Condensed matter physics is a very broad and fast-developing field, which studies emerging phenomena, interactions, phases, and symmetries in materials, such as solids. Predictive first-principles, or ab initio, methodologies play a significant role in understanding various phenomena and new physics. This dissertation is aimed at developing new ab initio methodologies for the investigation of important novel phenomena and applying various ab initio methods combined with analytical approaches to a broad range of condensed matter systems, including the high-transition-temperature superconductor Ba1−xKxBiO3, the two-dimensional (2D) ferromagnet Cr2Ge2Te6, Dirac fermions generated in few-layer black phosphorus, defects in hexagonal boron nitride, and non-trivial topological surface states of antimony.

This dissertation is divided into two parts. Part I is focused on methods development, and Part II is a collection of theoretical and computational studies of novel materials. The dissertation is organized as follows:

Part I: Electronic structure methodologies for condensed matter

In Chapter 1, we review some important ab initio methods to lay the foundation for the development of a new ab initio method − named GW perturbation theory (GWPT) − in Chapter 2, and for various applications to the materials studied in Part II. In Chapter 1, we review the basics of density functional theory (DFT), the GW method, the general phonon formalism and electron-phonon (e-ph) coupling formalism, density-functional perturbation theory (DFPT), and the Wannier representation of e-ph coupling.

In Chapter 2, we present a new ab initio method, which we named the GW perturbation theory (GWPT). This method is a linear-response theory of the GW method, and it gives efficient and accurate access to all e-ph matrix elements at the many-electron level in the full Brillouin zone and between any pairs of electronic states. We discuss its general formalism, implementation and verification in this Chapter.

In Chapter 3, we develop a general renormalized spin-wave theory (RSWT) by including full sublattice dependence. This RSWT method includes magnon-magnon interactions, and therefore can give quantitative predictions of magnetic transition temperatures, especially in 2D. This method is solved numerically and self-consistently. We discuss its formalism, implementation, and behavior in this Chapter.

Part II: Studies of superconductivity, and electronic and magnetic interactions in novel materials

In Chapter 4, we apply our newly developed GWPT method to study superconductivity in Ba1−xKxBiO3, which shows an experimental superconducting transition temperature (Tc) of 30−32 K at optimal doping. Our GWPT calculations show that many-electron correlations significantly enhance the e-ph interactions compared to DFPT values for states near the Fermi surface and renormalize the e-ph coupling constant lambda by a factor of 2.4, nicely explaining the high Tc as well as the doping dependence observed in this family of material.

In Chapter 5, we present a collaborative work with experimental groups on the discovery of the 2D van der Waals ferromagnet Cr2Ge2Te6, probed using the scanning magneto-optic Kerr effect (MOKE) technique. We apply our RSWT method to this system, and our calculation nicely reproduces and explains the experimentally observed strong dimensionality effect in this 2D ferromagnet. Furthermore, our theory reveals an intriguing interplay between anisotropy and dimensionality, which leads to an unprecedented magnetic-field control of ferromagnetism in this system.

In Chapter 6, we propose a strategy for the generation of novel anisotropic Dirac fermions in few-layer black phosphorus by applying inversely designed superlattice potentials. We show that these novel quasiparticles exhibit asymmetric Klein tunneling, in which the perfect transmission direction significantly differs from the normal incidence direction. These unusual states are highly tunable and accessible with experimentally achievable conditions. The findings revealed in this Chapter provide new platforms for device design.

In Chapter 7, we present a collaborative work with an experimental group to study the electron-irradiation-induced triangular and hexagonal defects in hexagonal boron nitride, observed in transmission electron microscopy (TEM) measurements. We use DFT to calculate the formation enthalpy of different structures (as well as the edges and corners), to provide an overall diagram of preferred structures under different conditions at equilibrium. Our theory provides important insights into the formation of these defects.

In Chapter 8, we present a collaborative work with experimental groups to study the unusual behavior of photoelectrons from the topological surface states of Sb(111), measured with spin- and angle-resolved photoemission spectroscopy (spin-ARPES). Our theory, using the ab initio tight-binding method, reproduces well the observed spin textures. Our theoretical analysis shows that the unexpected spin-polarization behavior comes from the interplay between strong spin-orbit coupling (SOC) and the symmetry requirement of the electron wavefunction in high symmetry regions of the Brillouin zone.

