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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.

Quasi-two-dimensional (quasi-2D) semiconductors are the subject of intense research interest as platforms for both developing atomically-thin devices and exploring novel physics. These are atomically-thin structured derived from layered materials with covalent bonding in each layer and weak coupling between layers so that individual monolayers can be easily peeled off. Changes in confinement and screening in reduced dimensions can lead to drastic changes in quasiparticle (QP) and optical properties when compared with bulk materials. In this dissertation, we use ab initio methods based on many-body perturbation theory (MBPT) to explain and predict the QP and optical properties of quasi-2D semiconductors. We describe the QP properties within the GW approximation, for single particle excitations, and the optical properties within the GW plus Bethe Salpeter equation (GW-BSE) approach, for two particle excitations, such as correlated electron-hole pairs, or excitons. We find that, in general, reduced dimensionality results in strong spatial variations in the screening of the Coulomb interaction as well as reduced total screening, allowing for strongly-bound, non-hydrogenic excitons. We then use this understanding to explore how changing the external screening environment through layering and substrate engineering can be used to tune properties of quasi-2D materials. Finally, we perform ab initio calculations of exciton dispersion in quasi-2D and show that the 2D Coulomb interaction can give rise to unusual, massless excitons. This dissertation is organized as follows:In chapter 1, we introduce the theoretical and computational techniques used to compute the QP and optical properties of real materials.In chapter 2, we calculate the QP bandstructure and optical spectrum of monolayer MoS2, a prototypical quasi-2D semiconductor. We find that monolayer MoS2 has very strongly-bound excitons, with binding energies that are two orders of magnitude larger than in the bulk. Moreover, we show that these excitons have excited states that do not follow the commonly used 2D hydrogenic model and that this strongly-bound, non-hydrogenic behavior arises as a consequence of fast spatial variations in the screening environment. For isolated systems, the screening is in fact diminished to zero in the limit of large distances compared to the layer thickness.The inhomogeneous screening found in quasi-low-dimensional systems introduces significant computational challenges because very fine spatial sampling is required to capture this variation in screening. In chapter 3, we develop new computational techniques to sample reciprocal space more efficiently, resulting in more than two orders of magnitude reductions in computational time for GW and GW-BSE calculations on low-dimensional systems.Based on our understanding of screening in MoS2, we then explore how screening from a substrate or capping layer might change the electronic and optical properties in other quasi-2D materials. In a joint experimental study, we find that a bilayer graphene substrate can renormalize the QP band gap and exciton binding energies in monolayer and few-layer transition metal dichalcogenides (TMDs) by as much as 30%. This work is discussed in chapters 4 and 5.In chapter 6, we discuss how the substrate screening effect is even more pronounced in black phosphorene, which has a lower intrinsic screening than TMDs. Consequently, encapsulation, which is commonly used to stabilize the material under ambient conditions, can completely eliminate the presence of bound excitons in few-layer systems, changing the optical spectrum qualitatively as well as quantitatively.Traditional implementations of the GW-BSE approach focus on excitons with zero center-of-mass momentum (Q), since these are the states probed by linear optical probes. However, exciton dispersion--energy as a function of Q--is essential to understanding properties such as exciton dynamics, lifetimes, and the formation of novel phases such as exciton condensates. In chapter 7, we implement GW-BSE for finite Q, and calculate the exciton bandstructure of MoS2. We find that, in general, the exchange interaction in 2D gives rise to a massless dispersion, while in MoS2 and other TMDs in particular, the interplay of the intervalley and intravalley exchange gives rise to a parabolic band and a massless, v-shaped band with a valley quantum phase of winding number two.

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.

We summarize the molgw code that implements density-functional theory and many-body perturbation theory in a Gaussian basis set. The code is dedicated to the calculation of the many-body self-energy within the G W approximation and the solution of the Bethe–Salpeter equation. These two types of calculations allow the user to evaluate physical quantities that can be compared to spectroscopic experiments. Quasiparticle energies, obtained through the calculation of the G W self-energy, can be compared to photoemission or transport experiments, and neutral excitation energies and oscillator strengths, obtained via solution of the Bethe–Salpeter equation, are measurable by optical absorption. The implementation choices outlined here have aimed at the accuracy and robustness of calculated quantities with respect to measurements. Furthermore, the algorithms implemented in molgw allow users to consider molecules or clusters containing up to 100 atoms with rather accurate basis sets, and to choose whether or not to apply the resolution-of-the-identity approximation. Finally, we demonstrate the parallelization efficacy of the molgw code over several hundreds of processors. Program title: MOLGW Catalogue identifier: AFAW_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AFAW_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU GPL v3 No. of lines in distributed program, including test data, etc.: 167871 No. of bytes in distributed program, including test data, etc.: 1309269 Distribution format: tar.gz Programming language: Fortran 2003 with a few C subroutines, Python scripts. Classification: 7.3, 16.6, 16.10. External routines: libint [2], libxc [3], SCALAPACK [4] (optional) Nature of problem: Prediction of the electronic structure of atoms, molecules, clusters with a particular interest in their spectroscopic features, such as quasiparticle energies and optical spectra. Solution method: Using the GW approximation to many-body perturbation theory, MOLGW calculates total-energies, quasiparticle energies, and optical excitations. Additional comments: Python3 is required to run the test suite provided. Running time: From 30 s to a few hours References: [1] http://www.gnu.org/copyleft/gpl.txt [2] https://github.com/evaleev/libint [3] http://www.tddft.org/programs/octopus/wiki/index.php/Libxc [4] http://www.netlib.org/scalapack