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Direct/indirect band gap and exciton dispersion: Monolayer and bulk hexagonal boron nitride

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Direct/indirect band gap
and exciton dispersion: monolayer and bulk hexagonal boron nitride.

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Direct/indirect band gap and exciton dispersion: Monolayer and bulk hexagonal boron nitride

  1. 1. Des questions ouvertes depuis quinze ans ! Direct/indirect band gap and exciton dispersion: Monolayer and bulk hexagonal boron nitride L. Sponza, L. Schué, H. Amara, C. Attaccalite, F. Ducastelle, A. Loiseau, J. Barjon Graphene 2018 26-29/06 Dresden
  2. 2. - The curious spectra of hexagonal boron nitride (hBN) contradiction between electronic and optical properties modeling free carriers and excitons - Tight-binding model of the exciton validation of the model in the monolayer insight from the monolayer to the bulk - Ab initio exciton dispersion in bulk hBN conciliation of the contraddictions (theory) experimental evidences - Predictions about the Bernal stacking Outlook
  3. 3. Hexagonal boron nitride: electronic structure Monolayer Bulk: AA' stacking Energy(eV)Energy(eV) quasiparticle gap GGA + 2.75 eV direct K indirect KM 7.25 eV 7.35 eV T L. Sponza et al., arXiv:1806.06201 (2018) direct T direct M indirect TM 6.45 eV 6.28 eV 5.80 eV quasiparticle gap LDA + G0W0
  4. 4. Direct gap coupling only to photons (q=0) - High probability - High efficiency - Low probability - Low efficiency Expectations from direct and indirect gaps Indirect gap Momentum Energy AbsorptionEmission coupling to photons (q=0) and phonons (q≠0) Momentum Energy AbsorptionEmission
  5. 5. Diamant indirect ∼0.1% hBN indirect ∼15% ZnO direct >50% 5.8 6.0 6.2 5.3 5.4 5.5 L. Schué et. al., arXiv:1803.03766 (2018) High luminescence efficiency No abs/lum mirror symmetry Experimental luminescence of bulk hBN energy (eV) energy (eV) Lum. PLE ∼ Abs. AbsorptionLuminescenceParadigmatic indirect gap material (diamond) has low luminescence efficiency and abs/lum mirror symmetry holds for spectra. Absorption Luminescence
  6. 6. Diamant indirect ∼0.1% hBN indirect ∼15% ZnO direct >50% 5.8 6.0 6.2 5.3 5.4 5.5 Absorption Luminescence High luminescence efficiency Experimental luminescence of bulk hBN energy (eV) energy (eV) Lum. AbsorptionLuminescenceParadigmatic indirect gap material (diamond) has low luminescence efficiency and abs/lum mirror symmetry holds for spectra. Despite the indirect gap, luminescence efficiency is very high abs/lum specularity does not hold in bulk hBN L. Schué et. al., arXiv:1803.03766 (2018) No abs/lum mirror symmetry PLE ∼ Abs.
  7. 7. Exciton: electron-hole pairFree carriers: electron + hole Excitonic Hamiltonian on a basis of free carriers. Excitonic levels. Quasiparticle: scissor, GW... two 1-particle propagators Dipole-allowed transitions between points of the band structure. 1-particle and 2-particle excitations Bethe-Salpeter equation single 2-particle propagator
  8. 8. 1-particle triangular lattice attractive source 1-particle and 2-particle excitations L. Sponza et al., arXiv:1806.06201 (2018) T. Galvani, PRB 94 (2016) Excitonic model eh N B Arbitraryunits 1-particle model h e energy(eV) Density of states q Brillouin zone q q ab initio tight-binding
  9. 9. t⊥ = -2.33 eV t|| = 0.5 eV t2⊥ = -0.4 eV t2|| = -0.1 eV Γ K -0.6 -0.3 0.0 Energy(eV) From monolayer to bulk AA' L. Sponza et al., arXiv:1806.06201 (2018) Γ KΓ KΓ K -0.6 -0.3 0.0 Energy(eV) TB exciton TB exciton TB excitonTB exciton