In recent times, there has been a significant interest in low-dimensional materials due totheir unique electronic, optical, magnetic, and topological properties that differ from 3D bulk materials. This dissertation focuses on a specific class of 1D carbon structures known as graphene nanoribbons (GNRs), which can be synthesized atomically with precision through a bottom-up method. The theoretical tools employed in this study are primarily topological theory and quantum many-body first-principles calculations. Chapter 1 introduces some basics about density functional theory, GW many-body perturbation theory and the Belthe-Salpeter equation. Chapter 2 of this dissertation delves into the topology of GNRs when chiral symmetry is approximately maintained. Building on this theory and in collaboration with experimentalists, Chapter 3 explores a metallic 1D nanowire known as saw-tooth GNRs, while Chapter 4 investigates various quantum dot systems with unique bonding and anti-bonding characters. In Chapter 5, a different type of metallic GNRs is studied using zero-mode (topologically protected in-gap electronic states) engineering. Chapter 6 takes the study beyond the Hermitian Hamiltonian and introduces the non-Hermitian skin effect. When 1D or 0D structures are interconnected, nanoporous graphene is formed. Its electronic properties are studied in Chapter 8. Furthermore, Chapter 9 examines a carbon kagome lattice’s excitonic properties. The content of each Chapter is elaborated as the following: • Chapter 1 provides a foundational understanding of density functional theory (DFT) for ground state properties by introducing the Kohn-Sham equation and different functionals. We also discuss the GW perturbation theory, which allows us to incorporate many-body effects into our calculations of excited-state properties. Specifically, we explore how the GW method can be utilized to calculate quasi-particle excitations. To study the two-particle excitation problem for optical properties, we introduce the Bethe-Salpeter equation (BSE) method. This equation provides a framework for calcu2 lating the interaction between an excited electron and the hole it leaves behind, which is crucial for understanding optical properties such as absorption and emission spectra. • In Chapter 2, we examine GNR structures under the first nearest neighbor tightbinding model, assuming chiral symmetry holds. In this scenario, we utilize the first Chern number to obtain a Z index for general 1D materials. From the general Z index formula, we derive the Chiral phase index in vector form, which enables us to obtain the analytic Z index formula for all types of unit cells in GNRs. Finally, we explore a spin-chain formed by topological junction states that exhibit strong spin-spin interactions.[1] • Chapter 3 builds on the chiral classification theory introduced in Chapter 2 by utilizing the topological junction states as building blocks and connecting them in a symmetric manner to form a 1D metallic nanowire. We use first-principles DFT calculations to study the electronic bandstructure, local density of states (LDOS), and mapping of wavefunctions. Our results are then compared with experimental STM measurements, and we achieve good agreement. In addition, we also investigate the topological properties of asymmetrically connected structures, and the predicted junction/end state matches well the corresponding experimental evidence.[2] • In Chapter 4, we employed the topological junction states that arise from the connection between 7-armchair graphene nanoribbons (7AGNR) and 9-armchair graphene nanoribbons (9AGNR) to construct topological quantum dots. We investigated two distinct types of quantum dots by means of DFT calculations, with the aim of studying their electronic properties, such as the bonding and anti-bonding traits of their valence and conduction states. In addition, we devised a tight-binding theory to elucidate the underlying factors contributing to the characteristics of the wavefunctions.[3] • In Chapter 5, we focus on a different variety of metallic graphene nanoribbon (GNR) called Olympicene GNRs that does not exhibit the Stoner instability, which was observed in the sawtooth GNRs presented in Chapter 3. This new GNR features coveshaped edges, and its low-energy behavior is governed by zero modes. The most notable distinction between this GNR and the sawtooth GNR is that the nearest zero modes localize on different sublattices, leading to a significant increase in electron hopping and precluding any magnetic instability. To verify this, we conduct DFT calculations and compare our findings with experimental observations. • In Chapter 6, we explore the topology of 1D non-Hermitian systems, extending our analysis beyond Hermitian topological classification. Specifically, we investigate a 1D non-Hermitian system with no symmetry constraints, and use a Z index that can be employed to classify such systems. We examine the well-known skin effect for non-trivial non-Hermitian topological models and identify a promising GNR material, Co-4AGNR, which could potentially be realized in experiments. By conducting firstprinciples DFT and full-frequency GW calculations, we establish that the material 3 exhibits non-trivial topology. Lastly, we present evidence of the asymmetric transport properties in this material by calculating the Green’s function for a finite segment of this system. • In Chapter 7, we examine the 2D carbon structure that results from linking 1D metallic GNRs. To accomplish this, we created a theoretical model with low energy states using modes that are found in the pentagons located at the edge of GNRs as the bases. This effective tight-binding model provides a description of a unique, distorted super-graphene. We also conducted DFT calculations and compared our findings with experimental results provided by our colleagues.[4] • Chapter 8 focuses on the examination of a kagome lattice that is formed by linking triangulene building blocks. This unique structure was predicted to exhibit excitonic insulator (EI) behavior. In partnership with experimentalists, we conducted an investigation of the electronic properties of this structure using multiple levels of theory, such as DFT, GW-BSE, and Bardeen-Cooper-Schrieffer (BCS) theory. Our research revealed that DFT based single-particle theory was insufficient for accurately capturing the features of the LDOS map observed in STM measurements. By incorporating a BCS-like theory for condensation of excitons, we were able to provide an explanation for the experimental observations.[5] In addition to the projects above, I was also involved in 3 other projects, including one studying the color center in twisted BN [6], one studying the kondo effect in magnetic Ndoped chevronGNR [7], one studying the pseodo-atomic orbitals in graphene nanoribbons [8]. These research projects are also very interesting, but beyond the scope of this dissertation.

