First-principles electron-phonon interactions with self-consistent Hubbard interaction: an application to transparent conductive oxides

The ab initio computational method known as Hubbard-corrected density functional theory (DFT+$U$) captures well ground electronic structures of a set of solids that are poorly described by standard DFT alone. Since lattice dynamical properties are closely linked to electronic structures, the Hubbard-corrected density functional perturbation theory (DFPT+$U$) can calculate them at the same level of accuracy. To investigate the effects of $U$ on electron-phonon (el-ph) interactions, we implemented DFPT+$U$ with a Hartree-Fock-based pseudohybrid functional formalism to determine $U$ self-consistently and applied our method to compute optical and transport properties of transparent conductive oxides of CdO and ZnO. For CdO, we find that opening a band gap due to $U$ restores the long-range Fr\"ohlich interaction and that its calculated mobility and absorption spectrum are in excellent agreement with experiments. For ZnO where a band gap already appears at the DFT level, DFPT+$U$ brings the results into much closer alignment with experiment, thus demonstrating improved accuracy of our method in dealing with el-ph interactions in these technologically important materials.