Influence of hyperfine interaction on optical orientation in self-assembled InAs/GaAs quantum dots

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1 Influence of hyperfine interaction on optical orientation in self-assembled InAs/GaAs quantum dots O. Krebs, B. Eble (PhD), S. Laurent (PhD), K. Kowalik (PhD) A. Kudelski, A. Lemaître, and P. Voisin Laboratoire de Photonique et de Nanostructures- CNRS, Marcoussis, France P.-F. Braun (PhD), B. Urbaszek, L. Lombez (PhD), P. Renucci J.-L. Gauffier, X. Marie and T. Amand Laboratoire de Nanophysique, Magnétisme et Optoélectronique (LNMO), INSA Toulouse, France LNMO FRISNO 9, Les Houches February 2007

, PRA57, 120 (1998) «Quantum computation with quantum dots» A quantum gate in condensed matter We still need to

2 Motivations General framework : using the spin degree of freedom of electrons for «quantum computation» in condensed matter. D. Loss and D.P. DiVincenzo et al., PRA57, 120 (1998) «Quantum computation with quantum dots» A quantum gate in condensed matter We still need to identify all the mechanisms influencing electron spin dynamics in actual semiconductor QD s. J.R. Peta et al., Science 309, 2180 (2005) Optical orientation is a very efficient technique to address this issue.

3 Outline Introduction : electron spin in InAs QD s Optical orientation of trions Role of the hyperfine interaction Conclusion

«islands» Lens-shaped QDs after capping with GaAs Growth

4 Self-assembled InAs/GaAs quantum dots 1 µm Molecular Beam Epitaxy of InAs / GaAs 7% lattice mismatch formation of «islands» Lens-shaped QDs after capping with GaAs Growth axis (AFM image, LPN) GaAs ~20 nm InAs ~ 4 nm Wetting Layer

5 Electron spin in InAs quantum dot Spin-orbit effect : no spin-splitting of the discrete states (Kramers s degeneracy) P e 50 mev Theory : Khaetskii et al., PRB64, (2000) T 1 ~ 1 µs Experiments : Kroutvar et al., Nature 432,81 (2004) for magnetic field above 4T. S e B z Strong exchange interaction between confined carriers Hyperfine interaction with a «frozen» configuration of nuclear spins Merkulov et al., PRB65, (2002) : T 1* ~ 1 ns in zero-magnetic field.

6 Electron-hole exchange : fine structure of neutral excitons [-110] D 2d [110] [-110] C 2v [110] 70µeV splitting Bright ±1 x = X 0 X + X 0 y = i 2 2X 0 Dark ± 2 Trions are required for optical orientation of electron spin in weak magnetic fields (<1 T)

7 No fine structure for trion ground state H = ( a X e h α= x, y, z α J α + b α J 3 α Negative trion X - ) ( σ (1) α + σ 0 (2) α ) Positive trion X + σ + σ + Circular polarization of PL emitted by trions monitors the spin-state of the unpaired carrier.

8 Optical selection rules in InAs/GaAs quantum dots (i) Spin-orbit interaction couples spin to orbital angular momentum (ii) Anisotropic confinement + biaxial strain in InAs QD s : Conduction Band Excitation λ~900 nm + σ VB ground state is a pure heavy-hole with J z = ±3/2 ψ ψ e ( r e ) S σ J z = ± PL 1 2 h ( r h ) ( X ± iy ) σ J z = ± J + J = e z + σ h z J photon z σ Valence Band «pure» selection rules

9 Outline Introduction : electron spin in InAs QD s Optical orientation of trions Role of the hyperfine interaction with the nuclei Conclusion

10 Charge-tunable structures InAs quantum dots 0.8 ev Schottky barrier 1 µm 5 nm NiCr n-gaas ev g GaAs 20 nm Ga 0.7 Al 0.3 As 100 nm GaAs 30 nm GaAs 25nm n-gaas 200nm GaAs This structure allows for the control of : (i) excess electron(s) under forward bias (ii) excess hole(s) under reverse bias by optical charging

11 µ-pl map of a single QD PL energy depends on the charge due to Coulomb interaction. T=5K E X X 0 6 mev X + X +* X + * X + S e S h P h S e S h P h Γ Lorentzian fit

12 Optical orientation set-up N liq. cooled CCD Double-Spectrometer Grating :1200 g/mm Focal length : 0.6 m Resolution : 25 µev (20pm) Excitation : σ + Detection : σ + or σ - Polarization : P = I I σ + σ + Analyzer + I I σ σ λ 4 Polarization-unsensitive beam-splitter He Liq. flux cryostat (T sample ~5 K) λ 4 Glan Polarizer x 50 cw Ti:Sa Laser

Spin relaxation in a longitudinal magnetic field B z? Linearly polarized excitation Measurement of PL circular polarization Exc. 1.34 ev, Det. 1.27 ev Polarization 0.2 Vg=1.

13 Spin relaxation in a longitudinal magnetic field B z? Linearly polarized excitation Measurement of PL circular polarization Exc ev, Det ev Polarization 0.2 Vg=1.1 V t spin=5.15 p0= Magnetic FieldHTL QD ensemble PL polarization Spin lifetime of hole, exciton and electron >> than radiative lifetime (1ns)

Optical orientation of an ensemble of QD s : Under σ+ polarized excitation : PL circular polarization of a QD ensemble Exc. 1.

