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Igor Reshetnyak, Lucia Reining

New starting point for the calculation of optical properties

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Outline

• State of art methods• Comparative analysis of TDLDA & BSE• Analysis of the details• Resonant only case• Conclusions

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Commonly used methods

TDDFT BSE

Groundstatefxc

GW

They work in a completely different ways!

+ e.h.

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Codes:

Bulk Si, q= 0.75 (1,1,1) c.c. units of 2pi/a = 0.612217 a.u.; Exp. from [1]

Comparison of real spectra

[1] H.C. Weissker et al. Phys. Rev. B, 81:085104, Feb 2010

For Si EELS, the TDLDA & BSE results very similar

Are the underlying objects connected?

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4-point equations & Hamiltonian form

TDLDABSE

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Hamiltonian form

4-point equations & Hamiltonian form

Formal solution

Both formulated the same way

• Comparative analysis• Mixed methods• Deeper understanding

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Underlying stuffJD

OS(

ε)

ε, eV

• For JDOS only difference – GW (scissor)• The vectors in transition space spread over a small range • For TDLDA spread larger than for BSE. Agrees with [2]

ε, eVCo

effici

ent

[2] Z.-h. Yang and C.A. Ullrich Phys. Rev. B, 87:195204, May 2013

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Digging into details...

ε, eV

Ove

rlap

Overlaps happen over a small range

But how do we explain similarity in spectra? The JDOS is shifted. Arethe eigenvectors making theopposite shift?

eigenvector, #

eige

nvec

tor,

#

Overlaps

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Digging into details...

• Interference is very important! Cancelations in • Not just , but also S is important v~

v~

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Can we replace parts of BSE by smth?

• The dE required is smaller without coupling• For EELS not particularly good

BSE, width = dETDLDA

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And for optics?

• The dE required is smaller without coupling

• For optical properties should do better

Usage for combined methods!

BSE, width = dETDLDA

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Some good & bad news

• Effect of coupling can be very important for large transferred momenta q.

• One should not interpret results in a basis with positive energies only

• Interference effects important• TDLDA and BSE give similar results for EELS• Space for combined methods & analysis

possible

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Thank you!

Question?

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(1)

TDDFT BSE

KS DFTfxc

GW

(2)

(2)

(3)

(3)

Commonly used methods

== (1)=

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• Average shift practically 0 • Nothing specific around ε = 0• Even if the effect !=0 cannot amount for the shift

Digging into details... (2)