Claudia Ambrosch-Draxl, University of Leoben, Austria Chair of Atomistic Modelling and Design of Materials
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1 Excited state properties p within WIEN2k Claudia Ambrosch-Draxl, University of Leoben, Austria Chair of Atomistic Modelling and Design of Materials
2 Beyond the ground state Basics about light scattering The dielectric tensor The WIEN2k code Outlook The program Input / output Examples TDDFT versus manybody perturbation theory Contents
3 Light-Matter Interaction
4 Resonse to external electric field E Polarizability Linear approximation susceptibility χ conductivity σ dielectric tensor Fourier transform Light-Matter Interaction
5 The dielectric tensor Free electrons: the Lindhard formula Bloch electrons intraband interband Light-Matter Interaction
6 Interband contributions Independent particle approximation RPA En nergy c k hω E F hω S E v k Light-Matter Interaction
7 Optical constants Complex dielectric tensor Optical conductivity Complex refractive index Reflectivity Absorption coefficient Loss function Light-Matter Interaction
8 Intraband contributions Dielectric tensor Ene ergy E F Optical conductivity Drude-like terms plasma frequency Light-Matter Interaction
9 Sumrules Light-Matter Interaction
10 Symmetry triclinic monoclinic (α,β=90 ) orthorhombic tetragonal, hexagonal cubic Light-Matter Interaction
11 Magneto-optics: optics: example without magnetic field, spin-orbit coupling: cubic KK with magnetic field z, spin-orbit coupling: tetragonal KK KK Light-Matter Interaction
12 The Program
13 SCF cycle converged potential x kgen dense mesh x lapw1 Kohn-Sham states (higher E max ) x lapw2 -Fermi Fermi distribution optic package x optic x joint x kram momentum matrix elements tensor components optical constants life time broadening scissors shift The Program Flow
14 optic Al.inop number of k-points, first k-point energy window for matrix elements 1 number of cases (see choices) 1 Re <x><x> OFF write unsymmetrized matrix elements to file? Ni.inop number of k-points, first k-point energy window for matrix elements 3 number of cases (see choices) 1 Re <x><x> 3 Re<><> <z><z> 7 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> Inputs
15 joint Al.injoint 1 18 lower and upper band index E min, de, Emax [Ry] ev output units ev / Ry 4 switch 1 number of columns to be considered broadening for Drude term(s) choose gamma for each case! 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) total 5...Im(EPSILON) for each band combination 6...intraband contributions 7...intraband contributions including band analysis Inputs
16 kram Al.inkram 0.1 broadening gamma 0.0 energy shift (scissors operator) 1 add intraband contributions 1/ plasma frequency 0.2 Γ(s) for intraband part Si.inkram 0.05 broadening gamma 1.00 energy shift (scissors operator) Silicon 60 Imε Reε Γ=0.05eV Energy [ev] Inputs
17 optic joint kram case.symmat case.mommat case.joint case.epsilon case.sigmaksigmak case.refraction case.absorpabsorp case.eloss Outputs
18 Results
19 Convergence m ε nterba and Im I k 286k 560k 1240k 2456k 3645k 4735k ω p k-points in IBZ Energy [ev] Example: Al
20 Sumrules N eff [ele ectrons s] k-points 4735 k-points Experiment Energy [ev] Example: Al
21 Loss function Loss fu unctio n 80 intraband total 20 interband Energy [ev] Example: Al
22 Band structure Band structure non-relativistic scalar-relativistic relativistic s gy [ev] s d f pd pf p Energ pd K X G L W W K X G L W W K X G L W W Example: Au
23 Density of states 4 DO OS [ states pe er ev and cell] 3 total d s p f Energy [ev] S / energy 2 joint DOS non-relativistic scalar-relativistic relativistic Energy [ev] Example: Au
24 Dielectric tensor joint DOS / ener rgy non-relativistic scalar-relativistic relativistic Energy [ev] ion Diele ectric Functi Au 12 Ree non-relativistic scalar-relativistic 10 8 Ime relativistic Energy [ev] Example: Au
25 Theory versus experiment K. Glantschnig and C. Ambrosch-Draxl (preprint) Example: Pt
26 Whom to ask? Robert Abt C. Ambrosch-Draxl and J. O. Sofo Linear optical properties of solids within the full-potential linearized augmented planewave method Comp. Phys. Commun. 175,, (2006) People
27 and Beyond
28 Discrepancies Ground state xc functionals Excited state Interpretation in terms of ground state properties Interpretation within one-particle picture Response function Manybody treatment needed 2 routes Time-dependent d DFT (TDDFT) Manybody perturbation theroy (MBPT) Beyond the Ground State
29 MBPT mixing of concepts 4 point functions involved very demanding 2 steps: GW & BSE linear-response regime TDDFT keeps spirit of DFT 2 point functions less demanding 1 functional needed in principle one step in practice: GW needed generally applicable linear-response regime strong laser fields etc. G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002) Beyond the Ground State
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