Christian Scheller Physical Review Letters PRL 100, (2008)

Transcription

1 Christian Scheller Physical Review Letters PRL 100, (2008)

2 Contents Overview D yakonov Perel spin relaxation Rashba effect Samples and symm. measurements (MPGE) Spin lifetime measurements (TRKR) Conclusions

3 Overview Spin dephasing for QW in (110)-oriented GaAs substrate, measured using time resolved Kerr rotation for different degrees of symmetry of the QW long spin lifetime in (110) crystal orientation since eff. B-field due to SO-coupling along growth direction Spins along growth do not precess D yakonov spin relaxation suppressed QW asymm. Structure Inversion symm. broken inplane B-field due to rashba effect

4 D yakonov Perel effect elastic scattering of electrons in 2DEG conserves Spin inplane B-field Spin precession mean free path << precession period Dephasing time τ SO Average phase change between two collisions due to precession: ϕ = Ωτ Ω : Lamor frequency τ : Collision time τ SO via random walk calculation M.I. D yakonov and V.I. Perel Sov.Phys. JETF 38 (1971) p.1053

5 Random walk in 1 Dimension N central limit theorem: Binomial distribution Gauss phase variance after N scatters: Dephasing condition: Dephasing time: var ( ) N ϕ =Ωτ N 1 var ( ) N ϕ 1 N = Ω 2 τ 2 1 τso = Nτ τso = Ω 2 τ

6 Rashba spin-orbit coupling Structure Inversion Asymmetry SIA (due to asymm. QW) Asymm. potential causes E-field: E = φ (relativistic) spin-orbit coupling: E B-field z

7 Rashba and Dresselhaus Hamiltonian 2 p H = + ( ) ( ) xky ykx xkx yky 2m α σ σ + β σ σ Rashba (SIA) Dresselhaus (BIA) rewrite in terms of effective B-field ur ur r ur r H = σ B k B k = k k ( ),where ( ) (, ) eff α SO eff x y k y ll [010] E=E F (β=0) B RSO p x k x ll [100] k-dependent effective in-plane magnetic field GaAs grown in [100]-direction E.I. Rashba, Sov. Phys. Solid State 2 (1960) S.D. Ganichev et al. Phys.Rev.Letters Vol (2004)

8 Overview long spin lifetime along (110) since eff. B-field II growth QW asymm. Structure Inversion symm. broken inplane B-field due to rashba effect D yakonov Perel spin relaxation meachanism

9 Samples and Symmetry QWs grown on (110)-oriented Si-δ-doped GaAs/Al 0.3 Ga 0.7 As

10 Symmetry measurements Symmetry is given by l r χ = l + r How to check the symmetry? -so far, rely on growth process -here: magnetophotogalvanic effect (MPGE) MPGE: absorption of light in QW in presence of B-field photocurrent (only observed for asymm. QWs) MPGE so far observed in QWs of: -(100)-grown GaAs -SiGe -InAs

11 Photocurrents measured at room temperature Sample excited by lin.pol. pulsed molecular NH 3 laser (THz) Current via voltage drop across 50Ω load resistor (unbiased) Ohmic contacts on each sample side Duration of photocurrent equals pulse duration (100ns) J = J B J MPGE BG subtraction: ( ) ( ) x x y x 0

12 Photocurrents measured at room temperature MPGE for lin.pol. radiation at normal incidence: * * EE MPGE γ δ + EE δ γ MPGE 2 jα = φαβγδbβ jx = φxβxxbβ E x αβγ 2 β Consider symm. arguments: C S (C 2V ) for asymm.(symm.) QWs MPGE current: coupl. x-comp. current pol.vector with B-field axial vector MPGE SIA 2 BIA 2 x = φxyxx y x + φxzxx z x j B E B E V.V. Bek kov et al. J.Phys.Condens.Matter 17, 3405 (2005)

13 C S, C 2V point group symmetry C 2V : methanal CH 2 O symm. QW C S : CHOCl asymm. QW replace one of the hydrogen atoms loose on mirror plane

14 Time resolved Kerr rotation reflect linear polarized beam on magnetized surface elliptical polarization, where θ (Kerr angle) is the angle between major axis and lin. polarization axis. θ uur M II, where the magnetization is given by need to spin polarize sample at first uur M r = s i

15 Nup Ndown Polarization P = (fully polarized for P=±1) N + N up down Band structure of GaAs Energy level diagram for GaAs Excite electrons using circular polarized light 3 γ( σ 1) 1 1 ( 1) 1 P M =+ γ σ j M j P M =+ = = > j = M j = Up to 30% spin polarization Seminar: Production of pol. electrons at Mainzer Mikrotron (MAMI)

16 Kerr rotation Exp. decay of magnetization and therefore the Kerr angle θ K exp Δt = θ0 τ SO Additional B-field spin precession with lamor freq. exponential decay, amplitude modulation with lamor freq. Δt θ ( ) K = θ0 cos ωlδt exp τ SO, where ω = L gμbb h

17 Spin dephasing time measurements Dephasing time increases for increasing degree of symm. B, D equal degree of symm. expect equal deph.time, but -different mobilities different scattering time different dephasing time: 1 τ SO -different photocurrents measured = (D yakonov Perel) Ω 2 τ

18 Conclusions longest spin lifetime for symm. doped QW upper limit for spin dephasing in GaAs QWs This is in contrast to (100) grown structures: -(110) structures grown at C -(100) structures grown above C - high growth temp. migration of dopants SIA

19 Thanks for your attention! Questions?

20 MPGE and BIA Measurement of the photocurrent by applying a B-field along the growth direction. BIA Due to the C 2V symm. of sample E (structure inversion symm.) no photocurrent is observed for B II y, but for all samples a photocurrent is observed for B II z.