Post on 22-Feb-2016
description
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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)