Electron-phonon interaction using Wannier functions

We introduce a technique based on the spatial localization of electron and phonon Wannier functions to perform first-principles calculations of the electron-phonon interaction with an ultradense sampling of the Brillouin zone. After developing the basic theory, we describe the practical implementation within a density-functional framework. The proposed method is illustrated by considering a virtual crystal model of boron-doped diamond. For this test case, we first discuss the spatial localization of the electron-phonon matrix element in the Wannier representation. Then, we assess the accuracy of the Wannier-Fourier interpolation in momentum space. Finally, we study the convergence of the electron-phonon self-energies with the sampling of the Brillouin zone by calculating the electron and phonon linewidths, the Eliashberg spectral function, and the mass enhancement parameter of B-doped diamond. We show that more than ${10}^{5}$ points in the irreducible wedge of the Brillouin zone are needed to achieve convergence.