Optical Properties of Solids within WIEN2k

2. Optical Properties of Solidswithin WIEN2k Claudia Ambrosch-DraxlInstitute for Theoretical PhysicsUniversity Grazclaudia.ambrosch@uni-graz.at

3. light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem Basics Outline program flow inputs Optics in WIEN2k Program outputs convergence results Examples Raman scattering beyond RPA Outlook

4. light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem Basics Outline program flow inputs Optics in WIEN2k Program outputs convergence results Examples Raman scattering beyond RPA Outlook

5. Properties & Applications Dielectric functionOptical absorptionOptical gapExciton binding energyPhotoemission spectraCore level spectraRaman scatteringCompton scatteringPositron annihilationNMR spectraElectron spectroscopy Light emitting diodesLasersSolar cellsDisplaysComputer screensSmart windowsLight bulbsCDs & DVDs Excited States understand physicscharacterize materialstailor special properties

6. Wavefunction vs. Density Janak's theorem auxiliary functions Hartree-Fock: ionization energies Excited States Koopman's theorem DFT: Lagrange parameters

7. Light – Matter Interaction Polarizability: Response to external electric field E Linear approximation: Optical Properties susceptibility c conductivity s dielectric tensor  Fourier transform:

8. band structure Energy w EF w intraband transition interband transition E S wave vector LightScattering Optical Properties

9. The Dielectric Tensor Bloch electrons: intraband interband Free electrons: Lindhard formula Optical Properties Interband contribution: independent particle approximation, random phase approximation (RPA)

10. Optical conductivity: Reflectivity: Absorption coefficient: Loss function: Complex dielectric tensor: Kramers-Kronig relations Optical "Constants" Optical Properties Complex refractive index:

11. Drude-like terms Dielectric Tensor: Intraband Contributions Metals Optical conductivity: Plasma frequency:

12. Sumrules Optical Properties

13. Symmetry triclinic monoclinic (a,b=90°) orthorhombic Dielectric Tensor tetragonal, hexagonal cubic

14. KK KK KK without magnetic field, spin-orbit coupling: cubic Magneto-optics Example: Ni with magnetic field ‖z, spin-orbit coupling: tetragonal

15. Open Questions Local Density Approximation (LDA) Generalized Gradient Approximation (GGA) Approximations used: Ground state: Excited State Properties Excited state: Interpretation within one-particle pictureInterpretation of excited states in terms of ground statepropertiesElectron-hole interaction ignored (RPA) Where do possible errors come from?How to treat excited states ab initio?

16. The Band Gap Problem Ionization energy Electro-affinity Band gap shift of conduction bands: scissors operator many-body perturbation theory:GW approach

17. light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem Basics Outline program flow inputs Optics in WIEN2k Program outputs convergence results Examples Raman scattering beyond RPA Outlook

18. SCF cycle converged potential kgen dense mesh lapw1 eigenstates lapw2 Fermi distribution optic momentum matrix elements joint dielectrixtensorcomponents optical coefficients broadening scissors operator kram Re e Im e Program Flow Optics in WIEN2k

19. al.inop 2000 1number of k-points, first k-point -5.0 2.2Emin, Emax: energy window for matrix elements 1 number of cases (see choices below) 1 Re <x><x> OFF unsymmetrized matrix elements written to file? "optic" ni.inop (magento-optics) Inputs • 800 1number of k-points, first k-point • -5.0 5.0Emin, Emax: energy window for matrix elements • 3 number of cases (see choices below) • 1 Re <x><x> • 3Re <z><z> • Im <x><y> • OFF Choices: 1......Re <x><x> 2......Re <y><y> 3......Re <z><z> 4......Re <x><y> 5......Re <x><z> 6......Re <y><z> 7......Im <x><y> 8......Im <x><z> 9......Im <y><z>

20. al.injoint 1 18lower and upper band index 0.000 0.001 1.000Emin, dE, Emax [Ry] eVoutput units eV / Ry 4switch 1number of columns to be considered 0.1 0.2broadening for Drude model choose gamma for each case! "joint" Inputs SWITCH 0...JOINT DOS for each band combination 1...JOINT DOS sum over all band combinations 2...DOS for each band 3...DOS sum over all bands 4...Im(EPSILON) 5...Im(EPSILON) for each band combination 6...INTRABAND contributions 7...INTRABAND contributions including band analysis

21. al.inkram "kram" 0.1 broadening gamma 0.0 energy shift (scissors operator) 1 add intraband contributions 1/0 12.6 plasma frequency 0.2 gamma(s) for intraband part as number of colums as number of colums Inputs si.inkram 0.05 broadening gamma 1.00 energy shift (scissors operator) 0 ....

22. light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem Basics Outline program flow inputs Optics in WIEN2k Program outputs convergence results Examples Raman scattering beyond RPA Outlook

23. Outputs

24. Convergence Example: Al

25. Sumrules Example: Al

26. Loss Function Example: Al

27. light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem Basics Outline program flow inputs Optics in WIEN2k Program outputs convergence results Examples Raman scattering beyond RPA Outlook

28. Raman Intensities Theory Experiment YBa2Cu3O7: A1g Modes CAD, H. Auer, R. Kouba, E. Ya. Sherman, P. Knoll, M. Mayer, Phys. Rev. B 65, 064501 (2002).

29. Current Developments Kohn-Sham theory Gradient Corrections (GGA)LDA + U Exact Exchange (EXX) non-local effects correlation effects band gap problem Generalized Kohn-Sham theory Self-interaction correction (SIC) Non-local exchange / screened exchange Time dependent DFT response to time-dependet perturbation Many-body perturbation theory band gap problem excitonic effects GW + Bethe-Salpeter equation

30. The Bethe–Salpeter Equation effective Schrödinger equation for the electron-hole pair Beyond RPA

31. Thank you for your attention!