<i>Ab initio</i>Sternheimer-GW method for quasiparticle calculations using plane waves

Abstract

We report on the extension and implementation of the Sternheimer-GW method introduced by Giustino et al. [Phys. Rev. B 81, 115105 (2010)] to the case of first-principles pseudopotential calculations based on a plane-waves basis. The Sternheimer-GW method consists of calculating the GW self-energy operator without resorting to the standard expansion over unoccupied Kohn-Sham electronic states. The Green's function is calculated by solving linear systems for frequencies along the real axis. The screened Coulomb interaction is calculated for frequencies along the imaginary axis by using the Sternheimer equation. Analytic continuation to the real axis is performed using Pad\'e approximants. The generalized plasmon-pole approximation is avoided by performing explicit calculations at multiple frequencies using Frommer's multishift solver. We demonstrate our methodology by reporting tests on common insulators and semiconductors, including Si, diamond, LiCl, and SiC. Our calculated quasiparticle energies are in agreement with the results of fully converged calculations based on the sum-over-states approach. As the Sternheimer-GW method yields the complete self-energy $\ensuremath{\Sigma}(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}},\ensuremath{\omega})$ and not only its expectation values on Kohn-Sham states, this work opens the way to nonperturbative GW calculations and to direct calculations of spectral functions for angle-resolved photoemission spectroscopy. As an example of the capabilities of the method we calculate the G${}_{0}$W${}_{0}$ spectral functions of silicon and diamond.