Excited state properties p p - WIEN 2k

Excited state properties
p
within WIEN2k
Claudia Ambrosch-Draxl, University of Leoben, Austria
Chair of Atomistic Modelling and Design of Materials

Beyond the ground state
Basics about light scattering
The dielectric i tensor
The WIEN2k code
Outlook
The program
Input / output
Examples
TDDFT versus manybody perturbation theory
Contents

Light-Matter Interaction

Resonse to external electric field E
Polarizability
Linear approximation
susceptibility χ
conductivity σ
dielectric tensor
∋
Fourier transform
Light-Matter Interaction

The dielectric tensor
Free electrons: the Lindhard formula
Bloch electrons
intraband
interband
Light-Matter Interaction

Interband contributions
Independent particle approximation
RPA
En
nergy
c k
hω
E F
hω
S
E
v k
Light-Matter Interaction

Optical constants
Complex dielectric tensor
Optical conductivity
Complex refractive index
Reflectivity
Absorption coefficient
Loss function
Light-Matter Interaction

Intraband contributions
Dielectric tensor
Ene
ergy
E F
Optical conductivity
Drude-like terms
plasma frequency
Light-Matter Interaction

Sumrules
Light-Matter Interaction

Symmetry
triclinic
monoclinic (α,β=90°)
orthorhombic
tetragonal, hexagonal
cubic
Light-Matter Interaction

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

The Program …

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

optic
Al.inop
2000 1 number of k-points, first k-point
-5.0 2.2 energy window for matrix elements
1 number of cases (see choices)
1 Re
OFF write unsymmetrized matrix elements to file?
Ni.inop
800 1 number of k-points, first k-point
-5.0 50 50 5.0 energy window for matrix elements
3 number of cases (see choices)
1 Re
3 Re
7 Im
OFF
Choices:
1......Re
2......Re
3......Re
4......Re
5......Re
6......Re
7......Im
8......Im
9......Im
Inputs

joint
Al.injoint
1 18 lower and upper band index
0.000 0.001 1.000 E min , dE, Emax [Ry]
eV
output units eV / Ry
4 switch
1 number of columns to be considered
0.1 0.2 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

kram
Al.inkram
0.1 broadening gamma
0.0 energy shift (scissors operator)
1 add intraband contributions 1/0
12.6 plasma frequency
0.2 Γ(s) for intraband part
Si.inkram
0.05 broadening gamma
1.00 energy shift (scissors operator)
0
....
80
70 Silicon
60
Imε
50
40
Reε
30
20
10
0
-10
Γ=0.05eV
-20
0 1 2 3 4 5 6
Energy [eV]
Inputs

optic
joint
kram
case.symmat
case.mommat
case.joint
case.epsilon
case.sigmaksigmak
case.refraction
case.absorpabsorp
case.eloss
Outputs

Results …

Convergence
m ε
nterba and Im
I
175
150
125
100
75
50
25
165k
286k
560k
1240k
2456k
3645k
4735k
12.8
12.7 12.6
ω p
12.5
12.4
12.3
12.2
12.1
12.0
0 1000 2000 3000 4000 5000
k-points in IBZ
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Energy [eV]
Example: Al

Sumrules
N eff
[ele ectrons s]
5
4
3
2
1
165 k-points
4735 k-points
Experiment
0
0 10 20 30 40 50 60 70 80 90 100
Energy [eV]
Example: Al

Loss function
120
100
Loss fu unctio n
80
intraband
60
40 total
20 interband
0
0 5 10 15 20
Energy [eV]
Example: Al

Band structure
Band structure
16
18
non-relativistic
scalar-relativistic
relativistic
8
10
12
14
16
s
2
4
6
8
rgy [eV]
s
d
f
pd
pf
p
-6
-4
-2
0
Energy
pd
-12
-10
-8
-6
K
X
G
L
W
W
K
X
G
L
W
W
K
X
G
L
W
W
Example: Au

Density of states
4
DOS
[ states per
eV and cell]
3 total
2
1
0
3 d
2
1
0
0.4
0.2
s
0.0
0.4 p
0.2
0.0
0.4
0.2
f
0.0
-10 0 10 20 30 40
Energy [eV]
S / energy 2
joint DOS
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
non-relativistic
scalar-relativistic
relativistic
0 5 10 15 20 25
Energy [eV]
Example: Au

Dielectric tensor
joint DOS / ener ergy 2
0.14
0.12
0.10
0.08
0.06
0.04
0.02
non-relativistic
scalar-relativistic
relativistic
0.00
0 5 10 15 20 25
Energy [eV]
Diele lectric Functio ction
14
12
10
8
6
4
2
0
-2
Au
12 Ree
non-relativistic
scalar-relativistic
10
8
Ime
6
4
2
0
-2
12
10
relativistic
8
6
4
2
0
-2
0 5 10 15 20 25 30 35
Energy [eV]
Example: Au

Theory versus experiment
K. Glantschnig and C. Ambrosch-Draxl (preprint)
Example: Pt

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, , 1-1414 (2006)
People

… and Beyond

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

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