Optical Properties of Solids. Claudia Ambrosch-Draxl Chair of Atomistic Modelling and Design of Materials University Leoben, Austria
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1 Optical Properties of Solids Claudia Ambrosch-Draxl Chair of Atomistic Modelling and Design of Materials University Leoben, Austria
2 Outline Basics Program Examples Outlook light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem program flow inputs outputs convergence results applications beyond linear optics beyond RPA Optics in WIEN2k
3 Outline Basics Program Examples Outlook light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem program flow inputs outputs convergence results applications beyond linear optics beyond RPA Optics in WIEN2k
4 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 understand physics characterize materials tailor special properties Excited States
5 Light Matter Interaction Response to external electric field E Polarizability: Linear approximation: Fourier transform: susceptibility χ conductivity σ dielectric tensor Optical Properties
6 The Dielectric Tensor Free electrons: Lindhard formula Bloch electrons: Interband contribution: intraband interband Optical Properties independent particle approximation, random phase approximation (RPA)
7 Light Scattering band structure hω S E Energy interband transition c k hω v k wave vector E F intraband transition Optical Properties
8 Optical "Constants" Complex dielectric tensor: Kramers-Kronig relations Optical conductivity: Complex refractive index: Reflectivity: Absorption coefficient: Loss function: Optical Properties
9 Intraband Contributions Dielectric Tensor: Drude-like terms Optical conductivity: Plasma frequency: Metals
10 Sumrules Optical Properties
11 Symmetry triclinic monoclinic (α,β=90 ) tetragonal, hexagonal orthorhombic cubic Dielectric Tensor
12 Magneto-optics without magnetic field, spin-orbit coupling: cubic KK with magnetic field H װ z, spin-orbit coupling: KK tetragonal Example: Ni KK
13 Be careful...
14 Wavefunction vs. Density Hartree-Fock: ionization energies DFT: Lagrange parameters auxiliary functions Koopman's theorem Janak's theorem Excited States
15 Open Questions Approximations used: Ground state: Excited state: Local Density Approximation (LDA) Generalized Gradient Approximation (GGA) 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? Excited State Properties
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 Basics Program Examples Outlook light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem program flow inputs outputs convergence results applications beyond linear optics beyond RPA Optics in WIEN2k
18 Program Flow SCF cycle converged potential kgen lapw1 lapw2 optic joint kram dense mesh eigenstates Fermi distribution momentum matrix elements dielectrix tensor components Re ε Im ε optical coefficients broadening scissors operator Optics in WIEN2k
19 al.inop "optic" number of k-points, first k-point E min, E max : energy window for matrix elements 1 number of cases (see choices below) 1 Re <x><x> OFF unsymmetrized matrix elements written to file? ni.inop (magneto-optics) number of k-points, first k-point Emin, Emax: energy window for matrix elements 3 number of cases (see choices below) 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
20 al.injoint "joint" 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 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) total 5...Im(EPSILON) for each band combination 6...INTRABAND contributions 7...INTRABAND contributions including band analysis Inputs
21 "kram" al.inkram 0.1 broadening gamma 0.0 energy shift (scissors operator) 1 add intraband contributions 1/ plasma frequency 0.2 gamma(s) for intraband part as number of colums as number of colums Dielectric function Silicon Imε Reε Γ=0.05eV Energy [ev] si.inkram 0.05 broadening gamma 1.00 energy shift (scissors operator) 0... Inputs
22 optic case.symmat case.mommat momentum matrix elements, symmetrized analysis, NLO case.joint Im ε joint SWITCH 4 case.epsilon case.sigmak case.refraction case.absorp case.eloss kram complex dielectric tensor optical conductivity refractive index absorption coefficient loss function Outputs
23 Outline Basics Program Examples Outlook light scattering dielectric tensor in the RPA sumrules symmetry the band gap problem program flow inputs outputs convergence results applications beyond linear optics beyond RPA Optics in WIEN2k
24 Results...
25 Convergence Interband Im ε k 286k 560k 1240k 2456k 3645k 4735k ω p k-points in IBZ Energy [ev] Example: Al
26 N eff [electrons] Sumrules 165 k-points 4735 k-points Experiment Energy [ev] Example: Al
27 Loss Function Loss function 80 intraband total 20 interband Energy [ev] Example: Al
28 Theory - Experiment Example: Platinum K. Glantschnig, and C. Ambrosch-Draxl, (preprint).
29 C. Ambrosch-Draxl and J. O. Sofo Comp. Phys. Commun., in print
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