  10. 10. 5.69 eV5.80 eV 6.28 eV Variations of the binding energy lead to a flattening of the excitonic dispersion. Direct (bright) and indirect excitons lie within 0.2 eV. ab-initio band structure Exciton dispersion in bulk AA' L. Sponza et al., arXiv:1806.06201 (2018) Free carriers Excitons bright ab initio e-h dispersion 5.50 eV Energy(eV) q 5.4 6.2 6.4 6.0 Energy(eV) dark
  11. 11. L. Sponza et al., arXiv:1806.06201 (2018) 5.69 eV Free carriers Excitons dark bright ab initio e-h dispersion q 5.4 6.2 6.4 6.0 Energy(eV) Consistent explanation of the optical properties The energy difference is comparable to phonon energies. Thus final states are strongly coupled by phonons, and effectively mixed. 5.8 6.0 PLE ∼ Abs. Lum. energy (eV) 2) No abs/lum mirror because absorption passes through a resonant state, while luminescence does not. 1) high luminescence efficiency due to coupling between the two states. 5.50 eV
  12. 12. L. Sponza et al., Phys. Rev. B 97, 075121 (2018) Confirmation from experimental evidences Loss function at finite q R. Schuster et. al., Phys. Rev. B (2018) experiment K 0.7 Å-1 1.1 Å-1 0.7 Å-1 1.1 Å-1 theory GW+BSE+0.47 eV experiment GW+BSE+0.47 eV 5.8 6.1 6.4 6.7 Energy (eV) 0.7 Å-1 1.1 Å-1 KK/2 6.0 6.1 6.2 6.3 Energy(eV) 6.4 5.5 6.0 6.5 7.0 Energy (eV)
  13. 13. Intriguing prediction about Bernal stacking L. Sponza et al., arXiv:1806.06201 (2018) Bernal stacking TB exciton Γ KΓ K Energy(eV) -0.6 -0.3 -0.1 -0.2 -0.4 -0.5 -0.7 TB exciton Standard stacking for comparison -0.6 -0.3 -0.2 -0.4 -0.5 -0.7 Energy(eV) Γ KK/2Γ K K' ΓM T 5.5 6.0 6.5 7.0 7.5 8.0 -2.0 -1.5 -1.0 -0.5 0.0 Energy(eV) Energy(eV) 5.6 6.2 5.7 5.8 5.9 6.0 6.1 ab initio band structure ab initio exciton dispersion 6.13 eV6.01 eV 5.63 eV Free carriers Excitons 5.64 eV
  14. 14. Intriguing prediction about Bernal stacking L. Sponza et al., arXiv:1806.06201 (2018) Bernal stacking TB exciton Γ KΓ K Energy(eV) -0.6 -0.3 -0.1 -0.2 -0.4 -0.5 -0.7 TB exciton Standard stacking for comparison -0.6 -0.3 -0.2 -0.4 -0.5 -0.7 Energy(eV) Γ KK/2Γ K K' ΓM T 5.5 6.0 6.5 7.0 7.5 8.0 -2.0 -1.5 -1.0 -0.5 0.0 Energy(eV) Energy(eV) 5.6 6.2 5.7 5.8 5.9 6.0 6.1 ab initio band structure ab initio exciton dispersion 6.13 eV6.01 eV 5.63 eV Free carriers Excitons 5.64 eV Even though the gap is indirect, the Bernal stacking is predicted to behave as a direct-gap material from the spectroscopic point of view.
  15. 15. 1) Tight-bidning model for excitons in 2D and layered hBN. Insight when applied to bulk and to different polymorphs. 2) Flattening of the exciton dispersion in hBN leads to a mixed direct/indirect transition. Consistent explanation of conflicting data coming from experimental spectra and theoretical band structure. Experimental evidence of the theoretical explanation. 3) Prediction of even stronger effect in Bernal hBN. Conclusions Reasoned bibliography: - K. Watanabe et al., Nat. Materials 3, 404 (2004) - L. Schué et al., Nanoscale 8, 6986 (2016) - G. Cassabois et al., Nat. Photonics 10, 262 (2016) - L. Schué, L. Sponza et. al., arXiv:1803.03766 (2018) - T. Galvani et al., Phys. Rev. B 94, 125303 (2016) - L. Sponza et. al., Phys. Rev. B 97, 075121 (2018) - L. Sponza et al., arXiv:1806.06201 (2018) mostly experimental on luminescence mostly theoretical TB & ab initio

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