The Electron-Phonon Interaction from First Principles

In this thesis the ground state electronic properties, lattice dynamics, electron-phonon coupling and superconductivity of a variety materials are investigated from first principles. The first chapter provides an introduction to the material and concepts of this thesis as well as motivation for the work done herein. Additionally, an overview is given on the theoretical background governing the calculations of this work. This includes overviews of the topics of density functional theory, the pseudopotential approximation, density functional perturbation theory, and applications of these approaches to the calculations of superconductivity. In the second chapter the mechanics of actually performing calculations within the methodology of chapter one are explained. This is accomplished through a detailed description of the computer software EPW. This software has been developed to allow computationally efficient approaches for calculating the electron-phonon interaction. A description of the software package, the particular quantities which it calculates and example calculations are given. The following two chapters present the results of calculations regarding electron-phonon coupling and superconductivity in bulk carbon compounds. The occurrence or absence of superconductivity is found to be related in these compounds to Fermi surface nesting and carrier concentrations. In chapter five we investigate the role of the fluorine dopant in the recently discovered (1111) Fe-pnictide superconductors. Contrary to the results of the literature published shortly after the discovery of these compounds, the presence of the dopant is found to actually result in a net decrease in the electron concentration on the Fe-plane within the local density approximation to density functional theory. In the two chapters which follow, we investigate the limits of two dimensional superconductivity in the recent experiments on ultra-thin Pb samples. Chapter six details calculations on freestanding Pb slabs constructed as thin as two monolayers. A useful formula predicting the electron-coupling strength and therefore estimating the superconducting transition temperature is developed. While in the next section a superconducting system is investigated wherein the important Pb-Si(111) interaction in ultra-thin Pb layers is taken into account. The observed superconductivity is explained by electron-phonon coupling and isotropic Migdal-Eliashberg theory. The observance of superconductivity in the nearly two-dimensional material is shown not to conflict with the predictions of the Mermin-Wagner theorem. In the final chapter, the phonon-assisted absorption of bulk silicon is calculated from first-principles. The calculated results are found to be in excellent agreement with experiment, and lead the way for the possibility of many first-principle studies on phonon-assisted optical processes in important technological devices.