The dynamics of electrons governed by the Coulomb interaction determines a large portion of the observed phenomena of condensed matter. Thus, the understanding of electronic structure has played a key role in predicting the electronic and optical properties of materials. In this dissertation, I present some important applications of electronic structure theories for the theoretical calculation of these properties. In the first chapter, I review the basics necessary for two complementary electronic structure theories: model Hamiltonian approaches and first principles calculation. In the subsequent chapters, I further discuss the applications of these approaches to nanostructures (chapter II), interfaces (chapter III), and defects (chapter IV).

The abstract of each section is as follows.

Section II-1

The sensitive structural dependence of the optical properties of single-walled carbon nanotubes, which are dominated by excitons and tunable by changing diameter and chirality, makes them excellent candidates for optical devices. Because of strong many-electron interaction effects, the detailed dependence of the optical oscillator strength of excitons on nanotube diameter, chiral angle, and electronic subband index (the so-called family behavior) however has been unclear. In this study, based on results from an extended Hubbard Hamiltonian with parameters derived from ab initio GW-BSE calculations, we have obtained an explicit formula for the family behavior of the oscillator strengths of excitons in semiconducting single-walled carbon nanotubes (SWCNTs), incorporating environmental screening. The formula explains well recent measurements, and is expected to be useful in the understanding and design of possible SWCNT optical and optoelectronic devices.

Section II-2

Wave supercollimation, in which a wavepacket is guided to move undistorted along a selected direction, is a highly desirable property that is difficult to achieve for photons and has yet to be experimentally seen for electrons. Disorder in a medium would inhibit supercollimation. Here, we report a counter-intuitive phenomenon of electron supercollimation by disorder in graphene, made possible by its Dirac fermion states. We show that one can use one-dimensional disorder potentials to control electron wavepacket transport along the potential fluctuation direction. This is distinct from all known systems where the wavepacket would be further spread by the disorder and hindered in the potential fluctuating direction. This phenomenon has significant implications in the understanding and applications of transport in graphene and other Dirac fermion materials.

Section III-1

The origin of magnetic flux noise in superconducting quantum interference devices with a power spectrum scaling as 1 / f ( f is frequency) has been a puzzle for over 20 years. This noise limits the decoherence time of superconducting qubits. A consensus has emerged that the noise arises from fluctuating spins of localized electrons with an areal density of 5×10¹⁷ m^-2. We show that the physical origin of the phenomenon are localized metal-induced gap states at the interface. In the presence of potential disorder at the metal-insulator interface, some of the metal-induced gap states become localized and produce local moments. A modest level of disorder yields the observed areal density.

