Claudia Ambrosch-DraxlInstitute for Theoretical Physics

University Grazclaudia.ambrosch@uni-graz.at

Optical Properties of Solidswithin WIEN2k

Outline

Opti

cs in W

IEN

2k

light scatteringdielectric tensor in the RPAsumrulessymmetrythe band gap problem

Basics

Program

Examples

Outlook

program flowinputs

Raman scatteringbeyond RPA

outputsconvergenceresults

Outline

Opti

cs in W

IEN

2k

light scatteringdielectric tensor in the RPAsumrulessymmetrythe band gap problem

Basics

Program

Examples

Outlook

program flowinputs

Raman scatteringbeyond RPA

outputsconvergenceresults

Exci

ted S

tate

s

Properties & Applications

Dielectric functionOptical absorptionOptical gapExciton binding energyPhotoemission spectraCore level spectraRaman scatteringCompton scatteringPositron annihilationNMR spectraElectron spectroscopy understand physics

characterize materialstailor special properties

Light emitting diodesLasersSolar cellsDisplaysComputer screensSmart windowsLight bulbsCDs & DVDs

Exci

ted S

tate

s

Wavefunction vs. Density

Hartree-Fock:

DFT:

ionization energies

Lagrange parameters

auxiliary functions

Janak's theorem

Koopman's theorem

Opti

cal Pro

pert

ies

Light – Matter InteractionResponse to external electric field E

Linear approximation: susceptibility

conductivity

dielectric tensor

Fourier transform:

Polarizability:

Light Scattering

ES

Opti

cal Pro

pert

ies

intraband transitioninterband transition

Ener

gy

wave vector

EF

band structure

kc

kv

Opti

cal Pro

pert

ies

The Dielectric TensorFree electrons: Lindhard formula

Bloch electrons:

interbandintraband

Interband contribution:

independent particle approximation, random phase approximation (RPA)

Optical "Constants"

Opti

cal Pro

pert

ies

Kramers-Kronig relationsComplex dielectric tensor:

Optical conductivity:

Loss function:

Absorption coefficient:

Reflectivity:

Complex refractive index:

Intraband Contributions

Meta

ls

Drude-like termsDielectric Tensor:

Optical conductivity:

Plasma frequency:

Sumrules

Opti

cal

Pro

pert

ies

Symmetry

Die

lect

ric

Tenso

r

cubic

monoclinic (,=90°) orthorhombic

tetragonal, hexagonal

triclinic

without magnetic field, spin-orbit coupling:

Magneto-optics

Exam

ple

: N

i

cubic

tetragonalwith magnetic field ‖z, spin-orbit coupling:

KK

KK

KK

Exci

ted S

tate

Pro

pert

iesOpen Questions

Approximations used:

Local Density Approximation (LDA)Generalized Gradient Approximation (GGA)

Ground state:

Excited state:Interpretation within one-particle pictureInterpretation of excited states in terms of ground state propertiesElectron-hole interaction ignored (RPA)

Where do possible errors come from?How to treat excited states ab initio?

The Band Gap Problem

many-body perturbation theory: GW approachshift of conduction bands: scissors operator

Electro-affinity

Ionization energy

Band gap

Outline

Opti

cs in W

IEN

2k

light scatteringdielectric tensor in the RPAsumrulessymmetrythe band gap problem

Basics

Program

Examples

Outlook

program flowinputs

Raman scatteringbeyond RPA

outputsconvergenceresults

Program Flow

Opti

cs in W

IEN

2k

SCF cycle converged potential

kgen dense mesh

eigenstateslapw1

Fermi distributionlapw2

momentum matrix elementsoptic

dielectrix tensor components joint

Re Im optical coefficients broadeningscissors operator

kram

"optic"

Inputs

2000 1 number of k-points, first k-point -5.0 2.2 Emin, Emax: energy window for matrix

elements1 number of cases (see choices below)1 Re <x><x>OFF unsymmetrized matrix elements written to

file?

al.inop

ni.inop (magento-optics)800 1 number of k-points, first k-point -5.0 5.0 Emin, Emax: energy window for matrix elements3 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>

"joint"

Inputs

al.injoint

1 18 lower and upper band index0.000 0.001 1.000 Emin, dE, Emax [Ry] eV output units eV / Ry 4 switch 1 number of columns to be considered0.1 0.2 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

"kram"

Inputs

al.inkram

0.1 broadening gamma0.0 energy shift (scissors operator)1 add intraband contributions 1/012.6 plasma frequency0.2 gamma(s) for intraband part

0 1 2 3 4 5 6-20

-10

0

10

20

30

40

50

60

70

80

Re

Im

=0.05eV

Silicon

Die

lect

ric

fun

ctio

n

Energy [eV]

si.inkram

0.05 broadening gamma1.00 energy shift (scissors operator)0....

as number of columsas number of colums

Outline

Opti

cs in W

IEN

2k

light scatteringdielectric tensor in the RPAsumrulessymmetrythe band gap problem

Basics

Program

Examples

Outlook

program flowinputs

outputsconvergenceresults

Raman scatteringbeyond RPA

Outp

uts

Convergence

Exam

ple

: A

l

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

25

50

75

100

125

150

175

0 1000 2000 3000 4000 500012.012.112.212.312.412.512.612.712.8

p

k-points in IBZ

165k 286k 560k 1240k 2456k 3645k 4735k

In

terb

an

d Im

Energy [eV]

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

165 k-points 4735 k-points Experiment

Nef

f [el

ectr

ons]

Energy [eV]

Sumrules

Exam

ple

: A

l

Loss Function

Exam

ple

: A

l

0 5 10 15 200

20

40

60

80

100

120

total

intraband

interband

L

oss

fun

ctio

n

Energy [eV]

Outline

Opti

cs in W

IEN

2k

light scatteringdielectric tensor in the RPAsumrulessymmetrythe band gap problem

Basics

Program

Examples

Outlook

program flowinputs

Raman scatteringbeyond RPA

outputsconvergenceresults

0 100 200 300 400 500 6000

20

40

60

80

100

Raman shift [cm-1]

= 35K Ba,Cu = 18K

(zz)

Spe

ctra

l den

sity

[10-7

sr-1]

Theory

Raman Intensities

YB

a2C

u3O

7:

A1

g M

odes

CAD, H. Auer, R. Kouba, E. Ya. Sherman, P. Knoll, M. Mayer, Phys. Rev. B 65, 064501 (2002).

Experiment

0 100 200 300 400 500 6000

20

40

60

80

100

Raman shift [cm-1]

A

1g

Current Developments

Gradient Corrections (GGA)LDA + UExact Exchange (EXX)

Self-interaction correction (SIC)Non-local exchange / screened exchange

Kohn-Sham theory

Generalized Kohn-Sham theory

Time dependent DFT

band gap problemexcitonic effects

non-local effectscorrelation effectsband gap problem

Many-body perturbation theory

GW + Bethe-Salpeter equation

response to time-dependet perturbation

The Bethe–Salpeter Equationeffective Schrödinger equation for the electron-hole pair

Beyond R

PA

Thank you for your attention!