Title: Electronic Properties of Next-Generation Semiconductors
Description: The need for efficient, cheap, and durable semiconductors for photovoltaic and optoelectronic applications has spurred a number of dramatic recent developments in semiconductor quantum physics. Aided by advanced synthetic and characterization techniques, the development of high-quality, nano-structured, tunable materials has resulted in the observation of many novel phenomena. The goal of this thesis is to develop and apply methods in theoretical condensed matter science to the study of these promising materials. In Chapter 1 I explore methylammonium lead iodide (MAPbI3), a paradigmatic hybrid organic-inorganic perovskite system. To explain charge carrier dynamics in this material, I develop a microscopic tight-binding model. The average band structure is calculated and the magnitude of the temperature-dependent band gap opening and Urbach energy is quantified. The charge carrier mobility is calculated within a linear response formalism and its temperature dependence is characterized. Overall, the fully ab initio model is found to explain several non-trivial experimental phenomena while making minimal assumptions concerning the nature of the electron-phonon coupling and the character of the nuclear motion in these materials.

In Chapters 2 and 3, I turn to the subject of atomically-thin transition metal dichalcogenides. I improve upon past variational calculations of exciton and trion binding energies in these materials by applying diffusion Monte Carlo to exactly calculate exciton, trion, and biexciton binding energies within an effective few-body Hamiltonian. Carriers are assumed to experience two-body interactions of the Keldysh type that have been parameterized previously from electronic structure calculations. The structures of the exact ground state wavefunctions are calculated and compared to those of the previous variational trial wavefunctions. Next, I calculate the doping dependence of the rate of exciton and trion elastic scattering with free electrons within first-order time-dependent perturbation theory. The calculation provides the first theoretical estimate of the intrinsic trion linewidth in these materials. Finally, in Chapter 4, I study variants of the GW approximation to the one-particle Green's function for calculating correlation energies and spectral weights for the three-dimensional homogeneous electron gas.

By relating the cumulant generating function to the improper GW self-energy, I develop a new cumulant-based GW approximation. The approach is compared to existing methods first via solution of a simple linearly-coupled electron phonon model and later through application to the electron gas problem.