Exciton and Biexciton Energies in GaN/AlN Quantum Dots G. Hönig, A. Schliwa, D. Bimberg, A. Hoffmann Teilprojekt A5 Institut für Festkörperphysik Technische Universität Berlin

2 c-plane GaN/AlN QDs - Vertical electron-hole separation - Redshift of X - X energy inverse proportional to QD-height

3 Outline (1) Exciton States (2) Biexciton Complex in Relation to Exciton (3) A New Approach: Wigner-crystals

4 Electron Hole Interaction Direct Coulomb Interaction related to charges attractive between electron and hole directexchange Exchange Interaction related to spins repulsive between electron and hole ( if spins are antiparallel, if parallel = 0 ) splits up energies related to spin orientation

5 Root of 4 Exciton States Diagonalization 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!

6 Exciton and Biexciton States 3,4 optically active (BRIGHT) 1,2 optically inactive (DARK)

7  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, (R) (2010)

8 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, (R) (2010) Series are calculated with 20% laterally elongated QD structures.

9 Outline (1) Exciton States (2) Biexciton Complex in Relation to Exciton (3) A New Approach: Wigner-crystals

10 Biexciton Relative to Exciton E bind = 2 E X - E XX

11 Meanfield Biexciton Exciton Biexciton Spatial electron hole separation leads to higher energy of the biexciton! Correlation Energy & Conditional Probabilities

12 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

13 Height Dependence ExcitonBiexciton

14 Height Dependence  E bind increases with decreasing QD height  Exciton DARK-BRIGHT splitting is important  Relative to BRIGHT states E bind can become positve

15 Height Dependence Slopes: Theo. = (47 ± 6) meV/eV Exp. = (51 ± 6) meV/eV D. Simeonov, …, N. Grandjean, Phys. Rev. B 77, (2008)  E bind increases with decreasing QD height  Exciton DARK-BRIGHT splitting is important  Relative to BRIGHT states E bind can become positve

16 Outline (1)Exciton States (2)Biexciton Complex in Relation to Exciton (3) A New Approach: Wigner-crystals

17 Wigner Crystal Biexciton

18 Wigner Crystal Biexciton Could declare absence of splitted biexciton emission lines in QD sepctra with visible exciton splitting.

19 Experimental Findings Is one of these lines the biexciton?

20 Experiment vs. Wigner-XX  Avoiding holes  Attractive exchange interaction between parallel hole spins  ≈ 25 meV energy reduction of biexciton state

21 Summary  Ground state exciton: 4 possible states  BRIGHT states splitting of meV  DARK states splitting of  EV  Biexciton and exciton emission line crossing  New sort of Wigner crystal like biexcitons possible  No split up biexciton emission lines