Section III-2

We present a microscopic theory of disorder-induced magnetic moment generation at nonmagnetic metal-insulator interfaces. Screened Hartree-Fock solution of a tight-binding Hamiltonian with electron-electron interaction, in which disorder is mimicked by the Anderson disorder model, shows that magnetic moments are originated from localized metal-induced gap states at the interface. Magnetic moment areal density becomes saturated at a maximum value of 4×10¹⁷ m^-2 as the disorder magnitude increases, consistent with the observed universality of measured local magnetic moment areal density. Dielectric screening effect is found to be essential for understanding the relatively universal behavior of the observed value.

Section IV-1

Optical initialization of the negatively charged nitrogen-vacancy (NV^-) center in diamond makes it one of the best candidates for realization of addressable spins in the solid state for quantum computing and other studies. However, its exact mechanism was not clear. We show that exact diagonalization of a many-electron Hamiltonian with parameters derived from ab initio GW calculations puts strong constraints on the mechanism. The energy surfaces of the low-energy many-body states and the relaxation processes of photo-excitation responsible for the optical initialization are calculated. Intersystem crossings are shown to be essential

Section IV-2

Graphene has been predicted to be a good test material for atomic collapse theory due to its linear band structure with a Fermi velocity 300 times slower than the speed of light. The Crommie group at UC Berkeley measured, using scanning tunneling microscopy, electrons bound to the positively charged calcium dimers on graphene, which corresponds to electrons collapsed to the super-heavy nucleus in artificial atoms. To compare measured bound states to atomic collapse theory in an artificial atom on graphene, the net charges associated with calcium dimers should be quantified. Here, we quantified the net charges associated with a calcium dimer using density function theory.

Recent advances in computational physics and chemistry have lead to greater understanding and predictability of the electronic and optical properties of materials. This understanding can be used to impact directly the development of future devices (whose properties depend on the underlying materials) such as light-emitting diodes (LEDs) and photovoltaics. In particular, density functional theory (DFT) has become the standard method for predicting the ground-state properties of solid-state systems, such-as total energies, atomic configurations and phonon frequencies. In the same period, the so called many-body perturbation theory techniques based on the dynamics of the single-particle and two-particle Green's function have become one of the standard methods for predicting the excited state properties associated with the addition of an electron, hole or electron-hole pair into a material. The GW and Bethe-Salpeter equation (GW-BSE) technique is a particularly robust methodology for computing the quasiparticle and excitonic properties of materials.

The challenge over the last several years has been to apply these methods to increasingly complex systems. Nano-materials are materials that are very small (on the order of a nanometer) in at least one dimension (e.g. molecules, tubes/rods and sheets). These materials are of great interest for researchers because they exhibit new and interesting physical and electronic properties compared to those of conventional bulk crystals. These physical properties can often be tuned by controlling the geometry of the materials (for example the chiral angle of a nanotube). Various DFT computer packages have been optimized to compute the ground-state properties of large systems and nano-materials. However, the application of the GW-BSE methodology to large systems and large nano-materials is often thought to be too computationally demanding.

In this work, we will discuss research towards understanding the electronic and optical properties of nano-materials using (and extending) first-principles computational techniques, namely the GW-BSE technique for applications to large systems and nano-materials in particular. While, the GW-BSE approach has, in the past, been prohibitively expensive on systems with more than 50 atoms, in Chapter 2, we show that through a combination methodological and algorithmic improvements, the standard GW-BSE approach can be applied to systems of 500-1000 atoms or 100 AU x 100 AU x 100 AU unit cells. We show that nearly linear parallel scaling of the GW-BSE methodology can be obtained up to tens of thousands (and beyond) of CPUs on current and future high performance supercomputers. In Chapter 3, we will discuss improving the DFT starting point of the GW-BSE approach through the use of COHSEX exchange-correlations functionals to create a nearly diagonal self-energy matrix. We show applications of this new methodology to molecular systems. In Chapter 4, we discuss the application of the GW-BSE methodology to semiconducting single-walled carbon nanotubes (SWCNTs) and the discovery of novel many-body physics in 1D semiconductors. In Chapter 5, we discuss the application of the GW-BSE methodology to metallic SWCNTs and graphene and the discovery of unexpectedly strong excitonic effects in low-dimensional metals and semi-metals.

