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.

💡 Research Summary

The paper presents an efficient implementation of the Bethe‑Salpeter equation (BSE) for calculating optical properties within the projector‑augmented‑wave (PAW) framework of the GPAW code. The key innovation lies in using single‑particle energies and wave functions obtained from the GLLBSC functional, which explicitly incorporates the derivative discontinuity (DD). This discontinuity corrects the Kohn‑Sham gap, yielding fundamental band gaps that are close to experimental values while keeping the computational cost comparable to standard semi‑local DFT.

In the BSE step, electron‑hole interactions are treated with the statically screened Coulomb interaction evaluated in the random‑phase approximation (RPA). By avoiding a full GW quasiparticle correction, the workflow remains inexpensive yet accurate enough to reproduce the onset of absorption, the real and imaginary parts of the dielectric function, and the lowest excitonic peaks for a broad set of bulk semiconductors and insulators (Si, GaAs, InP, ZnO, MgO, AlN, etc.). The calculated spectra match experimental measurements and previously published GW‑BSE results, demonstrating that the GLLBSC‑BSE combination captures both the quasiparticle gap (through DD) and the excitonic binding energy (through BSE) with high fidelity.

The methodology is then extended to two‑dimensional systems: pristine graphene, monolayer hexagonal boron‑nitride (h‑BN), and a graphene/h‑BN heterostructure. For free‑standing h‑BN, the fundamental gap is around 6 eV, but when placed on graphene the derivative discontinuity essentially vanishes, reducing the fundamental gap by about 2 eV and the optical gap by roughly 0.7 eV. This gap renormalization is attributed to image‑charge screening from the metallic graphene layer, an effect that is naturally reflected in the GLLBSC calculation as a suppression of the DD term. The resulting optical spectra for the heterostructure agree well with earlier many‑body perturbation theory studies, confirming that the approach can describe interfacial screening without an explicit GW step.

Overall, the paper makes four major contributions: (1) it demonstrates that a DD‑corrected semi‑local functional can replace the costly GW step for BSE calculations; (2) it provides a robust, PAW‑based implementation that can be applied to both three‑dimensional bulk crystals and two‑dimensional layered materials; (3) it validates the method against a wide experimental dataset, showing quantitative agreement for dielectric functions and excitonic features; and (4) it offers a physically transparent picture of image‑charge screening in heterostructures via the behavior of the derivative discontinuity. These results suggest that the GLLBSC‑BSE workflow is a powerful tool for high‑throughput screening of optoelectronic materials and for investigating the electronic‑optical interplay in complex interfaces.