Hubbard-$U$-corrected electron-phonon interactions in strongly correlated materials via the finite-displacement method

Abstract

Although the density functional theory plus Hubbard $U$ correction method (DFT+$U$) is broadly used to study electronic structure of strongly correlated materials, the extension of this method to electron-phonon $g$ matrices has received limited attention. Here, we implement an algorithm that integrates DFT+$U$ method with the finite-displacement method for the calculations of phonons and electron-phonon $g$ matrices. The Hubbard $U$ corrections are applied not only to electronic and phonon structures, but, more importantly, also to electron-phonon $g$ matrices. We demonstrate our algorithm in two prototypical correlated materials: infinite-layer nickelates LaNiO$_2$ and ruthenium dioxide RuO$_2$. We find that: i) While the Hubbard $U$ corrections weakly increase the electron-phonon interaction of 20% hole-doped LaNiO$_2$, its total electron-phonon coupling remains small and is insufficient to account for the observed superconducting transition temperature of about 10-30 K. Our results contrast with the recent work showing that the full GW corrections yield an elevated electron-phonon coupling of 20% hole-doped LaNiO$_2$ five times larger than its DFT value. We attribute this discrepancy to the differences in the Fermi surface topology between DFT+$U$ and GW methods. ii) The inclusion of Hubbard $U$ corrections eliminates the imaginary phonon modes of RuO$_2$ under strain on the TiO$_2$ substrate and substantially reduces the electron-phonon coupling. Our results alleviate the discrepancy between the reported large theoretical electron-phonon coupling and the low superconducting transition temperature observed experimentally. Our work provides an algorithm that fully includes the Hubbard $U$ corrections on electron-phonon properties of correlated materials, and highlights the importance of Fermi surface shape and correlation effects on phonon spectrum and electron-phonon $g$ matrices.