Electron-phonon interactions from first principles

This article reviews the theory of electron-phonon interactions in solids from the point of view of ab-initio calculations. While the electron-phonon interaction has been studied for almost a century, predictive non-empirical calculations have become feasible only during the past two decades. Today it is possible to calculate from first principles many materials properties related to the electron-phonon interaction, including the critical temperature of conventional superconductors, the carrier mobility in semiconductors, the temperature dependence of optical spectra in direct and indirect-gap semiconductors, the relaxation rates of photoexcited carriers, the electron mass renormalization in angle-resolved photoelectron spectra, and the non-adiabatic corrections to phonon dispersion relations. Here we review the theoretical and computational framework underlying modern electron-phonon calculations from first principles, as well as landmark investigations of the electron-phonon interaction in real materials. In the first part of the article we summarize the elementary theory of electron-phonon interactions and their calculations based on density-functional theory. In the second part we discuss a general field-theoretic formulation of the electron-phonon problem, and establish the connection with practical first-principles calculations. In the third part we review a number of recent investigations of electron-phonon interactions in the areas of vibrational spectroscopy, photoelectron spectroscopy, optical spectroscopy, transport, and superconductivity.