good agreement with Hall effect measurements. The phase of the oscillations showed that both Fermi surfaces have a Berry phase of $\pi$ associated with them, consistent with theoretical predictions for a Rashba system. As pressure is applied, it was observed that the inner Fermi surface expands while the outer Fermi surface shrinks. Phase analysis of the oscillations showed deviations from the ambient pressure value, hinting at a topological transition. For $\text{Bi}_2\text{Te}_3\,$, we report the observation of two oscillation frequencies ($\sim 40$ T and $\sim 340$ T) at ambient pressures. Based on the angular dependence of the oscillation frequencies, phase analysis, and comparison against band structure from published ARPES results, it is deduced that the higher frequency oscillation corresponds to the surface state of $\text{Bi}_2\text{Te}_3$. Non-linear behaviour in the Hall measurement also suggests the presence of multiple bands, and a two-band model with parameters derived from quantum oscillation measurements is used to fit the experimental data. Under pressure, a slight decrease in the low field Hall coefficient and a new frequency appearing at $\sim 20$ kbar was observed. These may be signatures of a change in the Fermi surface of $\text{Bi}_2\text{Te}_3\,$ caused by an electronic topological transition.

This thesis presents the results of torque magnetometry and resistivity measurements of the electronic structure of novel quantum materials, specifically using the techniques of quantum oscillations and angle-dependent magnetoresistance oscillations. Measurements of the Fermi surfaces of these materials, alongside comparisons to the electronic structure predicted by density functional theory calculations, can elucidate much about the novel physical properties they exhibit and the competing interactions which govern their phase diagrams. The first system studied is the Iron-based superconductor FeSe_1-xS_x, an isoelectronically doped version of a system of much current interest, FeSe. Doping up to x = 0.2 is found to suppress the structural transition in this system entirely, with superconductivity continually present at low temperatures. Shubnikov-de Haas measurements across this range find a small quasi-two dimensional Fermi surface that increases in size and warping continuously with doping, with orbital dependent effective masses that do not change significantly within the orthorhombic phase. The second material studied is the antiferromagnetic intermetallic CeZn₁₁ which, featuring an unpaired 4f electron, is considered a possible candidate for heavy fermion behaviour. De Haas-van Alphen oscillations are seen once the antiferromagnetic phase is suppressed, and comparable frequencies of oscillation are measured in the non-magnetic analogue LaZn11, although with relatively smaller effective masses. GGA+U calculations, once magnetic breakdown is considered, match well the measured frequencies, confirming CeZn₁₁ to be a localised moment system with the 4f electron well below the Fermi level. The final material studied is the transition metal dichalcogenide IrTe₂, which undergoes dimerisation upon cooling into a number of possible charge modulated structures. Low temperature de Haas-van Alphen measurements find multiple domains of a quasi-two dimensional Fermi surface, no longer perpendicular to the lattice planes. Angular-dependent magnetoresistance oscillations observe a similarly tilted quasi-one dimensional Fermi surface, again with many domains present. Together these measurements confirm the unusual dimensionality of the dimerised Fermi surface of IrTe₂.

This thesis presents experimental studies of the electronic and magnetic properties of several iron-based unconventional superconductors, primarily using the techniques of magnetotransport and torque magnetometry in high magnetic fields and synchrotron-based angle-resolved photo-emission spectroscopy (ARPES). Superconductivity in the iron-based superconductors is always found in proximity to a magnetic phase, and the details of the electronic structure and Fermi surface are also important in determining the strength of interactions, and ultimately superconductivity. This motivates the experimental studies of electronic, magnetic and superconducting properties of Fe-based superconductors presented in this thesis. First, quantum oscillation measurements using high-field torque magnetometry are used to provide a partial determination of the Fermi surface of superconducting LiFeAs. The data are compared with density functional theory calculations, finding strong mass enhancements on the observed electron bands, however the hole bands are not observed. A large portion of this thesis concerns experiments on FeSe, which uniquely has a structural transition but is not magnetically ordered at any temperature. High field magnetotransport measurements show quantum oscillations, revealing small quasi-two dimensional Fermi surfaces, and it is argued that both hole and electron pockets are observed. The low-temperature Fermi surface consisting of one hole pocket and two electron pockets is also deduced from low-field magnetotransport. ARPES studies show that both hole and electron pockets undergo a significant elongation when cooling through the structural transition at ~90 K, interpreted as the result of orbital order. Measurements of the resistivity anisotropy above the structural transition are used to show that the structural distortion is electronically-driven. By combining these data sets, a complete picture of the symmetry-broken electronic structure of FeSe is constructed. The final chapter concerns another iron-based superconductor with a more complex crystal structure, the so-called ``10-3-8" phase, and in particular finds an unusual field-induced magnetic transition.

