ambrosch-draxl optics bse

7/28/2019 Ambrosch-Draxl Optics Bse

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Contents

The dielectric tensor

The program

Inputs / outputs

Examples

The GW approach

The Bethe-Salpeter equation

Core excitons

X-ray circular dichroism


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Light-Matter Interaction


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Polarizability

susceptibility

conductivity

dielectric tensor


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Free electrons: the Lindhard formula

Bloch electrons

interbandintraband


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Independent particle approximation

h

v

c


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Complex dielectric tensor

Optical conductivity

Complex refractive index

Reflectivity

Absorption coefficient Loss function


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Dielectric tensor

Optical conductivity

Ene

rgy

E


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triclinic

monoclinic (,=90)

orthorhombic

tetragonal, hexagonal

cubic


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without magnetic field, spin-orbit coupling: cubic

with magnetic field z, spin-orbit coupling: tetragonal

KK

KK

KK


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The Program


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The Program Flow

x kgen dense mesh

x lapw1 Kohn-Sham states (higher Emax)

x lapw2 -Fermi Fermi distribution

x optic momentum matrix elements

x joint tensor components

x kram optical c o nsta n ts

life time broadeningsc isso rsshift


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Inputs

Al.inop

Ni.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?

800 1 number of k-points, first k-point-5.0 5.0 energy window for matrix elements3 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


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Inputs

Al.injoint

1 18 lower and upper band index0.000 0.001 1.000 Emin, dE, Emax [Ry]

eV output units eV / Ry4 switch1 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) total5...Im(EPSILON) for each band combination

6...intraband contr ibut ions

7...intraband contributions including band analysis


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0 1 2 3 4 5 6-20

-10

0

10

20

30

40

50

60

70

80

Re

Im

=0.05eV

Silicon

Energy [eV]

Inputs

Al.inkram

Si.inkram

0.1 broadening gamma0.0 energy shift (scissors operator)

1 add intraband contributions 1/012.6 plasma frequency0.2 (s) for intraband part

0.05 broadening gamma

1.00 energy shift (scissors operator)0

....


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Outputs

case.symmat case.mommat

case.joint

case.epsilon

case.sigmak

case.refraction

case.absorp

case.eloss


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Results


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Example: Al

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 500012.0

12.1

12.2

12.312.4

12.5

12.6

12.7

12.8

p

k-points in IBZ

165k

286k

560k

1240k

2456k

3645k

4735k

Interb

andIm

Energy [eV]


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Example: Al

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

165 k-points

4735 k-points

Experiment

Neff[e

lectrons]

Energy [eV]


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Example: Al

0 5 10 15 200

20

40

60

80

100

120

total

intraband

interband

Loss

function

Energy [eV]


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Example: Au


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Example: Au


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Examples: Ag, Au

W. S. M. Werner, M. R. Went, M. Vos, K. Glantschnig, and C. Ambrosch-DraxlPhys. Rev. B 77, 161404(R) (2008).

Ag

Au


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17 Elemental Metals

W. Werner, K. Glantschnig, and CADJ. Phys. Chem. Ref. Data 38, 1013 (2009).


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17 Elemental Metals

Overall excellent agreement in the entireenergy range (up to 100 eV)

New REELS data agree

much better with DFT

Details of the band

structure matter .

W. Werner, K. Glantschnig, and CADJ. Phys. Chem. Ref. Data 38, 1013 (2009).


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People

C. Ambrosch-Draxl and J. O. Sofo

Line a r o p tic a l p ro p e rt ie s o f so lid s w ithin the full-p o te nt ia l line a rize d

a u gm ente d p la n ewa ve m e tho d

Comp. Phys. Commun. 175, 1-14 (2006).

Robert Abt


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Exploring the Core Region


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A polarized photon beam excites electronsof different spin with different cross sections

X-Ray Magnetic Circular Dichroism

2p1/2

2p3/2

25% 63%75% 37%

Right Left

25% 63% 75% 37%

exchange

splitting

SO splitting


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XMCD

L. Pardini, F. Manghi, V. Bellini, and C. Ambrosch-Draxl,in Linear and Chiral Dichroism in the Electron Microscope,

Edt. P. Schattschneider, 2011).

Right

Left

Theory

ExperimentIntensity[arb.u

nits]

Energy [eV]Energy [eV]


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Beyond


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Elemental Metals: Ag

Interband transition onset:


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Can Functionals Help?


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Beyond the Ground State

Ground state

Excited state

Many-body treatment needed

2 routes


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h

Probing Electronic States

h

v

c

N-1 electrons

v

c

N+1 electrons


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The quasi horse according to Richard D. Mattuk

The Quasiparticle Concept


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The Quasiparticle Concept

The quasiparticle equation

The Kohn Sham equation

G0W0

G = GKS+

G0= G

KS


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The GWApproach

All-electron & pseudopotential results

R. Gmez-Abal, X. Li, M. Scheffler, and CAD, PRL 101, 036402 (2008).

G0W

0


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Beyond


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Effective H atom

effective mass m*

dielectric constant

h

v

c

The Bethe-Salpeter Equation


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Two-particle wavefunction

Effective two-particle Schrdinger equation

KS states from GS calculation



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Diagonal term

Direct term - attractive

Exchange term - repulsive



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Bethe-Salpether equation (BSE)

Independet particle approximation (IPA)



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P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. Lett. 89, 056405 (2002).P. Puschnig and C. Ambrosch-Draxl, Phys. Rev. B 66, 165105 (2002).



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Typical approach:

LAPW allows for a BSE treatment

How well do both approaches compare?

For deep core states they are basicallyequivalent

What about semi-core levels?

J. J. Rehr, J. A. Soininen, and E. L. Shirley, Phys. Scr. T115, 207 (2005).



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Li K edge in LiF

Core Excitations

Exp.: K. Handa et al., Memoirs of the SR Center Ritsumeikan University 7, 3 (2005).

W. Olovsson, I. Tanaka, T. Mizoguchi, P. Puschnig, and CAD, PRB 79, 041102(R) (2009).


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Status of Codes

Independent-particle approximation

XMCD

GW

BSE

CAD and J. O. Sofo, CPC 175, 1-14 (2006).

H. Jiang, R. Gmez-Abal, X. Li, Ch. Meisenbichler, CAD, and M. Scheffler,CPC to be published.

P. Puschnig and CAD, Phys. Rev. B 66, 165105 (2002).

L. Pardini, V. Bellini, CAD, and F. Manghi, submitted to CPC (preprint).


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