Ever since high-temperature cuprate superconductors were discovered in 1986, they have been a source of many mysteries and controversies among scientists. The biggest mystery is the mechanism of high-temperature superconductivity. While it is known that electrons bind together in Cooper pairs, it is not known why. A second mystery is the origin of the pseudogap, a state that exists above the superconducting critical temperature. To address these problems, experimentalists have been looking for new techniques to provide new perspectives.

In this dissertation, we study cuprate superconductors using the recently-developed technique of time- and angle-resolved photoemission spectroscopy (TARPES). This technique uses infrared laser pulses to excite materials out of equilibrium, and to probe their electronic structure. TARPES has matured to the point that we understand the technique, but have not fully explored the scientific possibilities. This work seeks to push the boundaries by finding and characterizing unusual phenomena in the TARPES data, and developing frameworks to understand them. In the process, we address the central mysteries of cuprate superconductors.

In Chapter 1, we outline the theory of conventional superconductors, including many technical details of electron-boson coupling. We then discuss cuprate superconductors, establishing the basic properties of their electronic structure and related controversies. In Chapter 2, we briefly discuss our experimental technique and what it measures. We also review the literature of TARPES studies on cuprates. Chapters 3, 4, and 5 describe three different studies on cuprates, each looking at a different phenomenon. Chapter 3 looks at the chemical potential, and finds a connection to the pseudogap state. Chapter 4 looks at the buildup time of non-equilibrium quasiparticles, and finds a connection to the stimulated recombination of Cooper pairs. Chapter 5 looks at the signatures of electron-boson coupling, and proposes a way to determine if it contributes to Cooper pairing. In Chapter 6, we briefly summarize the main findings and offer some concluding remarks.

Interest has been rising in systems, such as the iridates, where both spin-orbit coupling and Coulomb correlations play a prominent role, with theoretical proposals for a variety of exotic states. One such state, the spin-orbit Mott insulator, was discovered by Kim et al in Sr$_2$IrO$_4$ using angle-resolved photoemission spectroscopy, the experimental technique used in this work. Such states were later discovered in a variety of materials, including Sr$_3$Ir$_2$O$_7$, Na$_2$IrO$_3$, and RuCl$_3$ and provide a concrete testing ground for the physics of Mott insulators. This includes, naturally, the search for nearby exotic states which are the frequent companion of the Mott state. Indeed, significant attention has been given to doped Sr$_2$IrO$_4$ as an analog to the cuprate high-temperature superconductors, and to Na$_2$IrO$_3$, Li$_2$IrO$_3$, and RuCl$_3$ as candidates for hosting a spin-liquid state.

This work focuses on (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$, which is notable in the weakness of its parent Mott state and thus its likely proximity to other ground states. The substitution of La on the Sr site adds electrons as carriers to the system. This eventually destroys the insulating state, though manifestations of both Coulomb correlations and spin-orbit coupling remain well beyond the insulator-metal transition. Chapter 1 covers the physics relevant to the ground state of (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$, starting from the effects of Coulomb correlations and spin-orbit coupling in general and including an overview of the current experimental results in doped and undoped Sr$_2$IrO$_4$ and Sr$_3$Ir$_2$O$_7$. Chapter 2 summarizes the theory of (spin- and) angle-resolved photoemission spectroscopy (ARPES), and describes analysis techniques used in the later chapters. The main experimental results of the work obtained using spin-integrated photoemission are in chapter 3, including evidence for a novel ground state in lightly-doped (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ and a thorough exploration of the evolving role of Coulomb correlations with doping. Chapter 4 goes into more recent results from several spin-resolved ARPES measurements and their possible implications, including some outstanding puzzles in the results.

Interest in low-dimensional (<= 2-dimensional) semiconducting materials is ever growing as electronic device sizes shrink and new physics continues to emerge at such a microscopic scale. Heterostructures allow for a set of physical building blocks made from low-dimensional materials that can be used to tailor devices to obtain precise and unique electronic interactions and device characteristics. Over time as this field has grown, certain research materials that for a time were overlooked in favor of other materials have come into renewed interest as a result of their unique properties that were previously deemed not as useful or were simply left undetected. One such example of this is the family of thin film transition metal dichalcogenides (TMDs), whose unique monolayer and thin film photoluminescence, band gap transition, and spin-orbit-coupling-induced physics has recently been studied intensely as a result of their unique spintronics and valleytronics applications. Another example is C60 which has an extremely unique low-dimensional buckyball molecular structure. It too can take on a crystalline thin film form to be used in heterostructures and electronic devices, but experimental evidence of long-range electronic order in thin film C60 has been lacking until now.