In the 4d transition metal oxides, the extension of the 4d orbitals leads to comparable and thus competitive kinetic and coulomb energies. As a result, small perturbations can induce significant changes in their physical properties, giving rise to a class of exotic phenomena that are rarely found in other materials. The ruthenates materials with readily tunable parameters open an avenue to study the strong electronic correlation in the rarely explored territory: the 4d transition metal oxides. The bilayered system, Ca3Ru2O7, belongs to the Ruddlesden-Popper series in which the physical properties are intimately linked to the lattice degrees of freedom. Ca3Ru2O7, with its quasi-2D and severe structure distortion, is believed to be placed in a unique position at which the role of orbital degrees of freedom is highlighted. The system displays strikingly different behaviors when the field is applied along different crystalline axes. A ferromagnetic (FM) state with full spin polarization is achieved for B||a-axis, but colossal magnetoresistance is realized only for B||b-axis by avoiding the ferromagnetic state. In addition, for B rotating within the ac-plane, slow and strong SdH oscillations periodic in 1/B are observed for T.1.5 K in the presence of metamagnetism. For B|| [110], oscillations are also observed but periodic in B (rather than 1/B) and persist up to 15 K. These properties together with highly unusual spin-charge-lattice coupling near the Mott transition (48 K) are driven by the orbital degrees of freedom. Complex thermodynamic properties are also observed in the other ruthenates system such as Sr4Ru3O10 and Pr3RuO7. The Sr4Ru3O10 is a triple-layered system that shows a dedicate balance between fluctuations and order. Besides the anomaly at TC=102K, anomalous behavior at low temperatures are also observed in the thermal study, indicative of an unusual magnetic order in this material. The Pr3RuO7 shows one-dimensional structure with zig-zag chain of corner sharing RuO6 octahedra running in parallel with the rows of edge-shared PrO8 pseudo-cubes. Magnetic and thermal properties studies on its single crystals indicate that the exchange interaction is strongly anisotropic. A Schottky-type anomaly at low temperature suggests that the gorderedh chain Pr ions are still sensitive to a crystal field.

Fermi surface, the locus in momentum space of gapless low-energy excitations, is a concept of fundamental importance in solid state physics. Electronic properties of a material are determined by the long-lived low-energy excitations near the Fermi surface. Conventionally, Fermi surface is understood as a property exclusive to a metallic state, contoured by electronic bands crossed by the Fermi level, although there has been a continuing effort in searching for Fermi surface outside the conventional description. In this thesis, techniques developed to prepare high-quality single crystals of SmB$_6$ and YBa$_2$Cu$_3$O$_{6+x}$ (abbreviated as YBCO$_{6+x}$ hereinafter) are described. By utilising measurement techniques of exceptional sensitivity and exploring a wide range of temperatures, magnetic fields, and electrical currents, we found signatures of unconventional Fermi surfaces beyond the traditional description in these strongly correlated electronic systems. SmB$_6$ is a classic example of Kondo insulators whose insulating behaviour arises due to strong correlation between the itinerant $d$-electrons and localised $f$-electrons. The peculiar resistivity plateau onsets below 4 K has been a decades-long puzzle whose origin has been recently proposed as the manifestation of topological conducting surface states. We found that the insulating behaviour in electrical transport is robust against magnetic fields up to 45 T, while prominent quantum oscillations in magnetisation are observed above 10 T. Angular dependence of the quantum oscillations revealed a three-dimensional characteristics with an absolute amplitude consistent with a bulk origin, and temperature dependence showed a surprising departure from the conventional Lifshitz-Kosevich formalism. Complementary thermodynamic measurements showed results consistent with a Fermi surface originating from neutral itinerant low-energy excitations at low temperatures. Theoretical proposals of the unconventional ground state uncovered by our measurements in SmB$_6$ are discussed. YBCO$_{6+x}$ is a high-temperature superconductor with a maximum $T_{\rm c}$ of 93.5 K and the cleanest member in the family of copper-oxide, or {\it cuprate}, superconductors. The correct description of electronic ground state in the enigmatic pseudogap regime, where the antinodal density of states are suppressed below a characteristic temperature $T^*$ above $T_{\rm c}$, has been a subject of active debates. While the quantum oscillations observed in underdoped YBCO$_{6+x}$ have been predominately interpreted as a property of the normal state where the superconducting parameter is completely suppressed at $\approx$ 23 T, we made the discovery that YBCO$_{6.55}$ exhibits zero resistivity up to 45 T when a low electrical current is used, consistent with the observation of a hysteresis loop in magnetisation. Quantum oscillations in the underdoped YBCO$_{6+x}$ are thus seen to coexist with $d$-wave superconductivity. Characteristics of the quantum oscillations are consistent with an isolated Fermi pocket reconstructed by a charge density wave order parameter and unaccompanied by significant background density of states, suggesting the antinodal density of states is completely gapped out by a strong order parameter involving pairing correlations, potentially in addition to the other order parameters. Transport measurements performed over a wide doping range show signatures consistent with pairing correlations that persist up to the pseudogap temperature $T^*$. The surprising observation of quantum oscillations in insulating SmB$_6$ and superconducting YBCO$_{6+x}$ demonstrates a possible new paradigm of a Fermi surface without a conventional Fermi liquid. A new theoretical framework outside the realm of Fermi liquid theory may be needed to discuss the physics in these strongly correlated materials with enticing electronic properties.

