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Role of excitonic effects in nonlinear optical

properties of 2D materials

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- 1. Role of excitonic effects in nonlinear optical properties of 2D materials Myrta Grüning, Queen's University Belfast - Northern Ireland !?! 2 4 6 8 10 with e-h without e-h Claudio Attaccalite - CNRS Marseille - France OSI 12 - 27 June 2017 + + + + + + + ... ... ...
- 2. Interest of nonlinear optics in 2D materials: Second Harmonic Generation from Artiﬁcially Stacked Transition Metal Dichalcogenide Twisted Bilayers ACS Nano 8, 2951 (2014) Ultra-strong nonlinear optical processes and trigonal warping in MoS2 layers arXiv:1608.04101 (2016) see as well 2D Mater. 4 (2017) 011006 Imagining: Relatively strong (technological): Scientiﬁc Reports 4: 5530 (2014) Extraordinary Second Harmonic Generation in Tungsten Disulﬁde Monolayers Giant two-photon absorption in monolayer MoS2 Laser & Photonics Reviews (2015)
- 3. Several experiments argued the importance of excitonic eﬀects in nonlinear optics of 2D materials: Excitonic eﬀects important role in SHG edge detection in MoS2 ﬂakes [Science 344, (2014) 488]
- 4. Key questions explored in this talk: 2 4 6 8 10 with e-h without e-h Calculated at the GW+ Bethe-Salpeter equation How to get a feasible approach equivalent to GW+BSE Are excitonic eﬀects important for nonlinear properties?
- 5. Dynamical polarization obtained from real-time evolution of natural orbitals I. Souza et al, PRB 69, 085106 (2004) light-matter interaction Energy functional corresponding to zero-ﬁeld Hamitonian Natural orbitals: diagonalize the 1-e Green's function at each t
- 6. Dynamical polarization as a Berry-phase (consistent with PBC): I. Souza et al, PRB 69, 085106 (2004) Euler-Lagrange EOMs: Position operator consistent with PBC: expressed in terms of
- 7. How do we approximate our eﬀective Hamiltonian: Constraint: Total wave-function can be written as a single Slater potential Hamiltonian of the unperturbed system (Kohn-Sham) Independent particle level of approximation (IPA)
- 8. How do we approximate our eﬀective Hamiltonian: Constraint: Total wave-function can be written as a single Slater potential Scissor operator: QP renormalization eﬀects on the unperturbed system Quasiparticle approximation (QPA or IPA+GW)
- 9. How do we approximate our eﬀective Hamiltonian: Constraint: Total wave-function can be written as a single Slater potential Crystal local eﬀects: sensible to inhomogeneity of the system + - + + ++ - - -- Hartree-only approximation(TDH)
- 10. How do we approximate our eﬀective Hamiltonian: Constraint: Total wave-function can be written as a single Slater potential Static screened HF self-energy: TD renormalization eﬀects on QP energies on optical excitations (excitonic eﬀects) Screened Hartree-Fock (TDSHF)
- 11. By changing input/postprocessing in our computational set-up we can obtain diﬀerent (non)linear optical properties: in out post-processing: Obtain by Fourier transform in out Solve Euler-Lagrange equations: Kohn-Sham: C. Attaccalite, M. G. Phys. Rev. B 88, 235113 (2013) Absorption
- 12. In the linear response limit the approach reduces to GW+BSE results 0 10 20 30 40 50 60 Absorption Polarization 4 5 6 7 8 9 10 Energy (eV) 0 10 20 30 40 50 60 Absorption 0 5 10 15 Time (fs) Polarization post-processing TD-Hartree: TD-BSE: Exp BSE TD-BSE Exp RPA TD-Hartree C. Attaccalite, M.G, A Marini PRB 84, 245110 (2011)
- 13. By changing input/postprocessing in our computational set-up we can obtain diﬀerent (non)linear optical properties: in out post-processing: Obtain by Fourier matrix inversion: in out Solve Euler-Lagrange equations: Kohn-Sham: For do: e.g. C. Attaccalite, M. G. Phys. Rev. B 88, 235113 (2013)
- 14. In h-BN monolayer dramatic eﬀect of e-h interaction on SHG Intensities doubled at excitonic resonances @810nm exp [Y. Li et al NL(2013)]: ~20 pm/V ours : ~40 pm/V 0.2 0.4 0.6 0.8 1.0 (a): IPA Arb.units (b) 0.2 0.4 0.6 0.8 1.0 (c): IPA+GW Arb.units (d) 0.0 0.4 0.8 1.2 (e): TDSHF 2 4 6 8 10 Energy (eV) Arb.units (f) M. Grüning and C. Attaccalite, Phys. Rev. B 89(R), 081102 (2014) E: Phys. Rev. B 90, 199901 (2014) . IPA results validated against Guo&Lin (PRB 72,075416) EFFECTIVE THICKNESS 0.33 nm
- 15. In MoS2 we found SHG@810nm of ~1 nm/V (~3 orders of magnitude > nonlinear crystals) S Mo EFFECTIVE THICKNESS 0.615 nm M. Grüning and C. Attaccalite, Phys. Rev. B 89(R), 081102 (2014). E: Phys. Rev. B 90, 199901 (2014); agreement with Pedersen et al PRB 2014 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Energy (eV) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 TDSHF IPA EXPERIMENT x8 MoS2 Comparison with experimental estimates: + > exp: ~0.1 nm/V (Malard PRB 2013; Li NL 2013); + << ~100 nm/V (Kumar PRB 2013) + ~ Janisch (SciRep 2014) for WS2 Again e-h eﬀects 2x enhancement (important to include local ﬁelds as well)
- 16. Similar results found for SHG intensity in SiC, GaN and ZnO: C. Attaccalite, A. Nguerc, E.Cannuccia, M.G PCCP (2015) * Enhancement at excitonic resonances * Transparent in the 'interesting' frequency region * Intensities of 0.1 -1 nm/V (smaller than MoS2, but still larger than conventional NL crystals)
- 17. In THG of 1D nanostructures many-body eﬀects also key: C. Attaccalite, E. Cannuccia M. G. PRB 95.125403 # reduction of factor 3-4@ excitonic resonances # intensity redistribution 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Laser frequency (eV) 0 2 4 6 8 10 12 KS particles QP particles QP particles + e-h interaction ThirdHarmonicintensity(esux10-8 )
- 18. By changing input/postprocessing in our computational set-up we can obtain diﬀerent (non)linear optical properties: in out post-processing: Obtain by Fourier matrix inversion: in out Solve Euler-Lagrange equations: Kohn-Sham: For do: e.g. C. Attaccalite, M. G. work in progress + extrapolation from diﬀerent intensities For do:
- 19. Preliminary results for 2 photon absorption in 2D h-BN: C. Attaccalite, M. G. in progress 2.5 3.0 3.5 4.0 4.5 5.0 Energy (eV) 0.0 0.2 0.4 0.6 0.8 1.0 χ(3) (−ω;ω,−ω,ω)[esu] 1e 10 GW+BSE (0.025 eV) (0.1 eV)QPA
- 20. Role of excitonic effects in nonlinear optical properties of 2D materials in out in out e.g. e- h+ with e-h interaction e- h+ independent e-h pairs Real-time approach to calculate non linear optics which includes excitonic eﬀects (and consistent with PBC) Role of excitonic eﬀects for SHG in 2D: enhancement at excitonic resonances (and THG in 1D ...) nonlinear module of yambo-code https://github.com/attacc/lumen OSI 12 - 27 June 2017

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