This dissertation presents angle-resolved photoemission spectroscopy (ARPES) studies of multiple TMD and C60 compounds with supporting theory calculations to investigate the electronic stucture of these materials. Specific attention is given to the effects of spin-orbit coupling and orbital character. The relationship between the electronic properties of bulk and thin film TMDs is elaborated in detail with a focus on the valence band splitting at the K point. The first observation of a dispersive thin film C60 band structure is discussed as well as the unique photoemission traits of the C60 band manifolds. Study of the electronic properties of these low-dimensional TMD and C60 materials provides important considerations for current and future cutting-edge electronic device applications.

Novel electronic phases induced by unusual electronic structures have attracted central attention in condensed matter physics communities. One of such exotic electronic structures is a dispersionless flat band. The fundamental physics and possibility of the induced phases, including high-temperature superconductivity, magnetism, and fractional quantum Hall effects, have been discussed for past decades, and such a flat band has been considered as the driver of new exotic phenomena. Hence, the system with a flat band could be fertile to many novel states of the matter. However, due to the limited number of the systems hosting the flat bands, the detail mechanisms of the flat band-induced unconventional states remain still elusive. In this dissertation, we provide the new platforms to explore what phases can be driven in the proximity of a flat band when it is coupled to a strong correlation or topological physics. We show the experimental electronic structures on two different systems, measured using angle-resolved photoemission spectroscopy (ARPES).

Chapter 1 briefly introduces the basic concept of flat band systems with examples of the unconventional states with flat bands, establishing the flat band as the tool to achieve various quantum states of matter. We also provide the motivation of each study in this dissertation. Chapter 2 introduces an overview of the primary experimental technique used in this dissertation, ARPES, a direct probe of the electronic structure. Additionally, we briefly introduce the principle of density functional theory calculation.Chapters 3, 4, and 5 describe three different studies. In Chapter 3, we build the correlation by coupling different oxides and creating the states at the interface. Unlike conventional semiconductors, oxide interface systems host strong correlations. If some unconventional phases are driven by the combination of flat band and correlation effects, this system can be the analog of cuprate high-$T_\text{c}$ superconductors. Chapters 4 and 5 are the case of topological materials. We establish a new playground where the topological physics can couple to the flat band. We investigate the bulk electronic properties of a new topological semimetal in Chapter 4. On the other hand, we focus on the surface localized states of the same material in Chapter 5. Finally, in Chapter 6, we briefly summarize the main findings and offer some concluding remarks.

Strong interaction between the spin and orbital angular momentum of electrons in a material can give that material unusual quantum properties beyond what can be described by textbook band theory. It can lift the spin degeneracy of electronic bands and create a spin-momentum locking that can be a lever for electrical control of a material's magnetism. It creates a new state of matter: topological insulators, by twisting the energy ordering of electronic states. It adds complexity to how light interacts with the material, enabling some

means for pointing photoelectron spins in a chosen direction.

However, the way spin-orbit coupling is manifested in a material is shaped by the symmetries of the crystal. In presenting findings from topological insulators, this dissertation demonstrates how those symmetries can force a material to have multiple spin textures in momentum space, each coupled to a distinct atomic orbital. Further, it shows how changes to those symmetries can eliminate those orbital-dependent spin textures and leave a single overall spin texture. Lastly, it shows how symmetries can allow crystals to harbor hidden spin textures in certain parts of their real space unit cells even when the overall band structure is spin degenerate. This last point is demonstrated in a cuprate high temperature superconductor, in which the newly discovered spin structure could have profound implications for the nature of superconductivity.

The results presented in this dissertation come from spin- and angle-resolved photoemission measurements of several quantum materials using a uniquely efficient and high resolution spectrometer. The details of how the spectrometer works when coupled with a laboratory-based laser and how that enables new experiments that were otherwise infeasible are given.