14 Optical orientation of an ensemble of QD s : Under σ+ polarized excitation : PL circular polarization of a QD ensemble Exc ev, Det ev Excitation Energy 2D continuum P-P S-S σ + - Fidelity of spin orientation above 75 % for X - trions even in B=0T - A longitudinal magnetic field enhances optical orientation of X + 0

15 Spin dynamics in zero magnetic field X + X 0 X 0 & X - X - X 2-, X 3-, τ hole spin > 20 ns S. Laurent et al., PRL94, (2005) Time-resolved PL of a QD ensemble after a ps excitation pulse (streak camera) ThedifferencebetweenX + and X- spin dynamics points toward the hyperfine interaction as a source of spin relaxation for conduction electrons (X + )

16 Outline Introduction : electron spin in InAs QD s Optical orientation of trions Role of the hyperfine interaction Conclusion

17 Hyperfine interaction for an ensemble of InAs QD s z N nuclei with spin In (9/2) As (3/2) (I.A. Merkulov et al., PRB65, (2002)) Inhomogeneous spin dephasing in the time T due to Larmor precession about randomly oriented nuclear fields B 1 B 2 S 0

18 Non-resonant σ+ excitation GaAs 30 nm GaAs 30 nm GaAs 30 nm GaAs buffer Be δ-doping Observation of spin dephasing in p-doped QD s Circular Polarization (%) P.-F. Braun et al., Phys. Rev. Lett. 94, (2005) T = 10 K X + B z =400 mt B z =100 mt B z =0 Intensity B z =400m T Time (ps) Time (ps) B=0 T : Two regimes : Decay : ~ 700 ps Polarization plateau B>0.1 T : Screening of the ~30 mt fluctuations of nuclear «magnetic field» Yet, we observe polarization above theoretical value ( 53%) for X+ in a single QD I + I -

19 Spin relaxation causes Dynamic Nuclear Polarization (DNP) electron-nuclei flip-flop Overhauser shift Transfer of angular momentum to the nuclei spins S e 2 requirements : Screening dipolar interaction between nuclei (T 2 =10-4 s) external magnetic field along z ( 1 mt) Pumping the QD with spin polarized electrons along z δ n 300µeV for 100% polarization

20 Overhauser-shift of X + and X - in a small magnetic field QD magnet (i) 0.2 T magnetic field // z (ii) Optical orientation under intradot excitation (1.31 ev) P~70% σ- σ+ P~70% B.Eble et al., Phys. Rev. B 74, (R) (2006) Evidence of spin transfer from the electron in the QD to the QD nuclei

21 Dynamic nuclear polarization in a magnetic field B z (1) Stationnary Hamiltonian of hyperfine interaction : The flip-flop term is a random perturbation between states split in energy by ħω e. Its time dependence is characterized by a correlation time τ c Competition between the total splitting ħω e and the level broadening ħ/τ c.

22 Dynamic nuclear polarization in a magnetic field B z (2) Time-dependent perturbation theory (A. Abragam, 1961) Rate equation for <I z > The rate of nuclear polarization depends on the nuclear polarization! T d = depolarization time of the nuclei (dipole-dipole or quadrupolar) Implicit equation for the equilibrium nuclear polarization : Asymmetry in B z or S z, nonlinearity and possibly bistability.

23 Assymmetrical dependence of DNP on the field : Fixed σ+ excitation B n B z B n B z Polarizing the nuclei is more difficult in the direction which increases the total electron spin-splitting

Dependence of DNP on the electron spin polarization <S z > Excitation polarization is varied step by step from σ+ to σ- <S z > and δ n are both measured (See also C.

24 Dependence of DNP on the electron spin polarization <S z > Excitation polarization is varied step by step from σ+ to σ- <S z > and δ n are both measured (See also C.W Lai et al., PRL 96, (2006)) This explains the strong polarization (>70%) of X+ observed under steady excitation (see also A.Ebbens et al., PRB72, (2005)).

25 Bistability of the Nuclear Polarization Vs electron spin polarization Theory B z B n Unstable solution P.-F. Braun et al., Phys. Rev. B 74, (2006) B z B n See also : A.I. Tartakovskii, et al., PRL 98, (2007) (Sheffied University) P. Maletinsky, et al. Phys. Rev. B 75, (2007) (ETH Zurich)

26 Optical orientation of a single X+ state in zero nuclear field σ+/σ- excitation modulated at 50 khz with time-gated detection. σ σ + σ σ + theoretical fit Regime of spin relaxation in the randomly oriented nuclear field B n I.A. Merkulov et al., PRB65, (2002))

27 Electron spin - nuclear spins : a strongly coupled system Circular polarization of a QD ensemble Exc. σ ev, Det.1.27 ev

28 Summary Trion states allow the optical orientation of a single electron or hole spin Demonstration of electron spin dephasing due to the hyperfine interaction with nuclei A small magnetic field (100mT) can screen this effect but dynamic nuclear polarization occurs (even in zero field) and contributes to the spin dynamics!

Nuclear spins in semiconductor quantum dots. Alexander Tartakovskii University of Sheffield, UK

Nuclear spins in semiconductor quantum dots Alexander Tartakovskii University of Sheffield, UK Electron and nuclear spin systems in a quantum dot Confined electron and hole in a dot 5 nm Electron/hole