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Exciton and Biexciton Energies in GaN/AlN Quantum Dots
G. Hönig, A. Schliwa, D. Bimberg, A. Hoffmann
Teilprojekt A5
Institut für FestkörperphysikTechnische Universität Berlin
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c-plane GaN/AlN QDs
- Vertical electron-hole separation- Redshift of X- X energy inverse proportional to QD-height
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Outline
(1) Exciton States
(2) Biexciton Complex in Relation to Exciton
(3) A New Approach: Wigner-crystals
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Electron Hole Interaction
Direct Coulomb Interaction• related to charges
• attractive between electron and hole
direct exchange
Exchange Interaction• related to spins
• repulsive between electron and hole
( if spins are antiparallel, if parallel = 0 )
• splits up energies related to spin orientation
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Root of 4 Exciton StatesDiagonalization of the Hamilton-matrix leads to the eigenstates:
&
Imagine the particle states stem from the conduction and heavy hole valence band, respectively. (neglecting the intermixed band structure)
The spins would be:
Total spin of exciton states: BRIGHT: ±1 DARK: ±2
Because of the repulsive nature of exchange interaction between electron and hole, BRIGHT states have always higher energy than DARK states!
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Exciton and Biexciton States
3,4 optically active(BRIGHT)
1,2 optically inactive(DARK)
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full linear polarization 180° periodicity 90° phase shift between states fine-structure splitting on the order of meV
Experimental Findings
C. Kindel, …, Y. Arakawa, G. Hönig, …, A. Hoffmann, D. Bimberg Phys. Rev. B 81, 241309(R) (2010)
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Investigations of FSS
comparatively huge FSS on the order of meV height increase (with constant aspect ratio) causes decrease of FSS diameter increase (with constant height) causes decrease of FSS agreement with experimental findings (black squares)
C. Kindel, …, Y. Arakawa, G. Hönig, …, A. Hoffmann, D. Bimberg Phys. Rev. B 81, 241309(R) (2010)
Series are calculated with 20% laterally elongated QD structures.
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Outline
(1) Exciton States
(2) Biexciton Complex in Relation to Exciton
(3) A New Approach: Wigner-crystals
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Biexciton Relative to Exciton
Ebind = 2 EX - EXX
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Meanfield Biexciton
Exciton Biexciton
Spatial electron hole separation leads to higher energy of the biexciton!
Correlation Energy & Conditional Probabilities
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Weak lateral hole confinement => hole can move freely at QD bottom => X: Hole can correlate its density to the electron position => XX: Hole can correlate its density to the positions of e, e, h
=> repulsive interactions strongly decrease, => attractive interactions strongly increase
Nature of Correlation Energy
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Height DependenceExciton Biexciton
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Height Dependence
Ebind increases with decreasing QD height
Exciton DARK-BRIGHT splitting is important
Relative to BRIGHT states Ebind can become positve
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Height Dependence
Slopes:Theo. = (47 ± 6) meV/eVExp. = (51 ± 6) meV/eV
D. Simeonov, …, N. Grandjean, Phys. Rev. B 77, 075306 (2008)
Ebind increases with decreasing QD height
Exciton DARK-BRIGHT splitting is important
Relative to BRIGHT states Ebind can become positve
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Outline
(1)Exciton States
(2)Biexciton Complex in Relation to Exciton
(3) A New Approach: Wigner-crystals
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Wigner Crystal Biexciton
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Wigner Crystal Biexciton
Could declare absence of splitted biexciton emission lines in QD sepctra with visible exciton splitting.
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Experimental Findings
Is one of these lines the biexciton?
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Experiment vs. Wigner-XX
Avoiding holes
Attractive exchange interaction between parallel hole spins
≈ 25 meV energy reduction of biexciton state
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Summary
Ground state exciton: 4 possible states BRIGHT states splitting of meV DARK states splitting of mEV
Biexciton and exciton emission line crossing New sort of Wigner crystal like biexcitons possible No split up biexciton emission lines
