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Second Harmonic Generation From Surfaces Nicolas Tancogne-Dejean, Valérie Véniard. Laboratoire des Solides Irradiés,Ecole Polytechnique, CNRS, CEA/DSM European Theoretical Spectroscopy Facility. Outline. Nonlinear optic and second harmonic generation Surfaces - PowerPoint PPT Presentation
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Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 1
Second Harmonic Generation From Surfaces
Nicolas Tancogne-Dejean, Valérie Véniard
Laboratoire des Solides Irradiés,Ecole Polytechnique, CNRS, CEA/DSM
European Theoretical Spectroscopy Facility
2
Outline
Nonlinear optic and second harmonic generation
Surfaces
How do we get the surface spectrum for SHG
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
• …
• Kerr effect
• Four-wave mixing
Response to a perturbation
3Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
Perturbation Response
Linear Response Nonlinear Response
Electric field Polarisation
• Absorption
• Refraction
• Birefringence
• Pockels effect
• Sum frequency Generation
• …
4
Second harmonic generation
First nonlinear term Centrosymmetric material : 𝜒 (2)=0
𝜒 (3)First nonlinear term :
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 G. Frankel
Non centrosymmetric material :
𝜒 (2)≠0
5
Applications of second harmonic generation (SHG)
Nanotubes characterization (PRB 77 125428)
Biological tissues/neurons imaging (Biophys. J. 81 493; PNAS 103, 786)
Nanoparticles imaging and microscopy
( C-L Hsieh PhD thesis, Caltech 2011 )
Thin films and surfaces characterization (PRB 89 075110)
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
6
Outline
Nonlinear optic and second harmonic generation
Surfaces
How do we get the surface spectrum for SHG
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
7
SurfacesDifferent surfaces for the same material (e.g.
Silicon)
Si(111) 7x7 Si(001) 2x1 Si(001) 4x2
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
Asymmetric dimersDangling bonds
Surface = symmetry breaking
Model of surface – Super-cells
Surface SupercellSystem with 2 surfaces
(slab)
8Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
What we want
Plane waves Best representation
of a surface
∞ ∞
Model of surface – Super-cells
Construction of super-cell (atoms
+ vacuum)
System with 2 surfaces (slab)
inversion symmetry
(artificial)
9Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
10
Outline
Nonlinear optic and second harmonic generation
Surfaces
How do we get the surface spectrum for SHG
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
11
Second order response in Time-Dependent DFT
Independent Particles Approximation (IPA) Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
Ground state (DFT)
Second order response
- Electronic structure : LDA functional
- ABINIT code
Extraction of one surface signal
It is possible to extract the signal from only one surface, using a new operator instead of p[1]
12Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
[1] L. Reining et al., Phys. Rev. B 50, 8411 (1994)
Inversion symmetry
𝜒 (2)=0
Direct Calculation
C(z)
Vacuum
BackSurf.
Vacuum
FrontSurf.
13
Second-order response
Extracted Signal
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
z
𝜒 (2)≠0
C(z) function ab initio calculation
C(z)
Extraction from two super-cells
Signal from clean surface from two different super-cells
14Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
z z
Extraction from two super-cells
Signal from dihydride surface from two different super-cells
15Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
z zIndependence of the two surfaces
Extraction from two super-cells
Signal from dihydride surface from two different super-cells
16Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
z zIndependence of the two surfaces
Calculation of the second order response from only one surface
Some results for Si(001)2x1
17Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
Adapted fromJ. I. Dadap, et al., Phys. Rev. B 56,
13367 (1997)
Clean SurfaceMonohydride
Some results for Si(001)2x1
18Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
Adapted fromJ. I. Dadap, et al., Phys. Rev. B 56,
13367 (1997)
Clean SurfaceMonohydride
ab initio calculations40 Si atoms – 256 k-points
Conclusion
We have presented a scheme for extracting the response from one surface in a super-cell approach
Beyond the Independent Particle Approximation
- Local-field effects- Many body effects
19
Conclusion
Perspective
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
Thank you for your attention
Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 20
21Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
z
Validation of the approach
Comparison with exact results for some specific components of the tensor
22Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
z
Validation of the approach
Comparison with exact results for some specific components of the tensor
23Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
Some results for Si(001)2x1
24Condensed Matter in Paris - CMD 25 JMC 14 - August 2014
Adapted fromJ. I. Dadap, et al., Phys. Rev. B 56,
13367 (1997)
Clean SurfaceMonohydride
ab initio calculations40 Si atoms – 256 k-points