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

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Presentation on theme: "Claudia Ambrosch-Draxl Institute for Theoretical Physics University Graz Optical Properties of Solids within WIEN2k."— Presentation transcript:

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

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

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

5 Excited States 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 understand physics characterize materials tailor special properties Light emitting diodes Lasers Solar cells Displays Computer screens Smart windows Light bulbs CDs & DVDs

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

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

8 Light Scattering E S  Optical Properties intraband transition interband transition Energy wave vector EFEF  band structure

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

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

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

12 Sumrules Optical Properties

13 Symmetry Dielectric Tensor cubic monoclinic ( ,  =90°) orthorhombic tetragonal, hexagonal triclinic

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

15 Excited State Properties Open Questions Approximations used: L ocal D ensity A pproximation (LDA) G eneralized G radient A pproximation (GGA) Ground state: 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 many-body perturbation theory: GW approach shift of conduction bands: scissors operator Electro-affinity Ionization energy Band gap

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

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

19 "optic" Inputs number of k-points, first k-point Emin, Emax: energy window for matrix elements 1 number of cases (see choices below) 1Re OFFunsymmetrized matrix elements written to file? al.inop ni.inop (magento-optics) number of k-points, first k-point Emin, Emax: energy window for matrix elements 3 number of cases (see choices below) 1 Re 3 Re 7Im OFF Choices: Re Re Re Re Re Re Im Im Im

20 "joint" Inputs al.injoint 1 18 lower and upper band index Emin, dE, Emax [Ry] eV output units eV / Ry 4 switch 1 number of columns to be considered broadening for Drude model choose gamma for each case! 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 0.1 broadening gamma 0.0 energy shift (scissors operator) 1add intraband contributions 1/0 12.6plasma frequency 0.2 gamma(s) for intraband part si.inkram 0.05 broadening gamma 1.00 energy shift (scissors operator) as number of colums

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

23 Outputs

24 Convergence Example: Al

25 Sumrules Example: Al

26 Loss Function Example: Al

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

28 Theory Raman Intensities YBa 2 Cu 3 O 7 : A 1g Modes CAD, H. Auer, R. Kouba, E. Ya. Sherman, P. Knoll, M. Mayer, Phys. Rev. B 65, (2002). Experiment

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

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

31 Thank you for your attention!


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