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Invisible excitations in hexagonal Boron Nitride

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In this work we show how invisible excitations at zero or finite momentum can be probed with different experimental techniques.

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Invisible excitations in hexagonal Boron Nitride

  1. 1. Invisible excitations  in hexagonal Boron Nitride Claudio Attaccalite
  2. 2. Outline ● h­BN introduction ● Indirect excitations – EELS – Exciton interference ● Dark excitons in bulk h­BN – Origin – Non­linear spectroscopy ● Conclusions: excitons and luminescence
  3. 3. Hexagonal Boron Nitride h­BN is a  layered  crystal homo­structural to graphite. As graphite, h­BN can be easily exfoliated, and for this  reason it finds applications as lubricant .
  4. 4. Hexagonal Boron Nitride h­BN has a large band  gap and its transparent  h­BN emits light in the  ultraviolet
  5. 5. 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)*
  6. 6. 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)* Hexagonal boron nitride is an indirect band­gap  semiconductor G. Cassabois et al.,  Nature Photonics, 10, 262 (2016)* *) results from Luminescence measurements
  7. 7. h­BN band structure
  8. 8. h­BN band structure and ARPES
  9. 9. h­BN optical properties
  10. 10. Electron loss spectroscopy on h­BN
  11. 11. Theory: how to calculate e(w)  Excitons in boron nitride single layer T. Galvani et al., Phys. Rev. B 94, 125303 (2016)G. Strinati, Nuovo Cimento 11, 1 (1988)
  12. 12. Theory vs experiments Angular resolved electron energy loss spectroscopy in hexagonal boron nitride F. Fossard et al. Phys. Rev. B 96 115304 (2017)
  13. 13. May we probe indirect nature of h­BN  with EELS?
  14. 14. Theoretical results on EELS Exciton interference in hexagonal boron nitride L. Sponza, et al. arXiv preprint arXiv:1709.07397
  15. 15. Origin of the EELS peaks Exciton interference in hexagonal boron nitride L. Sponza, H. Amara, C. Attaccalite, F. Ducastelle, A. Loiseau arXiv preprint arXiv:1709.07397 Loss function  Peaks of L(q, ω) can be put in relation  to inter­band excitations (  Im[∝ ε(q, ω)]) and plasmon resonances (|ε|   0)≈
  16. 16. Origin of the EELS peaks Exciton interference in hexagonal boron nitride L. Sponza, H. Amara, C. Attaccalite, F. Ducastelle, A. Loiseau Physical Review B 97 (7), 075121 (2018) Loss function  Peaks of L(q, ω) can be put in relation  to inter­band excitations (  Im[∝ ε(q, ω)]) and plasmon resonances (|ε|   0)≈
  17. 17. 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) May we probe indirect nature of h­BN  with EELS?
  18. 18. Theory vs Experiment
  19. 19. Origin of peak intensity The contribution from K→M and M→ K’ has opposite sign When they have the same intensity the exciton is dark otherwise is bright
  20. 20. ● Indirect nature of h-BN can be probed by EELS ● Peaks intensity in EELS originates from constructive/destructive sum of finite momentum transition between M→K and K→M ● Theory explains recent experiments on h-BN at finite momentum Conclusions {at finite momentum}
  21. 21. Invisible excitons at zero  momentum (2n part)                           do you  have a finite  momentum?              Not, but I’m invisible             like you INVISIBLE EXCITONS
  22. 22. Nature of excitons in single­layer h­BN Tight-binding amplitudes for the two degenerate states, symmetric and antisymmetric with respect to the y- axis. Excitons in boron nitride single layer T. Galvani et al., Phys. Rev. B 94, 125303 (2016) Schematic splitting scheme of the 2p levels. (Lowest states are degenerate, one bright and one dark)
  23. 23. Nature of excitons in bulk h­BN Excitons in van der Waals materials: From monolayer to bulk hexagonal boron nitride J. Koskelo, et al, Phys. Rev. B 95, 035125 (2017) Combinations with respect to the exchange of the e-h pair between two inequivalent layers The two lowest excitons Third and fourth excitons Splitting due to the interlayer hopping
  24. 24. How to probe dark states at q=0?
  25. 25. Non­linear response can probe dark states due to  the different selection rules!!!
  26. 26. How to calculate non­linear response  in  h­BN Nonlinear optics from an ab-initio approach by means of the dynamical Berry phase Attaccalite, C., & Grüning, M. PRB, 88(23), 235113. (2013)
  27. 27. TPA coefficients  from real­time simulations Real-time dynamicsReal-time dynamics
  28. 28. TPA coefficients  from real­time simulations Real-time dynamicsReal-time dynamics Polarization
  29. 29. TPA coefficients  from real­time simulations Richardson extrapolation Real-time dynamicsReal-time dynamics Polarization
  30. 30. TPA coefficients  from real­time simulations Richardson extrapolation Real-time dynamicsReal-time dynamics Polarization