La découverte de l'effet Hall quantique par von Klitzing en 1980 a ouvert la voie à ce qui sera connu plus tard comme la théorie topologique des bandes. Dans le cadre de cette théorie, on ne s'intéresse plus uniquement à la relation de dispersion énergétique des électrons dans les cristaux, mais aussi à l'organisation topologique de la structure de bande. Cette théorie a permis la découverte d'une nouvelle phase de la matière, représentée par les isolants topologiques. Ces isolants topologiques ont de particulier qu'ils se comportent comme des isolants normaux dans le bulk, mais présentent des états de surface conducteurs. Dans cette thèse, on s'intéresse particu- lièrement aux isolants topologiques dits Z2, pour lesquels les états de surface sont protégés par la symétrie de renversement du temps : ils ne peuvent disparaître en présence d'une perturbation qui préserve cette symétrie sans que le système ne traverse une transition de phase quantique. Pour les isolants topologiques à trois dimensions, nous proposons dans cette thèse, un critère expérimental utilisant les oscillations quantiques magnétiques, permettant d'identifier un type particulier d'isolants topologiques : les isolants topologiques forts. Pour les systèmes à deux dimensions, nous nous sommes intéressés aux phénomènes liés à la rupture de la symétrie par renversement du temps à cause de la présence d'un ordre antiferro- magnétique. Dans ce cas, la symétrie d'importance devient le renversement du temps fois une translation. Dans ce contexte, nous avons tout d'abord établi analytiquement l'expression d'un invariant topologique pour les systèmes présentant aussi la symétrie d'inversion. Nous avons ensuite adapté trois méthodes numériques normalement utilisées dans le cadre des isolants topo- logiques invariants par renversement du temps : la méthode de la phase de jonction, la méthode des centres de charge des fonctions de Wannier et la construction explicite des états de bord. Nous avons montré qu'elles permettaient de tester la nature triviale ou topologique de plusieurs modèles théoriques pour lesquelles aucune méthode n'existait, par exemple les systèmes sans symétrie d'inversion. / The discovery of the quantum Hall effect by von Klitzing in 1980 paved the way for what is now known as topological band theory. In this theory, we are interested not only in the energy spectra of the electrons in crystals, but also in the topological structure of the bands. A new phase of matter was discovered thanks to this theory : the topological insulators. Topological insulators are unique in the sense that they behave like trivial insulators in the bulk, but possess metallic edge states. In this thesis, we are particularly interested in so-called Z2 topological insulators, whose edge states are protected by time reversal symmetry : they cannot disappear in the presence of a perturbation that respects this symmetry, without the system undergoing a quantum phase transition. For three-dimensional topological insulators, we propose an experimental criterion based on magnetic quantum oscillations to identify a special kind of topological insulators : the strong topological insulator. In two dimensions, we study the consequences of time reversal symmetry breaking due to anti-ferromagnetic order. In this case, the important symmetry is time reversal times a trans- lation. In this context, we first establish an analytical expression for systems that also have inversion symmetry. We then adapt three numerical methods usually employed for time reversal symmetric systems : the reconnection phase method, the Wannier charge center method and the explicit construction of edge states. We show that they are useful to probe the topology of models for which no methods were available ; such as non-centrosymmetric systems.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第22986号 / 理博第4663号 / 新制||理||1669(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 松田 祐司, 教授 石田 憲二, 准教授 笠原 裕一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

