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.
