## Optical properties of bulk semiconductors and graphene/boron nitride: the Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

Publication: Research - peer-review › Journal article – Annual report year: 2012

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**Optical properties of bulk semiconductors and graphene/boron nitride: the Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies.** / Yan, Jun; Jacobsen, Karsten W.; Thygesen, Kristian S.

Publication: Research - peer-review › Journal article – Annual report year: 2012

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*Physical Review B (Condensed Matter and Materials Physics)*, vol 86, no. 4, pp. 045208., 10.1103/PhysRevB.86.045208

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*Physical Review B (Condensed Matter and Materials Physics)*,

*86*(4), 045208. 10.1103/PhysRevB.86.045208

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*Physical Review B (Condensed Matter and Materials Physics)*. 2012, 86(4). 045208. Available: 10.1103/PhysRevB.86.045208

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TY - JOUR

T1 - Optical properties of bulk semiconductors and graphene/boron nitride: the Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

AU - Yan,Jun

AU - Jacobsen,Karsten W.

AU - Thygesen,Kristian S.

N1 - ©2012 American Physical Society

PY - 2012

Y1 - 2012

N2 - We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method Grid-based projector-augmented wave method (GPAW). Single-particle energies and wave functions are obtained from the Gritsenko, Leeuwen, Lenthe, and Baerends potential [Phys. Rev. A51, 1944 (1995)] with the modifications from Kuisma et al. [Phys. Rev. B82, 115106 (2010)] 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 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.

AB - We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method Grid-based projector-augmented wave method (GPAW). Single-particle energies and wave functions are obtained from the Gritsenko, Leeuwen, Lenthe, and Baerends potential [Phys. Rev. A51, 1944 (1995)] with the modifications from Kuisma et al. [Phys. Rev. B82, 115106 (2010)] 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 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.

U2 - 10.1103/PhysRevB.86.045208

DO - 10.1103/PhysRevB.86.045208

M3 - Journal article

VL - 86

SP - 045208

JO - Physical Review B (Condensed Matter and Materials Physics)

T2 - Physical Review B (Condensed Matter and Materials Physics)

JF - Physical Review B (Condensed Matter and Materials Physics)

SN - 1098-0121

IS - 4

ER -