Second Harmonic Generation From Surfaces Nicolas TancogneDejean Valrie

Second Harmonic Generation From Surfaces Nicolas Tancogne-Dejean, Valérie Véniard Laboratoire des Solides Irradiés, Ecole Polytechnique, CNRS, CEA/DSM European Theoretical Spectroscopy Facility Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 1

Outline Ø Nonlinear optic and second harmonic generation Ø Surfaces Ø How do we get the surface spectrum for SHG Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 2

Response to a perturbation Perturbation Electric field Linear Response Polarisation Nonlinear Response • Absorption • Sum frequency Generation • Refraction • Pockels effect • Kerr effect • Four-wave mixing • Birefringence • … Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 3

Second harmonic generation First nonlinear term Centrosymmetric material : First nonlinear term : Non centrosymmetric material : G. Frankel Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 4

Applications of second harmonic generation (SHG) Nanotubes characterization (PRB 77 125428) Nanoparticles imaging and microscopy ( C-L Hsieh Ph. D thesis, Caltech 2011 ) Biological tissues/neurons imaging (Biophys. J. 81 493; PNAS 103, 786) Thin films and surfaces characterization (PRB 89 075110) Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 5

Outline Ø Nonlinear optic and second harmonic generation Ø Surfaces Ø How do we get the surface spectrum for SHG Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 6

Surfaces Different surfaces for the same material (e. g. Silicon) Si(111) 7 x 7 Si(001) 2 x 1 Si(001) 4 x 2 Surface = symmetry breaking Dangling bonds Asymmetric dimers Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 7

Model of surface – Super-cells What we want Surface Plane waves Supercell Best representation of a surface System with 2 surfaces (slab) Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 8

Model of surface – Super-cells Construction of super-cell (atoms + vacuum) System with 2 surfaces (slab) Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 9

Outline Ø Nonlinear optic and second harmonic generation Ø Surfaces Ø How do we get the surface spectrum for SHG Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 10

Second order response in Time-Dependent DFT Ground state (DFT) - Electronic structure : LDA functional - ABINIT code Second order response Independent Particles Approximation (IPA) Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 11

Extraction of one surface signal Vacuum • Front Surf. Direct Calculation C(z) Back Surf. Inversion symmetry Vacuum [1] L. Reining et al. , Phys. Rev. B 50, 8411 (1994) Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 12

Second-order response C(z) function ab initio calculation Extracted Signal z C(z) Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 13

Extraction from two super-cells Signal from clean surface from two different super-cells z Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 z 14

Extraction from two super-cells Signal from dihydride surface from two different super-cells z z Independence of the two surfaces Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 15

Extraction from two super-cells Signal from dihydride surface from two different super-cells z z Independence of the two surfaces Calculation of the second order response from only one surface Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 16

Some results for Si(001)2 x 1 Clean Surface Monohydride Adapted from J. I. Dadap, et al. , Phys. Rev. B 56, 13367 (1997) Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 17

Some results for Si(001)2 x 1 Clean Surface Monohydride Adapted from J. I. Dadap, et al. , Phys. Rev. B 56, 13367 (1997) ab initio calculations 40 Si atoms – 256 k-points Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 18

Conclusion We have presented a scheme for extracting the response from one surface in a super-cell approach Perspective Beyond the Independent Particle Approximation - Local-field effects - Many body effects Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 19

Thank you for your attention Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 20

Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 21

Validation of the approach z Comparison with exact results for some specific components of the tensor Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 22

Validation of the approach z Comparison with exact results for some specific components of the tensor Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 23

Some results for Si(001)2 x 1 Clean Surface Monohydride Adapted from J. I. Dadap, et al. , Phys. Rev. B 56, 13367 (1997) ab initio calculations 40 Si atoms – 256 k-points Condensed Matter in Paris - CMD 25 JMC 14 - August 2014 24