In this thesis, I discuss the understanding and control of the optical properties of quasi-two-dimensional materials, an emerging field since the discovery of graphene. This thesis not only aims to understand and predict the distinct optical properties of quasi-two-dimensional materials from theoretical and numerical approaches, but also incorporates and quantitatively explains relevant experimental data when available. This thesis is organized as follows:

In the first chapter, I give a brief background overview on 1) research on excited states in general, 2) first-principles GW-BSE method that calculates the electron quasiparticle bands and exciton properties, and 3) recent progress on the optical properties of two-dimensional semiconductors and light-matter interactions in these materials.

In the second chapter, I review the valley physics in transition metal dichalcogenide monolayers, which builds the foundation of the more advanced topics that we discuss in the next chapters.

In the third chapter, I present several studies on the unusual optical properties of transition metal dichalcogenide monolayers arising from the novel exciton physics, including strongly-bound non-hydrogenic exciton series, light-like exciton dispersion, and magnetic brightening of the dark states. These results show the distinct optical properties of two-dimensional semiconductors compared with those in other dimensions.

In the fourth chapter, I demonstrate some consequences of topological effects on optical transitions in two-dimensional semiconductors, which leads to a new set of optical selection rules dictated by the winding number of interband optical matrix elements. The new selection rules go beyond the selection rules for conventional semiconductors which have been used for over 6 decades, and explains the experimental results on the photo-current spectroscopy of gapped bilayer graphene.

In the last chapter, I present materials engineering aspects of two-dimensional materials via van der Waals interfacial engineering. We show that by changing the interlayer stacking configurations and by applying out-of-plane electric fields, the electronic and optical properties of van der Waals layers can be rationally engineered and controlled.

Interactions (e.g., spin-orbit coupling (SOC), electron-hole, magnetic ordering, etc.) often give rise to dramatic new features in the excited-state physics of two-dimensional (2D) materials. Advanced first-principles methods greatly deepen our understanding of these interactions, and enable us to predict novel phenomena with high accuracy. In this dissertation, I discuss the formalism of several new features – i.e., full-spinor wavefunctions, magneto-optical (MO) effects, and self-consistency with vertex corrections in screening – in the framework of the GW and GW plus Bethe-Salpeter equation (GW-BSE) methods, the state-of-the-art many-body theoretical tools to explore condensed matter physics (Chapters 1–4). These techniques are then applied to 2D materials of recent interest (Chapters 5–8). This dissertation not only aims to understand and predict the excited-state physics of 2D materials with theory and first-principles calculations but also to elucidate relevant experimental data when available. The contents of this dissertation are organized as follows:

In Chapter 1, I briefly review some important concepts used throughout the dissertation: density-functional theory (DFT), many-body perturbation theory (MBPT), dielectric responses, and 2D materials. In particular, I review the basics of DFT and MBPT, from which the first-principles GW and GW-BSE methods are derived. Dielectric responses of materials are introduced as an application of the linear response theory to a many-electron system under external electromagnetic perturbations. Relevant physical quantities measured in experiments are explained and connected to first-principles calculations.

In Chapter 2, I introduce the SOC effect in solids and the formalism of full-spinor GW and GW-BSE methods. I focus on the total dielectric function, matrix elements involving spinor wavefunctions, the macroscopic transverse dielectric function tensor calculated at the GW-BSE level, and matrix elements of the current operator. Benchmark results of the full-spinor GW and GW-BSE methods are also presented.

In Chapter 3, I discuss the formalism of first-principles modeling of MO effects. The basics of magneto-optics are introduced, emphasizing the magneto-optical Kerr effect (MOKE) and Faraday effect (FE). MO signals are connected to the macroscopic transverse dielectric function tensor that can be calculated from first principles. Since this formalism will be applied to 2D magnetic insulators in Chapter 8, I also discuss the definition of dielectric function in 2D materials.

In Chapter 4, I present a new first-principles method – self-consistent with appropriate polarizability GW (swapGW). With swapGW, we can perform self-consistent GW calculations and incorporate the effects of vertex corrections in the polarizability through a BSE. Different self-consistent GW methods and the effect of vertex corrections are reviewed in detail. Our implementation of the swapGW method is benchmarked using bulk silicon.

