1. Phonon coupling to exciton complexes in single quantum dots D. Dufåker a, K. F. Karlsson a, V. Dimastrodonato b, L. Mereni b, P. O. Holtz a, B. E. Sernelius a, and E. Pelucchi b a IFM Semiconductor materials, Linköping University, Sweden b Tyndall National Institute, University College Cork, Ireland The 11th edition of the international conference PLMCN: Physics of Light-Matter Coupling in Nanostructures Cuernavaca (Mexico), 12-16 April, 2010

2. Outline Introduction to Pyramidal QDs Introduction to LO-phonon coupling Experimental results Interpretation/Computational results Conclusions

3. Pyramidal QDs InGaAs QDs in AlGaAs barriers Patterned GaAs substrate (111)B G. Biasiol et al., PRL 81, 2962 (1998); Phys. Rev. B 65, 205306 (2002) self-limiting profile growth anisotropy capilarity effects alloy segregation A. Hartmann PRL 84 5648(2000) GaAs AlGaAs Barrier InGaAs QD MOCVD

4. Pyramidal QDs Simplified model AlGaAs layer 30 % Al InGaAs layer 15 % In InGaAs QD 15 % Surrounding AlGaAs Barrier 20-30 % AlGaAs VQWR 1 4 % 1 Q. Zhu el al., Nano Lett. 6 1036 (2006)

5. Pyramidal QDs Efficient light extraction >120 kcnts/sec Site-controlled, isolated QDs C 3v -symmetry – emitters of entangled photons 1 1 R. Singh et al., PRL 103 063601 (2009); K. F. Karlsson el al., PRB Accepted (R) (2010); A. Schliwa et al., PRB 80 161307R (2009); A. Mohan et al., Nature Phot. 2 (2010) Designed with excited electron levels (x2) s (x4) p (x2) s 2X X Vac C 3v

6. Pyramidal QDs Control of charge population by excitation conditions 1 1 A. Hartmann PRL 84 5648(2000) Normalized PL Intensity QD2

7. LO-phonon coupling Coupling of LO-phonons with excitons is electric (Fröhlich) The total coupling is given by the difference between the couplings of electrons and holes An exciton formed by an electron-hole pair is a neutral entitiy Equal probability density function of electrons and holes  vanishing coupling In real systems: electrons and holes have different charge distribution Side view Top view Gray:Quantum dot profile Red: Hole probability density (10% of max) Blue:Electron probablity density (10% of max) Side view Charge distribution Charge density

8. LO-phonon coupling Excitation spectrum T = 0 K No spectral linewidth Dispersion less phonon branch Huang-Rhys parameter S 0-phonon 1-phonon 2-phonon Energy ħ  LO 0-phonon 1-phonon 2-phonon Energy Emission spectrum ħ  LO

9. LO-phonon coupling Ensemble measurements InAs/GaAs QDs S ~ 0.015 R. Heitz et al., PRL 83 4654 (1999) Single CdSe/ZnCdSe QD (X, 2X) S ~0.035, 0.032 F. Gindele et al., PRB 60 2157R (1999) P. Hawrylak et al., PRL 85 389 (2000) Single InAs/GaAs QDs, PL-excitation spectroscopy

10. LO-phonon coupling Extra charge? Spherical GaAs microcrystallities (r>11 nm) S enhanced from 0.001 to 0.01 by an extra charge Nomura & Kobayashi PRB 45 1305 (1992) PRL 85 389 (2000) PL-excitation spectroscopy InAs/GaAs QDs

11. Experimental results X X+X+ XX 2X  1000 XX X X2X2 X2X2 Direct emission Phonon replicas (1 st order) T=4K QD1

12. Experimental results QD1 Replica of X + significantly weaker than X and X - Replica of X - similar strength as replica of X LO-phonon energy 36.4  0.1 meV Larger spectral linewidth of replicas

13. Experimental results Measured Huang-Rhys Parameter 17 QDs

14. Computations Excitonic ground states computed self-consistently by 8  8 band k  p theory in Hartree approximation Strain induced deformation potentials simulated by continuum elastic theory

15. Computations X X+X+ XX 2X Charge density (e/nm 3 ) Real space maps Huang-Rhys parameters S  1000

16. Interpretation XX+X+ Side Top Repulsion  Delocalization Attraction  Localization Coulomb interactions induces changes in the charge distribution; different exciton complexes have different charge distributions J. J. Finley et al., PRB 70 201308R (2004)

17. Computations   initial Charge density (e/nm 3 ) X X+X+ XX 2X Integrated diagonal phonon scattering matrix elements relative X Strong phonon coupling for an exciton comples does not imply strong phonon replicas.

18. Interpretation Measured LO-phonon energy: 36.4  0.1 meV (GaAs bulk: ~36.6 meV) VQWR (4% Al) ħ  LO = 36.4 meV Surrounding barrier (20-30% Al) ħ  LO = 35.0-35.5 meV GaAs-like LO-phonon energy in AlGaAs 0  4%:  E  -0.2 meV

19. Interpretation Spectral linewidth Bulk-like LO-phonon dispersion  broadening < 50  eV GaAs LO-phonon lifetime  broadening ~ 70  eV 1 Composition variations and alloys disorder 2 1 M. Canonico PRL 88 215502 (2002) 2 B. Jusserand PRB 24 7194 (1981)

20. Comparison of phonon replicas of charged and neutral exciton complexes. S = 0.001 – 0.004 X+X+ X Coulomb induced charge cancellation of an electron- hole pair Extra positive charge may result in strongly reduced phonon replicas due to the heavier mass of the hole X + : Strongest LO-phonon scattering matrix element and simultaneously the weakest phonon replicas Adiabatic independent-phonon model yield values of the Huang-Rhys parameter in agreement with experiments Conclusions