Quasiparticle states of hexagonal BN: A van der Waals density functional study

TL;DR

The paper addresses quasiparticle states in hexagonal BN under the influence of truly nonlocal-correlation effects by launching KI-DFT calculations from the consistent-exchange vdW-DF-cx functional (KI-CX) and comparing to KI-PBE, KS-DFT (PBE/CX), and GW benchmarks. It introduces and exploits the KI-CX framework, including a Koopmans correction that enforces piecewise-linearity, and uses DFPT with MLWFs to compute QP energies efficiently. The results show that KI-CX generally yields valence downshifts and CBM adjustments that bring QP gaps closer to GW values, capturing indirect vdW fingerprints and interlayer coupling in BN1, AB, and AA$'$ forms. The findings demonstrate that KI-CX provides a fast, robust alternative for vdW-inclusive QP predictions in layered materials, with broader implications for structure-QP correlations and potential integration with advanced vdW-DF hybrids for future materials discovery.

Abstract

We compute and track the impact of truly nonlocal-correlation effects on the quasi-particle (QP) band-structure of hexagonal boron-nitride (h-BN) systems. To that end, we start with the consistent-exchange vdW-DF-cx version [PRB 89, 035412 (2014)] of the van der Waals density functional (vdW-DF) method [JPCM 39, 390001 (2020)] for exchange-correlation (XC) functional design and enforce piece-wise linearity in the energy changes with partial charging, using the Koopmans-integer (KI) DFT framework [JCTC 19, 7079 (2023)]. Our approach and results (denoted KI-CX) extends present-standard use of KI DFT (denoted KI-PBE as it is based on the semilocal PBE [PRL 77, 3865 (1996)] XC functional) to capture, for example, the impact of the interlayer coupling on the QPs. We contrast KI-CX and KI-PBE results for the QP band-structure and compare with both $GW$ calculations and experimental observations of the (direct and indirect) QP gaps. We find that KI-CX brings improvements in the h-BN QP energy description and generally agrees with $GW$ studies.

Figures (6)

• Figure 1: Atomic as well as Brillouin-zone structure of h-BN structures in the single-sheet form, denoted BN1, and in the two stable bulk forms, AB and AA. The panels of the first and second row show the atomic structures as shown from a perspective perpendicular and parallel to the slide plane. The bottom panel shows the Brillouin zone (BZ) of the bulk h-BN forms in blue and the reduced BZ zone in red. This panel also identifies the set of high-symmetry $k$-points of the reduced BZ as relevant for these hexagonal systems.
• Figure 2: Comparison of BN1 QP band-structure predictions, as evaluated in PBE, CX and in KI-CX in a $c=20$ Å cell to minimize the impact of spurious couplings between repeated images in our planewave-DFT studies. The top of the KI-CX QP-valence band is used as a shared reference energy, as motivated in the text.
• Figure 3: Band structure comparison for h-BN structures AB and AA$'$, with KI-PBE and KI-CX results provided in KI-DFT and PBE and CX results in KS-DFT, i.e., using the same underlying CX functionals.
• Figure 4: Real-space canonical orbital densities $\abs{\langle \mathbf{r} \ket{\widetilde{w}_{\mathbf{R}i}}}^{2}$ at the CBM for h-BN structures BN1, AB, and AA$'$, computed using Koopmans-DFT as KI-CX. The iso-surface constant for BN1 is 5 meV and for AB and AA$'$ corresponds to 7 meV.
• Figure 5: Deviations with respect to $GW$ of our set of predictions for QP-transitions between the indicated set of high-symmetry $k$-points for AA$'$. We highlight the performance comparison at the fundamental gap, that is, for the QP transition that corresponds to having the smallest valence-conduction-band QP energy separation.