This dissertation is organized into six chapters. Chapter 1 reviews atomic spin-orbit coupling and ways it can influence the properties of materials. Chapter 2 explains spin- and angle-resolved photoemission and the unique instrumentation used for experiments in this work. Chapter 3 details experiments that show how spin textures in materials can couple to different orbitals. Chapter 4 shows how that coupling can break down when symmetry no longer requires it. Chapter 5 presents surprising findings of a spin texture hidden in a cuprate superconductor. Chapter 6 presents discussion of future research directions on the study and manipulation of the spin-orbit interaction in materials.

The demands for new technologies with fast computation, efficient data storage, and low energy cost encourage the search for new matter of phases as well as novel quantum mechanisms. Exotic phenomena, such as high-temperature superconductivity, colossal mag- netoresistence, and topological insulator, naming three examples out of many, of quantum materials open the route to achieve these goals in which the conventional materials can- not easily accomplish. The underlying physics of these novel properties originate from the crystal symmetry, band topology, and the interplay between different degrees of freedom in the condensed phase of matter including electron charge, spin, orbital, and lattice, can- not be explained by the traditional quantum theory. Understand the multiple role of these determinants in quantum materials is not only pivotal from the viewpoint of fundamental physics research, it also encapsulates potential for exciting future applications, such as fast electronics and spintronics.

Angle-resolved photoemission spectroscopy (ARPES) has shown its power of revealing the electronic band structure in the reciprocal space by measuring the energy distribution of photo-ejected electrons with respect to kinetic energy and momentum. The development of spin polarimetry and efficient association with the energy analyzer allow direct measurements of the spin, energy, and momentum of the photoelectrons at the same time. As the electron spin has become one of the focus in condensed matter research, direct probe of such degrees of freedom is essential. By utilizing the unique power of spin-resolved ARPES (SARPES), we show the impacts of the crystal symmetry on the electron spin in the selected quantum materials, one with strong atomic spin-orbit coupling (SOC) but the electrons are weakly correlated and another with strong electron-electron correlation but weak atomic SOC, in this dissertation.

Content is organized into six chapters. Chapter 1 gives an introduction to the symme- try operations and the symmetry-driven spin asymmetry in the condensed phase. Chapter 2 reviews the working principle and the corresponding efficiency of various spin polarime- ters including the home-built SARPES station which collected the data presented in chap- ters 3–5. Chapter 3 contains a brief discussion of topology physics and the detailed spin-momentum locking pattern of topologically trivial and non-trivial surface states of a strong three-dimensional topological insulator. Chapter 4 details the hidden spin texture found a high Tc superconductor. The strong spin polarization observed in such bulk centrosym- metric crystal with weak atomic SOC suggests the importance of local crystal symmetry which depends on the lattice distortion and atomic valency, which is addressed in Chapter 5. Finally, conclusions and future research directions are outlined in Chapter 6.

Single-layer graphene has been widely researched in recent years due to its perceived technological applicability and its scientific importance as a unique model system with relativistic Dirac Fermions. Because of its unique geometric and electronic structure, the properties of graphene can be tuned or manipulated in several ways. This tunability is important for technological applications in its own right, and it also allows us to study the fundamental properties of Dirac Fermions, including unique many-body interactions and the nature of the quasiparticles at half-filling. This thesis is a detailed examination of the electronic and structural properties of graphene, studied with angle-resolved photoemission spectroscopy (ARPES) and other surface science techniques like low-energy electron microscopy and diffraction.

This thesis is organized as follows. Chapter 1 gives an introduction to the electronic and structural properties of single-layer graphene. It provides a brief historical overview of major theoretical and experimental milestones and sets the stage for the important theoretical and experimental questions that this thesis addresses.

Chapters 2 and 3 describe the experimental setup. Chapter 2 discusses the experimental techniques used in this thesis with particular focus on the mechanics of ARPES. Chapter 3 discusses the different graphene growth techniques that were used to create our sample with particular focus on our characterization of epitaxial graphene on SiC(0001).

