PowerPointPrsentation

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Friedrich-Schiller-Universität Jena Institut für
Festkörpertheorie und -optik Roman Leitsmann,
W.G. Schmidt, P.H. Hahn and F. Bechstedt
Excitons in Second-Harmonic Generation (SHG)
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Structure of the Talk

• Motivation
• Theoretical Overview
• Results for the linear Response
• Results for the SHG-spectra
• Conclusion

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Motivation
What is SHG ?
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Motivation
1) SHG signal is due to symmetry reasons highly
surface specific (unusuall sensitive non-invasive
method to investigate surfaces / interfaces)
2) Different approaches yield formulas, which are
not easily be seen equivalent.
3) Calculated spectra differ appreciable from
each other and from the experimental data.
How can we explain this ?
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Theoretical Overview
Time dependent perturbation theory (interaction
picture) External Hamiltonian (minimum coupling
convention)
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Theoretical Overview
Induced current density operator - series in
the external potential - the expectation values
can be written as
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Theoretical Overview
Polarization and response of the system
We can write the response functions in the
following form
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Theoretical Overview
Level of (quasi)particle interactions -
independent (quasi)particle DFT-LDA (GW)
- Coulomb correlated (quasi)particle
DFT-LDA (GW) excitonic effects
local field effects
(single-particle states)
(two-particle states)
orthonormal complete
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Theoretical Overview
Bloch representation of the current operator

• so we have to evaluate terms like
• this can be done by using the Wicks theorem

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Theoretical Overview
Independent (quasi)particle
Independent (quasi)particle - dielectric
function (Bloch representation) - SHG
susceptibility (Bloch representation)
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Theoretical Overview
Excitons
Coulomb correlated (quasi)particles - the time
evolution of ? ? ? is given by - the Exciton
Hamiltonian (Bloch represent.) is given by
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Theoretical Overview
Excitons
Too hard to solve the eigenvalue problem (rank H
250000) ? change to initial value problem
- time evolution is calculated with finite time
steps of 0.02 eV-1
? dielectric function
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Theoretical Overview
Excitons
? SHG susceptibility
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Results for the linear Response

• good agreement with experiment Phys.Rev.B 27,
  985(1983)
• quasiparticle effects are very important
• excitonic effects are less important, but still
  improve the agreement

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Results for the SHG response
Exp.1 - Bergfeld/Daum PRL 90 (2003) 036801 Exp.2
- Bethune et al. PRB 11 (1975) 3867 Exp. 3 -
Chang et al. PRL 15 (1965) 415 Exp. 4 -
Parson/Chang Opt. Com. 3 (1971) 173
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Conclusion
Major achievements
? showed the analytical equivalence of the
approaches from Sipe et al., Aspnes,
Adolph-Bechstedt and this work.
? explained the large discrepancy between
Adolph-Bechstedt and other theoretical works
? developed an approach to implement excitonic
and local field effects in the SHG spectra
? the calculated SHG response agrees well with
the experiment in the overall structure
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Conclusion
Open questions
? still problems with the convergence for
excitonic SHG spectra

• large under estimation of the experimental SHG
  signal at 1.5eV (--gt surface contribution ? )

? need more experimental data, especially for
higher energies
? surface calculations should be performed
complete work will be published in PRB (status
accepted)
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Thank you for your attention.