Transcript EXCITING - WIEN 2k

Optical Properties of Solids
within WIEN2k
Claudia Ambrosch-Draxl
Institute for Theoretical Physics
University Graz
[email protected]
Basics
Program
Examples
Outlook
light scattering
dielectric tensor in the RPA
sumrules
symmetry
the band gap problem
program flow
inputs
outputs
convergence
results
Raman scattering
beyond RPA
Optics in WIEN2k
Outline
Basics
Program
Examples
Outlook
light scattering
dielectric tensor in the RPA
sumrules
symmetry
the band gap problem
program flow
inputs
outputs
convergence
results
Raman scattering
beyond RPA
Optics in WIEN2k
Outline
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
Properties & Applications
Wavefunction vs. Density
Hartree-Fock:
Koopman's theorem
DFT:
Lagrange parameters
Janak's theorem
auxiliary functions
Excited States
ionization energies
Light – Matter Interaction
Polarizability:
Linear approximation:
susceptibility c
conductivity s
Fourier transform:

dielectric tensor
Optical Properties
Response to external electric field E
Light Scattering
w
E
S
interband transition
ck
EF
w
intraband transition
vk
wave vector
Optical Properties
Energy
band structure
The Dielectric Tensor
Bloch electrons:
intraband
Interband contribution:
interband
independent particle approximation, random phase approximation (RPA)
Optical Properties
Free electrons: Lindhard formula
Optical "Constants"
Optical conductivity:
Complex refractive index:
Reflectivity:
Absorption coefficient:
Loss function:
Kramers-Kronig relations
Optical Properties
Complex dielectric tensor:
Intraband Contributions
Dielectric Tensor:
Drude-like terms
Plasma frequency:
Metals
Optical conductivity:
Optical Properties
Sumrules
Symmetry
monoclinic (a,b=90°)
orthorhombic
tetragonal, hexagonal
cubic
Dielectric Tensor
triclinic
Magneto-optics
without magnetic field, spin-orbit coupling:
cubic
with magnetic field ‖z, spin-orbit coupling:
KK
KK
tetragonal
Example: Ni
KK
Approximations used:
Ground state:
Local Density Approximation (LDA)
Generalized Gradient Approximation (GGA)
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?
Excited State Properties
Open Questions
The Band Gap Problem
Ionization energy
Electro-affinity
Band gap
shift of conduction bands: scissors operator
many-body perturbation theory: GW approach
Basics
Program
Examples
Outlook
light scattering
dielectric tensor in the RPA
sumrules
symmetry
the band gap problem
program flow
inputs
outputs
convergence
results
Raman scattering
beyond RPA
Optics in WIEN2k
Outline
Program Flow
converged potential
kgen
dense mesh
lapw1
eigenstates
lapw2
Fermi distribution
optic
momentum matrix elements
joint
dielectrix tensor components
kram
Re e
Im e optical coefficients
broadening
scissors operator
Optics in WIEN2k
SCF cycle
al.inop
2000 1
-5.0 2.2
1
1
OFF
"optic"
number of k-points, first k-point
Emin, Emax: energy window for matrix elements
number of cases (see choices below)
Re <x><x>
unsymmetrized matrix elements written to file?
800 1
-5.0 5.0
3
1
3
7
OFF
number of k-points, first k-point
Emin, Emax: energy window for matrix elements
number of cases (see choices below)
Choices:
Re <x><x>
1......Re <x><x>
Re <z><z>
2......Re <y><y>
Im <x><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
ni.inop (magento-optics)
"joint"
al.injoint
lower and upper band index
Emin, dE, Emax [Ry]
output units eV / Ry
switch
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
Inputs
1 18
0.000 0.001 1.000
eV
4
1
0.1 0.2
"kram"
al.inkram
0.1
0.0
1
12.6
0.2
broadening gamma
energy shift (scissors operator)
add intraband contributions 1/0
plasma frequency
gamma(s) for intraband part
as number of colums
as number of colums
Silicon
70
Dielectric function
60
Ime
50
si.inkram
Ree
40
30
20
10
0
-10
=0.05eV
-20
0
1
2
3
Energy [eV]
4
5
6
0.05 broadening gamma
1.00 energy shift (scissors operator)
0
....
Inputs
80
Basics
Program
Examples
Outlook
light scattering
dielectric tensor in the RPA
sumrules
symmetry
the band gap problem
program flow
inputs
outputs
convergence
results
Raman scattering
beyond RPA
Optics in WIEN2k
Outline
Outputs
Convergence
Interband Im e
150
125
100
75
165k
286k
560k
1240k
2456k
3645k
4735k
12.8
12.7
12.6
12.5
12.4
12.3
12.2
12.1
12.0
wp
0
1000 2000 3000 4000 5000
k -points in IBZ
50
25
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Energy [eV]
Example: Al
175
Sumrules
5
165 k-points
4735 k-points
Experiment
3
Example: Al
Neff [electrons]
4
2
1
0
0
10 20 30 40 50 60 70 80 90 100
Energy [eV]
Loss Function
120
80
intraband
60
40
total
20
0
Example: Al
Loss function
100
interband
0
5
10
Energy [eV]
15
20
Basics
Program
Examples
Outlook
light scattering
dielectric tensor in the RPA
sumrules
symmetry
the band gap problem
program flow
inputs
outputs
convergence
results
Raman scattering
beyond RPA
Optics in WIEN2k
Outline
100
Experiment
(zz)

= 35K
Ba,Cu = 18K
-7
-1
Spectral density [10 sr ]
Theory
80
100
80
60
60
40
40
20
20
0
0
0
100
200
300
A1g
400
-1
Raman shift [cm ]
500
600
0
100
200
300
400
500
600
-1
Raman shift [cm ]
CAD, H. Auer, R. Kouba, E. Ya. Sherman, P. Knoll, M. Mayer, Phys. Rev. B 65, 064501 (2002).
YBa2Cu3O7: A1g Modes
Raman Intensities
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
GW + Bethe-Salpeter equation
band gap problem
excitonic effects
The Bethe–Salpeter Equation
Beyond RPA
effective Schrödinger equation for the electron-hole pair
Thank you
for your attention!