In Chapter 5, I demonstrate a new set of optical selection rules dictated by the winding number of interband optical matrix elements, which is in fact due to a topological effect on optical transitions in 2D materials [1]. These selection rules are later verified by GW and GW-BSE calculations of gapped graphene systems.

In Chapter 6, I present a work in collaboration with experimentalists to study the strain engineering of the band gap in 2D InSe flakes [2]. We discover the ultrasensitive tunability of the direct band gap in few-layer InSe flakes by photoluminescence spectroscopy. We also develop a theoretical understanding of the strain-induced band gap change through first-principles DFT and GW calculations.

In Chapter 7, I discuss the important roles of the excitonic exchange interaction and SOC in reshaping the exciton states and modifying the optical properties of monolayer transition metal dichalcogenides [3]. Full-spinor GW and GW-BSE methods are employed to demonstrate the exchange-driven mixing of exciton states in monolayer MoS2. Our experimental collaborators use the 2D electronic spectroscopy (an ultrafast four-wave mixing spectroscopy technique) to demonstrate the intravalley exchange interaction unambiguously in both time and frequency domains.

In Chapter 8, I investigate the physical origin of giant excitonic and MO responses in 2D ferromagnetic insulators [4]. We show, with the full-spinor GW and GW-BSE methods, that excitonic effects dominate the optical and MO responses in the prototypical 2D ferromagnetic insulator, monolayer CrI3. In this work, we also predict the sensitive frequency- and substrate-dependence of MO responses by simulating the MOKE and FE signals in realistic experimental setups.

In condensed matter physics, first-principles methodologies play a significant role in understanding various interesting phenomena and physical laws, such as electronic and optoelectronic properties of crystals. And low dimensional materials exhibit many extraordinary physical properties due to quantum confinement, enhanced interaction, and special screening effects, and so on. Quasi-one-dimensional graphene nanoribbons (GNRs) are a promising new platform for future nanoelectronics applications, and the recent booming development of bottom-up synthesis techniques enables atomically precise synthesis of GNRs, so that GNRs of different widths, edge shapes and dopants could be well-studied.

This dissertation mainly focuses on the theoretical and computational study of the topological electronic properties of GNRs, the substrate interaction of doped GNRs, the design of a double-quantum-well GNR transistor, and the optical properties of conjugated polymers. This dissertation is organized as follows:

• In Chapter 1, we review the theoretical and computational methodologies that we used to calculate the electronic and optical properties of relevant low-dimensional materials in the dissertation, including density functional theory (DFT) for ground-state properties as well as the GW and the GW plus Bethe-Salpeter equation (GW-BSE) methods for excited-state properties.

• In Chapter 2, we present our study on the topological phases of armchair, cove-edged, and chevron GNRs, as well as GNRs with dopants by first-principles calculations and model-related methods. We further present a novel design of a periodically doped GNR structures with electric field tunable topological properties, which may have potential application in nanoelectronics.

• In Chapter 3, we show our detailed investigation of the bulk-edge correspondence in Z2 classification of quasi 1D systems by using model and first-principles calculations.

• In Chapter 4, we present a first-principles study of electronic properties of GNRs collaborated with the experimental groups. We investigate the strong interaction between the metallic substrate and the dopant states of the boron-doped armchair GNR for different doping concentrations. Strong substrate interactions have been observed both by first-principles calculations and scanning tunneling spectroscopy (STS) measurements.

• Chapter 5 focuses on an application study of the GNRs. We design a double-quantum-well GNR transistor and analyze the possibility of using such a device to break the thermal limit in the swing voltage in order to build energy efficient transistors. We test the validity of a double-quantum-well GNR transistor, and obtain the analytical form of spectral lineshapes of a quantum dot state coupled to a metallic wire with finite band width. The findings shown in this chapter reveal the theoretical principles in designing nanoelectronic transistors with low swing voltages.

• In Chapter 6, we present our first-principles study on the optical and excitonic properties of conjugated polymers using the GW-BSE methodology. We present detailed investigations on different approximations used in density functional theory and GW-BSE calculations and their effects to the calculated results. The new calculated absorption spectrum with improved methodologies agrees much better with the experiments than previous reported first-principles results. We also present a new development on the interface code bridging the BerkeleyGW code with an ab initio DFT code to enable GW-BSE calculations starting from DFT using metaGGA and hybrid exchange-correlation functionals.