  31. 31. Two­photon absorption Two-photons absorption in hexagonal boron nitride C. Attaccalite et al., unpublished Monolayer h­BN 
  32. 32. Two­photon absorption Two-photons absorption in hexagonal boron nitride C. Attaccalite et al., arXiv preprint arXiv:1803.10959 Monolayer h­BN  Bulk h­BN 
  33. 33. Tight­binding modeling 1/2  Monolayer h­BN  1 - Photon The excitonic states can then be classified according to the representations of the C3v point group. Among the three representations A1, A2 and E, only the two-dimensional representation E is optically active. 2 - Photon In the discrete which indicates also that all excitons are in principle bright. We have seen in particular that the oscillator strength for the ground state 1s exciton is very strong.
  34. 34. Tight­binding modeling 2/2  2 – Photon In the presence of a symmetry centre odd (even) states are one(two)-photon allowed. In the case of the AA’ stacking combining both processes can be used to discriminate between the components of the Davydov doublets. Bulk h­BN 
  35. 35. Experimental results
  36. 36. Experimental results 1/2 Giant Enhancement of the Optical Second-Harmonic Emission of WSe2 Monolayers by Laser Excitation at Exciton Resonances Phys. Rev. Lett. 114, 097403 (2015) Probing the 1s state in WS2 explanation in terms of magnetic dipoles
  37. 37. Experimental results 2/2 Hexagonal boron nitride is an indirect band­gap  semiconductor G. Cassabois et al.,  Nature Photonics, 10, 262 (2016)
  38. 38. Experimental results 2/2 Hexagonal boron nitride is an indirect band­gap  semiconductor G. Cassabois et al.,  Nature Photonics, 10, 262 (2016)
  39. 39. Other theoretical results
  40. 40. Part of the selection rules were  already published in the literature “Optical selection rule of excitons in gapped chiral fermion systems,” PRB 91 075310 (2015) “Nonlinear optical selection rule based on valley- exciton locking in monolayer ws2,” Light: Science &Amp; Appli-cations 4, e366 (2015). “Optical selection rules for excitonic rydberg series in the massive dirac cones of hexagonal two- dimensional materials,” Phys. Rev. B 95, 125420 (2017). “Intrinsic exciton-state mixing and non-linear optical properties in transition metal dichalcogenide monolayers,” Phys. Rev. B 95, 035311 (2017).
  41. 41. … but continue to be rediscovered...  “Optical selection rule of excitons in gapped chiral fermion systems,” Phys. Rev. Lett. 120, 077401 (2018). “Unifying optical selection rules for excitons in two- dimensions: Band topology and winding numbers,” Phys. Rev. Lett. 120, 087402 (2018) Part of the selection rules were  already published in the literature “Optical selection rule of excitons in gapped chiral fermion systems,” PRB 91 075310 (2015) “Nonlinear optical selection rule based on valley- exciton locking in monolayer ws2,” Light: Science &Amp; Appli-cations 4, e366 (2015). “Optical selection rules for excitonic rydberg series in the massive dirac cones of hexagonal two- dimensional materials,” Phys. Rev. B 95, 125420 (2017). “Intrinsic exciton-state mixing and non-linear optical properties in transition metal dichalcogenide monolayers,” Phys. Rev. B 95, 035311 (2017).
  42. 42. ● Two-photon absorption can probe 1s excitons with in two-dimensional crystals ● Dark excitons have too high energy at zero momentum, but at finite q they produce the double peaks structures ● If you don’t know group theory you can publish on better journals! Conclusions {at zero momentum}
  43. 43. Conclusions Using a combinations of different spectroscopic techniques all excited states of h-BN can be found!!! This presentation is available on: http://attaccalite.com References  Exciton interference in hexagonal boron nitride L. Sponza, H. Amara, C. Attaccalite, F. Ducastelle, A. Loiseau Phys. Rev. B 97, 075121 (2017) Angle-resolved electron energy loss spectroscopy in h-BN F. Fossard, et al. Phys. Rev. B 96, 115304 (2017) Two-photons absorption in hexagonal boron nitride C. Attaccalite et al., arXiv preprint arXiv:1803.10959 Lumen code for the non-linear response (GPL) http://www.attaccalite.com/lumen/
  44. 44. Acknowledgments  Lorenzo Sponza François Ducastelle Hakim Amara Frédéric Fossard Myrta Grüning  Annick Loiseau Léonard Schué
  45. 45. h­BN optical properties Excitons in boron nitride nanotubes: dimensionality effects Phys. Rev. Lett. 96, 126104 (2016)
  46. 46. Origin of peak intensity
  47. 47. Excitons analysis q=0.7A The strength of the peak is explained by the fact that the KM transitions take place between regions of the band structure where bands are particularly, from top valence to the M point. Positive Negative
  48. 48. Positive Negative At this q point the contribution from K→M and M→ K’ is of the same order but with opposite sign, therefore the exciton is dark. Excitons analysis q=1.12A

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