Abstract

Density Functional Theory (DFT) is widely used as a powerful tool for studying the electronic structure of materials. However, due to the local or semilocal nature of exchange-correlation functionals, such as the local density approximation and generalized gradient approximation functional, DFT often underestimates the electronic band gap. Many-body perturbation theory (MBPT) within the GW approximation provides more accurate quasiparticle energies calculation by incorporating many-electron screening effects. Additionally, solving the Bethe-Salpeter Equation (BSE) allows for a detailed analysis of excitonic effects in optical spectra. Despite their accuracy, GW-BSE calculations are computationally expensive, particularly for large-scale systems such as defects and substrate-supported materials, making direct calculations impractical. In this thesis, I present comprehensive first-principles studies of excited-state properties in large-scale systems, addressing the primary computational challenges while ensuring accuracy. In Chapter 1, we provide an overview of first-principles approaches, starting from DFT and extending to MBPT. We emphasize the importance of accurately predicting excited-state properties and discuss the main computational challenges associated with large-scale systems. To overcome these challenges, we introduce two methods: the defect-patched screening method for systems containing point defects, and the fractional folding method for substrate- or encapsulation-influenced systems. These methods enable the practical treatment of large-scale systems that would otherwise be computationally prohibitive. Chapter 2 presents the detailed computational framework used throughout this work. We begin by introducing the Kohn-Sham equations within DFT, followed by a description of the MBPT within GW approximation for obtaining quasiparticle energies. To investigate the optical response of materials, we first outline the single-particle transition picture and then incorporate electron-hole interactions by introducing the concept of excitons. Finally, we present the BSE, which enables the calculation of exciton excitation energies and wavefunctions, providing a comprehensive description of excitonic effects in optical spectra. In Chapter 3, we investigate the quasiparticle energies and excitonic properties of α-phase Ruthenium (III) chloride (α-RuCl3) using first principles many-body perturbation theory calculation. α-RuCl3 has garnered significant attention due to its potential realization of Kitaev quantum spin liquid. By employing the GW calculation and solving the BSE, we find enhanced many body effects that dominate quasiparticle energies and optical responses in α-RuCl3. Our calculated quasiparticle band gap of bulk structure is about 1.75 eV that agree well with recent scanning tunneling spectroscopy and angle-resolved photoemission spectroscopy measurements. Our calculated primary excitonic features show good consistency with observed the optical absorption spectrum. Moreover, we extend our investigation to monolayer α-RuCl3, examining the zigzag antiferromagnetic (AFM) and ferromagnetic (FM) phases. In addition to significant excitonic effect., the optical spectrum of the zigzag AFM phase exhibits anisotropic behavior, while the FM phase demonstrates isotropic characteristics. The different optical response behaviors provide an efficient approach to identify the energy nearly degenerate magnetic states, which can both potentially exist in fabricated samples. In Chapter 4, we focus on accelerating GW calculations for point defects in supercell systems. While GW calculation provides accurate defect energy levels, modeling realistic isolated point defects often requires large supercells, making computations prohibitively expensive. To address this challenge, we propose the “defect-patched screening method”, which reduces the simulation cost of many-electron screening calculation — the primary computational bottleneck. This method decomposes the random-phase approximation screening into two parts: intrinsic screening, computed from the unit cell of the pristine structure, and defect-induced screening, evaluated within a small energy window in the supercell. Depending on the defect type, only intrinsic screening or both contributions may be needed, significantly reducing computational cost by avoiding the summation over numerous conduction states. We apply this method to a range of neutral and charged defects in both two-dimensional and bulk materials, demonstrating results consistent with direct GW simulations. In Chapter 5, we investigate twisted homobilayer transition metal dichalcogenides (TMDs) and introduce the “fractional folding technique” to account for substrate and encapsulation screening effects in GW calculations. A fundamental challenge in pursuing topological states in twisted TMD is the relative energies between the valence band extrema at the topologically trivial Γ and nontrivial K/K' valleys. We employ many-body perturbation theory within the GW approximation to investigate the energy difference of the valence band extrema in homobilayer WSe2 and MoTe2, the two most promising candidate platforms hosting various quantum phases. Notably, these quantum phases strongly prefer the K/K' valley to reside at the valence band maximum (VBM) to ensure the doped hole occupies the topologically nontrivial valleys. In contrast to the results obtained from density functional theory, the GW calculation predicts quasiparticle energies of the K/K' valley as the VBM above those of the Γ valley for all high-symmetry stackings. We further employ the "fractional folding" technique to include the substrate and encapsulation dielectric screening effects in GW simulations. We find that while environmental dielectric screening from h-BN reduces the energy difference between the K/K' and Γ valley extrema, the VBM remains situated at the topologically nontrivial K/K' valley. Finally, many-body effects can enhance the depth of the moiré potential, leading to a shift of the "magic angle", compared to the result from density functional theory. Our study offers quasiparticle energy landscapes to guide the search for twisted homobilayers of topological interest.

Committee Chair

Li Yang

Committee Members

Chong Zu; Rohan Mishra; Sheng Ran; Zohar Nussinov

Degree

Doctor of Philosophy (PhD)

Author's Department

Physics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

5-5-2025

Language

English (en)

Author's ORCID

https://orcid.org/0009-0007-9493-0426

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