Chapters 4 and 5 form the meat of this thesis: they provide a thorough discussion of the electronic properties of graphene as studied by ARPES. Chapter 4 describes how various perturbations can result in the manipulation of the bare electronic band structure, including the deposition of atomic or molecular species on top of an epitaxial graphene sheet as well as the interactions between graphene and its substrate. Chapter 5 describes the many-body physics in single-layer graphene. It begins with a discussion of the electron-electron interaction in undoped graphene, demonstrating that these interactions qualitatively differ from ordinary metals and semiconductors and depart from the standard Fermi liquid picture for quasiparticles; it then continues by describing how screening the electron-electron and electron-impurity interactions can impact the electronic properties of graphene. Chapter 5 ends with a discussion of the doping-dependent coupling strength of the electron-phonon interaction.

With more than a quarter century of study, the high temperature superconducting cuprates still represent one of the most active areas of research in condensed matter physics. Its complex phase diagram continues to present challenges to our understanding, stemming from its correlated electronic nature. Being able to tease out the effect of different lattice orderings and their effects on electronic states may be crucial to understanding the physics of the cuprates where such orderings may be crucial to the phase diagram. Thus, because of its ability to directly probe electronic band structure, Angle Resolved Photoemission Spectroscopy (ARPES) is an ideal probe to study the effects of competing orders on electronicstates near EF.

This thesis will be organized in the following way. Chapter 1 provides a broad introduction to the physics central to our work including concepts of band structure and Fermi liquid theory, as well as more exotic phenomena explored throughout the thesis. Chapter 2 introduces the ARPES technique, how it is physically understood via concepts like Green's functions, and traditional methods of data analysis. Chapter 3 explores magnetic ordering and its effect on both core level and valance band states in the iron oxypnictides. From the near-EF electronic states, we find that the magnetic physics of the parent compound may still be present even at superconducting dopings. Chapter 4 explores charge density wave (CDW) ordering by looking at the rare earth ditellurides. This ARPES work establishes LaTe2 as the first quasi-2D CDW system to behave like a true Peierls transition, with both Fermi surface nesting tied to a metal - to - insulating transition. Chapter 5 explores the effect

of lattice strain on electronic states by studying the single layered Bi2201 cuprates with lanthanide substitution. The effect of this substitution competes with superconductivity and appears to enhance bosonic modes acting on the nodal point states which are otherwise unaffected. Chapter 6 takes the specific case of Nd-Bi2201 and finds evidence of a distinct crossover point in the electronic states near EF segregating the nodal point states. Finally, Chapter 7 provides a summary of our work and its conclusions.

The origin of high-temperature superconductivity in cuprate ceramics is one of the great outstanding mysteries in physics. Discovered by Bednorz and Muller in 1986, the phenomenon has continued to both fascinate and baffle scientists for almost 30 years. At the heart of the cuprate problem lies the microscopic mechanism responsible for binding together Cooper pairs, which are a superconductor's lossless charge carriers. For most low-temperature superconductors, phonons are responsible, but Cooper pairs in the high- temperature superconductors may be bound together by magnetic interactions or even more exotic phenomena.

Although this most fundamental question remains unresolved, important insights continue to be gained in the field of high-temperature superconductivity, and many of them have originated from improved experimental methods and instrumentation. This thesis details progress in understanding the cuprate problem through the development and implementation of a high-resolution apparatus for conducting time- and angle-resolved photoemission spectroscopy (time-resolved ARPES). The technique works by using a near-infrared optical pump pulse to drive an electronic system out of equilibrium, and using an ultraviolet probe pulse to measure the subsequent dynamics of the nonequilibrium state using photoemission. Sub-picosecond time resolution is obtained by varying the path length of the pump pulse, and the net result is a movie of the relaxation dynamics of the band structure. Experimental results on the bi-layered cuprate superconductor Bi2212 are presented and discussed in detail.

Content is organized into eight chapters. Chapter 1 gives an introduction and overview of superconductivity research. Chapter 2 summarizes basic theoretical underpinnings of the ARPES technique, and reviews analysis techniques that are relevant to ARPES and time- resolved ARPES as well as simple models of quasiparticle recombination. Chapter 3 contains a detailed overview of the time-resolved ARPES system constructed in the Lanzara research group. Chapters 4, 5, 6, and 7 present scientific results obtained using time-resolved ARPES to study Bi2212. Finally, conclusions and future directions are discussed in Chapter 8.