The development of new technology for computing and renewable energy sources requires new insight into the physics governing state-of-the-art materials for these applications. To optimize the search for transistors and solar cells to supplant silicon, it is desirable to have them investigated in advance of their large-scale manufacture. One potentially fruitful avenue of investigation is the study of the electronic and optical properties of materials containing heavy atoms. Such atoms have a large spin-orbit coupling, which can be responsible for relatively exotic physics. Topological insulator materials such as $\Bi2Se3$ may have utility in the development of, for example, spin-tronics, in which information may be conveyed without the need for transporting electrical charge.

The details of charges moving through a material, as well as a material absorbing light, require a suitable theoretical treatment. Within the purview of the quantum theory of solids, the technique of many-body perturbation theory gives researchers access to the means of calculating one-particle and two-particle excited states, the exact scenario needed to understand charged excitations and optical absorption, respectively.

In this work, we further extend the ability of the many-body perturbation theory software package of BerkeleyGW to allow for more accurate description of solids containing heavy atoms. Namely, we investigate the properties of materials with large spin-orbit coupling by allowing for the treatment of two-component spinor wavefunctions. In the introduction, we review the physics of one- and two-particle excitations, entirely within a formalism allowing for the presence of spin-orbit coupling. In Chapter 2, we further discuss the implementation of spinor wavefunction functionality in BerkeleyGW and provide many test calculations using materials with varying strengths of spin-orbit coupling, with varying geometries, and including the metallic system of bulk gold. In Chapter 3, we present a calculation of the quasiparticle bandstructure of $\beta$-HgS as a further benchmark material, for which there requires elucidation of the bandstructure topology. We find very close agreement with experiment for both the effective mass and band gap. In Chapter 4, we present the bandstructure of the prototypical topological insulator $\Bi2Se3$, finding significant qualitative differences in the bandstructure from a quasiparticle calculation and the more readily available description from Density Functional Theory (DFT). Namely, we find that, in agreement with experiment, the conduction and valence bands are both nearly parabolic, in contrast to the well-known camel-back feature in the valence band of previous DFT calculations. Finally, in Chapter 5, we use DFT calculations to determine the ground-state geometry of Ir dimers adsorbed to graphene and confirm this geometry, that of a horizontal dimer across the so-called bridge sites, by comparing the resulting density of states to that measured by experiment. We find both have a strong central peak near the graphene Dirac point energy.

In this dissertation, I discuss the electronic and optical properties of materials for energy-related applications, with a focus on silicon (Si), gallium arsenide (GaAs) and the transition metal dichalcogenides (TMDs) in particular.

Si is the most widely used photovoltaic material today, dominating the photovoltaic industry by more than 90%. This is because Si is non-toxic, abundant and benefits from technologies developed over the years in the microelectronics industry. Despite its widespread usage as a photovoltaic material, Si does not efficiently absorb most of the light in the solar spectrum because it has an indirect bandgap. On the other hand, GaAs has a direct bandgap that is optimal for solar energy conversion, even though it is more expensive than Si and is also toxic due to the presence of arsenide. Nonetheless, in the atomically-thin film limit, both cannot be compared with the TMDs, absorbing significantly less light than the TMDs in the solar spectrum. This optical property of the TMDs makes them a very appealing class of candidate materials for flexible ultra-thin solar cells.

In Chapter 1, I give an overview of the different approaches that we use to address different problems in this dissertation. In Chapter 2, I discuss our work that aims to understand how the structure of an alternative Si phase can lead to an improved calculated absorption relative to diamond-Si. In Chapter 3, I discuss how we can use first-principles to calculate the hot carrier dynamics in GaAs, such as by calculating its electron-phonon relaxation times. In the Chapters 4, 5 and 6, I discuss the electronic and optical properties of mono- to few-layer TMDs. Not only are their quasiparticle bandgap and exciton energy levels affected by dielectric screening due to substrates, the dielectric screening environment can also be modified to engineer an intrinsic lateral heterojunction within a homogeneous TMD monolayer. In Chapter 7, we report the first observation and control of the Berry-phase induced splitting of the 2p-exciton states in monolayer MoSe2, and in Chapter 8, we study that the dynamics of atomically-sharp lateral heterojunctions between differently-stacked TMD domains.