Optical properties of bulk semiconductors and graphene/boron-nitride: The Bethe-Salpeter equation with derivative discontinuity-corrected DFT energies

We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method GPAW. Single-particle energies and wave functions are obtained from the GLLBSC functional which explicitly includes the derivative discontinuity, is computationally inexpensive, and yields excellent fundamental gaps. Electron-hole interactions are included through the BSE using the statically screened interaction evaluated in the random phase approximation. For a representative set of semiconductors and insulators we find excellent agreement with experiments for the dielectric functions, onset of absorption, and lowest excitonic features. For the two-dimensional systems of graphene and hexagonal boron-nitride (h-BN) we find good agreement with previous many-body calculations. For the graphene/h-BN interface, we find that the fundamental and optical gaps of the h-BN layer are reduced by 2.0 eV and 0.7 eV, respectively, compared to freestanding h-BN. This reduction is due to image charge screening which shows up in the GLLBSC calculation as a reduction (vanishing) of the derivative discontinuity.