Electronic Transport: Electrons, Phonons and Their Coupling within the Density Functional Theory

This chapter considers the coupling between the ab initio description of the electronic and vibrational properties of materials, and the solution of transport equations. The purpose is to provide a more accurate description of transport with respect to usual models. Transport properties can be tackled from at least two viewpoints. In the first approach, an electrical current is seen as the consequence of an applied electric field. This led to the Drude model, Kubo formalism and the Boltzmann transport equation (BTE). The chapter particularly focuses on the latter formalism, and its coupling with the density functional theory (DFT). It provides basics of the description of the electronic structure within DFT, and discusses the interaction of electrons with the phonons. DFT and density functional perturbation theory (DFPT), have proved to be well grounded and practical tools of high added value that allow for the study of electronic transport properties with a minimum of fitting parameters.