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Hexagonal Boron Nitride (hBN) as graphite is a lamellar compound. They share many physical properties and they can be exfoliated in monolayers for Van der Waals heterostructures. However a difference does exist, graphite is a gapless compound while hBN is a wide band gap material. In particular first principles calculations agree upon the existence of an indirect quasiparticle band gap: the conduction band minimum sits at the M point while the valence band maximum is around the K point of the Brillouin zone. On the experimental side the nature of the electronic band structure of hBN has animated a long-standing debate. Pioneering works of Watanabe et al. [1] have revealed the high UV radiative efficiency of hBN at room temperature. He first came to the conclusion that hBN was driven by direct excitonic recombination. Recently Cassabois et al. instead explained the luminescence lines to phonon-assisted recombination from an indirect exciton. Aiming to describe phonon-assisted luminescence a theoretical formulation that combines electron-hole interactions and electron-phonon coupling is needed. In recent years the method of finite differences turned out to be a powerful tool to treat the electron-phonon coupling in a perturbative way. So we combine Green’s function theory with finite difference electron-phonon coupling to get an accurate description of the phonon assisted luminescence spectrum of hBN.

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- 1. Phonon-Assisted Luminescencein hexagonal Boron Nitride ElenaCannuccia PhysicsDepartment, University of Rome“Tor Vergata” Aix-Marseille Université (France)
- 3. 3 Opto-electronic devices Fiber Optic Telecommunications Solid-State lighting Photodiode Solar Cell Laser Communication
- 4. 4 Blue LED
- 6. 6 Hexagonal Boron Nitride h-BN isa layered crystal iso-structural to graphite. Asgraphite, h-BN can beeasily exfoliated, and for this reason it findsapplicationsaslubricant.
- 7. 7 h-BN hasawideband gap and it’stransparent h-BN emitslight in theultraviolet Hexagonal Boron Nitride Yoichi Kubota et al. Science 317, 932 (2007); W. Aggoune C.Cocchi et al. PHYSICAL REVIEW B 97, 241114(R) (2018)
- 8. 8 Breaking news on h-BN !!! Directbandgap properties and evidence for ultraviolet lasing of hBN single crystal K. Watanabe et al. Nature Materials 3, 404 (2004)* *) results from Luminescence measurements Energy: 5.765 eV
- 10. 10 Direct vsindirect semiconductors : Phonon assistance Indirect band gap semiconductors are not efficient for photonics/optoelectronics
- 11. 11 Internal quantum yield 50% ZnO Bright Luminescence from Indirect and Strongly Bound Excitons in h-BN. L. Schue et al. Phys. Rev. Lett. 122, 067401 (2019)
- 12. 12 50% 0.1% ZnO Diamond Internal quantum yield Bright Luminescence from Indirect and Strongly Bound Excitons in h-BN. L. Schue et al. Phys. Rev. Lett. 122, 067401 (2019)
- 13. 13 45% 0.1% ZnO DiamondhBN 50% Internal quantum yield Bright Luminescence from Indirect and Strongly Bound Excitons in h-BN. L. Schue et al. Phys. Rev. Lett. 122, 067401 (2019)
- 14. 14 Direct or indirect band gap ...? … That isthequestion
- 15. 15 h-BN band structure and ARPES Direct observation of the band structure in bulk hexagonal boron nitride H. Henck, et al. PRB 95, 085410(2017)
- 16. 16 Electron energy loss spectroscopy on h-BN: probing its indirect nature
- 17. 17 Origin of the EELS peaks Loss function Peaksof L(q, ω) can beput in relation to inter-band excitations(∝ Im[ε(q, ω)]) and plasmon resonances(|ε| ≈ 0) Direct Observation of the Lowest Indirect Exciton State in the Bulk of Hexagonal Boron Nitride R. Schuster C. Habenicht, M. Ahmad, M. Knupfer, B. Büchner, PRB 97, 041201 (2018)
- 18. 18 hBN optical properties and excitons IP Electronhole interaction W. Aggoune C.Cocchi et al. PHYSICAL REVIEW B 97, 241114(R) (2018)
- 21. 21 Second step: Time dependent perturbation theory 1/2 Westart with theelectron-phonon Hamiltonian: exciton wave-function, Hamiltonian written in theexcitonic basisset: Thenew excitonic wave-functions: Emission Absorption
- 22. 22 Second step: Time dependent perturbation theory 2/3 Static approximation for dipoles but not for thetransitions and phonon modes are mapped at Γ point in asupercell Exciton-phonon dipolematrix elementscan bewritten in termsof derivatives and calculated by finite differences
- 23. 23 Second step: Time dependent perturbation theory 3/3 Electron–phonon coupling from finite differences B. Monserrat J. of Phys.: Cond. Matt. 30, 083001(2018) finite difference method T
- 25. 25 Something is missing Higherorder phonon sidebands Overtones of interlayer shear modes in the phonon-assisted emission spectrum of hexagonal boron nitride. T. Q. P. Vuong et al, PRB, 95(4), 045207 (2017) TheEPscattering is limited to onephonon at atime. Wecannot reproduce theovertonesinvolving interlayer shear modes and theasymmetric tails of theemission peaks. afinesampling of theexciton and phonon dispersions.
- 26. 26 Excitons and Luminescence Since excitons and optical phonons responsible for luminescence have similar radius, their coupling is efficient
- 27. 27 Conclusions Codes ● Exciton interference in hexagonal boron nitride L. Sponza, H. Amara, C. Attaccalite, F. Ducastelle, A. Loiseau Phys. Rev. B 97, 075121 (2017) ● Theory of phonon-assisted luminescence in solids: application to hexagonal boron nitride E. Cannuccia, B. Monserrat and C. Attaccalite arXiv preprint arXiv:1807.11797 https://journals.aps.org/prb/accepted/0f07dY44I2c17655543b6447ed3bcca77be0b885f ● Direct and indirect excitons in boron nitride polymorphs: a story of atomic configuration and electronic correlation L Sponza, H Amara, C Attaccalite, S Latil, T Galvani, F Paleari, L Wirtz, F. Ducastelle arXiv preprint arXiv:1806.06201 ● Two-photon absorption in two-dimensional materials: The case of hexagonal boron nitride C. Attaccalite, M Grüning, H Amara, S Latil, F Ducastelle arXiv preprint arXiv:1803.10959 ● We extended luminescence theory to include phonon scattering and interpret the luminescence spectra of h-BN in terms of phonon replica References