La plupart des matériaux étudiés en physique de la matière condensée sont à base de fermions massifs vérifiant les relations de dispersion paraboliques usuelles. Récemment, sont apparus un certain nombre de matériaux dotés de relations de dispersion linéaires : le graphène, système purement bidimensionnel et les isolants topologiques, composés tridimensionnels à base de Bismuth où les fermions de Dirac surfaciques coexistent avec les fermions massifs volumiques. À côté de ces deux grandes familles de matériaux de Dirac, on trouve le composé organique α-(BEDT-TTF)2I3, un système quasi-bidimensionnel du point de vue du transport électronique en raison de sa structure cristalline lamellaire et qui présente une phase de Dirac sous forte pression hydrostatique (P>1,5 GPa). Cette phase de Dirac est singulière puisque ses cônes de Dirac sont inclinés, et donc fortement anisotropes, et qu'ils émergent aux côtés d'une bande de porteurs de charge massifs. Ce travail de thèse porte ainsi sur l'étude, à la fois expérimentale et théorique, des effets des spécificités de la phase de Dirac du α-(BEDT-TTF)2I3 sur son transport électronique en régime quantique. Il examine notamment plusieurs modèles théoriques pour tenter d'interpréter les oscillations quantiques apériodiques mesurées dans le composé organique, ainsi que l'impact de l'inclinaison des cônes de Dirac. Les effets de dopage, surfacique et volumique, sur le α-(BEDT-TTF)2I3 sont également discutés. / The physics of most of the materials studied within condensed matter are based on massive fermions which verify the usual parabolic dispersion relations. Recently, a certain number of materials with linear dispersion relation have appeared: graphene, purely bidimensional and topological insulators, tridimensional compounds based on Bismuth where the surfacic Dirac fermions coexist with bulk massive fermions. Alongside these two families of Dirac materials, there is the organic α-(BEDT-TTF)2I3 compound, a quasi-bidimensional system from an electronic transport point of view because of its lamellar crystalline structure and which exhibits a Dirac phase under high hydrostatic pressure (P>1,5 GPa). This Dirac phase is singular: the Dirac cones are tilted, and highly anisotropic, and they emerge with a massive band. This work is then focus on the study, experimentally and theoretically, of the effects of the α-(BEDT-TTF)2I3 Dirac phase specificities on its electronical transport in quantum regime. It examines particularly several theoretical models to understand the aperiodic quantum oscillations measured in the organic compound, and the impact of Dirac cones tilting. Doping effects, surfacic and in the bulk, on the α-(BEDT-TTF)2I3 are also discussed.

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.

<p>In this thesis, we investigate the properties of a model of an anti-phase modulated d-wave superconductor, particularly in the presence of a magnetic field. This so-called model of $\pi$-striped superconductor has been proposed to describe the decoupling between Cu-O planes in $1/8$ doped La$_{2-x}$Ba$_{x}$CuO$_{4}$. The d-wave superconducting order parameter in a $\pi$-striped superconductor oscillates spatially with period 8 and zero average value. Unlike a uniform d-wave superconductor, this model has non-zero density of states at zero energy and exhibits an extended Fermi surface. Within Bogoliubov-de Gennes theory, we study the mixed state of this model and compare it to the case of a uniform d-wave superconductor. We find a periodic structure of the low-energy density of states, with a period that is proportional to $B$, corresponding to Landau levels that are a coherent mixture of particles and holes. These results are also discussed in the context of experiments which observe quantum oscillations in the cuprates.</p> <p>Furthermore, within Bogoliubov-de Gennes theory, a semiclassical approximation is used to study quantum oscillations and to determine the Fermi surface area associated with these oscillations in this model. The Fermi surface is reconstructed via Andreev-Bragg scattering, and the semiclassical motion is along these Fermi surface sections as well as between them via magnetic breakdown. Oscillations periodic in 1/B are found in both the positions and widths of the lowest Landau levels. The area corresponding to these quantum oscillations for intermediate pairing interaction is similar to that reported for experimental measurements in the cuprates. A comparison is made of this theory to data for quantum oscillations in the specific heat measured by Riggs et al.</p> / Doctor of Philosophy (PhD)