2. Optical Properties of Solids within WIEN2k
Claudia Ambrosch-Draxl Institute for Theoretical Physics University Graz

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

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

5. Properties & Applications
Dielectric function Optical absorption Optical gap Exciton binding energy Photoemission spectra Core level spectra Raman scattering Compton scattering Positron annihilation NMR spectra Electron spectroscopy
Light emitting diodes Lasers Solar cells Displays Computer screens Smart windows Light bulbs CDs & DVDs
Excited States
understand physics characterize materials tailor special properties

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

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

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

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

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

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

12. Sumrules
Optical Properties

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

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

15. Open Questions Excited State Properties Approximations used:
Ground state:
Local Density Approximation (LDA)
Generalized Gradient Approximation (GGA)
Excited State Properties
Excited state:
Interpretation within one-particle picture Interpretation of excited states in terms of ground state properties Electron-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. Outline Optics in WIEN2k Basics Program Examples Outlook
light scattering
dielectric tensor in the RPA
sumrules
symmetry
the band gap problem
Basics
program flow
inputs
Program
Optics in WIEN2k
outputs
convergence
results
Examples
Outlook
Raman scattering
beyond RPA

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

19. "optic" Inputs al.inop ni.inop (magento-optics)
number of k-points, first k-point
Emin, Emax: energy window for matrix elements
number of cases (see choices below)
1 Re <x><x>
OFF unsymmetrized matrix elements written to file?
ni.inop (magento-optics)
Inputs
number of k-points, first k-point
Emin, Emax: energy window for matrix elements
number of cases (see choices below)
Re <x><x>
Re <z><z>
Im <x><y>
OFF
Choices:
Re <x><x>
Re <y><y>
Re <z><z>
Re <x><y>
Re <x><z>
Re <y><z>
Im <x><y>
Im <x><z>
Im <y><z>

20. "joint" Inputs al.injoint 1 18 lower and upper band index
Emin, dE, Emax [Ry]
eV output units eV / Ry
switch
number of columns to be considered
broadening for Drude model
choose gamma for each case!
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. "kram" Inputs al.inkram si.inkram 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
broadening gamma
energy shift (scissors operator)
....

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

23. Outputs

24. Convergence
Example: Al

25. Sumrules
Example: Al

26. Loss Function
Example: Al

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

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

29. Current Developments Kohn-Sham theory Generalized 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!