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Lorenzo Sponza1 3
, Claudio Attaccalite2
, Frederic Fossard1
, Hakim Amara1
, François Ducastelle1
Modeling excitons
in bu...
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Modeling excitons in bulk and single-layer hBN

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Modeling excitons in bulk and single-layer hBN

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  • Light and its nature have caused a lot of ink to flow during these last decades. Its dual behavior is partly explained by (1)Double-slit experiment of Thomas Young - who represents the photon’s motion as a wave - and also by (2)the Photoelectric effect in which the photon is considered as a particle. A Revolution: SALEH THEORY solves this ambiguity and this difficulty presenting a three-dimensional trajectory for the photon's motion and a new formula to calculate its energy. More information on : https://youtu.be/mLtpARXuMbM
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Modeling excitons in bulk and single-layer hBN

  1. 1. Lorenzo Sponza1 3 , Claudio Attaccalite2 , Frederic Fossard1 , Hakim Amara1 , François Ducastelle1 Modeling excitons in bulk and single-layer hBN single-layer with simple tight-binding model N N N N N N B B B B B B N 0 -1 1 0 -1 1 antisymmetric symmetric N N N N N N N B B B B B B τ1 τ3 τ2 densityofstates(arb.units) Two parameters are enough to give a good description of single-particle properties: 1) the hoping integral T, adjusted on the band dispersion and 2) the difference of in-site energies, parametrised from the gapwidth. single-particle properties two-particle neutral excitations (excitons) Two intercalated triangular lattices. 1) electrons move on π* orbitals of B, 2) holes move on π orbitals of N. The model predicts excitonic features (wavefunction, dispersion ...) in close agreement with BSE. spectroscopic measurements and ab-initio simulations of bulk AA' Depending on the filter employed, monochromator or slit, two different acquisition framework are accessible. cut at 8 eV experiment simulation exp. | sim. cut at 12 eV experiment simulation exp. | sim. N N N N N N N B B B B B B A powerful experimental setup selecting the direction with a slit vertical slices: ω-q maps The loss function is recorded simultaneously for several transferred momenta. Analysis of the excitations details and references The energy-filtered transition electron microscope is a powerful technique providing accurate information on the electronic structure, especially conceived for the investigation of electronic excitations at small q. Thanks to its simplicity, the experimental setup is particularly suited for 2D systems. The ab-initio simulations have been validated rigorously against experiment in AA' bulk hBN, the tight-binding model has been parametrised using ab-initio calculations and validated against BSE results on the single-layer hBN. The two theoretical approaches can be combined in a promising and versatile strategy: 1) First one performs accurate ab-initio simulations on benchmark systems (bulk, single-layer, building blocks...); 2) Then one optimizes the parameters of the tight-binding model using the results of the benchmark simulations; 3) Finally one applies the tight-binding model to more complex structures (allotropes, heterostructures, defects, impurities....). Conclusions and future development 1 Laboratoire d'étude des microstructures (LEM), ONERA - CNRS, Châtillon, France 2 Centre Interdisciplinaire de Nanoscience de Marseille, Aix Marseille University - CNRS, Marseille, France 3 lorenzo.sponza@onera.fr Paper submitted. See also arXiv:1701.05119 RPA calculations code: GPAW k-point grid: 24x24x8 Γ-centered N. bands: 20 cutoff: 60 eV BSE calculations code: GPAW k-point grid: 12x12x4(8) Γ-centered N. bands: 20, 6 valence + 8 conduction cutoff: 60 eV scissor operator: 1.73 eV excitonic wave function at Γ Γ M Γ M BSE dispersion tight-binding On the tight-binding model see also Phys. Rev. B 94, 125303 (2016) On the dispersion see also Phys. Rev. Lett. 116, 066803 (2016) Paper in preparation The simplicity of the tight-binding framework and its formulation in real-space permit clear and insightful interpretations Solving the Bethe-Salpeter equation (BSE) accounts quantitatively for excitonic effects in the complex dielectric function at different momenta. The comparison between different levels of the theory and of different quantities allow for thorough analysis and great insight. The energy-filtered transition electron microscope permits the acquisition of electron energy loss spectra (EELS) in the form of a datacube. ab-initio EELS within the random phase approximation (RPA) reproduces correctly in-plane excitations. The single-layer is an ideal system for a tight-binding model because of the relatively simple band structure close to the gap. 6.0 6.5 7.0 7.5 6.0 6.5 7.0 7.5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.4 0.6 0.8 1.0 1.2 1.4 angstrom-1 Energy(eV) Energy(eV) angstrom-1 A Real Imag. 4 6 8 10 12 14 Energy (eV) Experiment SO-BSE Re(ε) crosses 0 plasmon Real Imag. K 4 6 8 10 12 14 Energy (eV) Experiment SO-BSE structures in Im(ε) inter-band energy filtered diffraction patterns horizontal slices losses of a given energy are mapped on planes of the reciprocal-space. Real Imag. M 4 6 8 10 12 14 Energy (eV) Experiment RPA SO-RPA SO-BSE excitonic effect

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