Electron-electron interactions using Wannier functions

Electron-electron interactions are responsible for many condensed matter phenomena, and the related carrier dynamics plays a crucial role in advancing the next-generation energy and information technologies. Here we introduce a first-principles scheme that allows an efficient evaluation of the electron-electron screened interaction matrix elements, combining many-body perturbation theory calculations and the Wannier interpolation method. We highlight the locality of those matrix elements, thanks to the exponential decay in real space of the Wannier functions. Such a localized representation enables an efficient and accurate calculation of the momentum- and band-resolved electron-electron matrix elements, achieving an ultradense sampling of the Brillouin zone. By implementing the proposed methodology in the Phoebe code [1], we further investigate the Coulomb-mediated electron scattering and predict the electron hydrodynamics in graphene.

[1] A. Cepellotti et al., Journal of Physics: Materials 5 (2022).