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.