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Electron-nuclear spin dynamics in optically pumped semiconductor quantum dots
K.V.Kavokin
A.F.Ioffe Physico-Technical Institute, St.Petersburg, Russia
Thanks to: Igor Merkulov, Vladimir Kalevich, Vladimir Korenev,Roslan Dzhioev (Ioffe Institute)Alexander Tartakovskii, Evgeniy Chekhovich, Maurice Skolnick (Sheffield)Thierry Amand, Xavier Marie, Bernhard Urbaszek (Toulouse)
Single QD spectroscopy
Quantum dots
Electrons in conduction band: contact Fermi interaction
nn
nhf IsaHˆ
20 nn rAva eVA 100
Valence band holes: magnetic dipole interaction,much weaker
Nuclear spin fields acting on a localized electron
b) Disordered nuclear spinsa) Polarized nuclear spins
Ig
ABeB
N
NB
g
IIArvB N
eB
nnnnN
Nmax
2
222420
21
TBN 3.5max For GaAs
D. Gammon, Al.L. Efros, T.A. Kennedy, M. Rosen, D.S. Katzer, D. Park, S.W. Brown,V.L. Korenev, I.A. Merkulov, Phys. Rev. Lett. 86, 5176 (2001)
-1/2
+3/2
Bulk semiconductor with cubic lattice
+3/2 +1/2 -1/2 -3/2
+1/2-1/2
25.0max
S
Quantum wells, quantum dots
+3/2
+1/2 -1/2
-3/2
+1/2-1/2
5.0max
S
Relaxation by nuclei:M.I.Dyakonov, V.I.Perel JETP 65, 362 (1973)
Nuclear spins
“Motional slowing” (short correlation time):
cLs 21
1 2
Spin relaxation of donor-bound electrons
R.I.Dzhioev, K.V.Kavokin, V.L.Korenev, M.V.Lazarev, B.Ya.Meltser, M.N.Stepanova, B.P.Zakharchenya, D.Gammon, D.S.Katzer, Phys.Rev.B 66, 245204 (2002)
22
1
1 c
cLs
Electron spin precession in hyperfine field of nuclearspin fluctuations
I.A. Merkulov, Al.L. Efros, M. Rosen, Phys. Rev. B 65, 205309 (2002)
P.F. Braun, X. Marie, L. Lombez, B. Urbaszek, T. Amand, P. Renucci, V. Kalevich, K. Kavokin, O. Krebs, P. Voisin, Y. Masumoto, Phys. Rev. Letters 94, 116601 (2005)
B
S
Electrons in conduction band: contact Fermi interaction
2ˆ nnz
nzn
nnn
nhfIsIsIsaIsaH
20 nn rAva eVA 100
The total angular momentum is conserved!
jRJ
Dynamic polarization of nuclear spinsby hyperfine interaction
Spin influx into the nuclear spin system:R is the rate of a non-equilibrium processis a pseudovector changing sign under time inversionj
Optical orientation: eSj
~
BTIBSSQIBWBWI NT~/**
0*
1
Bj
||If
1
1
SSIIQ NBBB *
eBBB ~
1*0
~1
BTBW
SQI
N
eBN gIAB /
f
Bg
W
cB
cN
22*20
1
BBBN *
P. Maletinsky, C.W. Lai, A. Badolato, A. Imamoglu, Phys. Rev. B 75, 035409 (2007)
P.-F. Braun, B. Urbaszek, T. Amand, X. Marie, O. Krebs, B. Eble, A. Lemaitre, P. Voisin, Phys. Rev. B 74, 245306 (2006)
Dynamic polarization of nuclear spinsby hyperfine interaction with unpolarised electrons
B
+1
-1
0Nuclear spins
Electron spinsublevels
+BN
BTIBSSQIBWBWI NT~/**
0*
1
Pump
Pump
V.L.Korenev “Dynamic self-polarization of nuclei in low-dimensional systems”, JETP Letters, 1999
M.I.Dyakonov, V.I.Perel, JETP Letters, 1972 – dynamic self-polarization via Overhauser effect in the nuclear magnetic field
NT BSj
~requires low temperatures (below 1K)
0
1
2
2/3,2/1
2/3,2/1
2/3,2/1
2/3,2/1
Darkexcitons
Brightexcitons
2)/(11
Ew
Why magnetic field is needed to polarize nuclei?
1S
2S
12R
2
12
122121213
12
21ˆR
RSRSSSR
H dd
Magnetic dipole-dipole interaction
Local field BL
B>>BL : TN=T1, 103 s
B~BL : TN=T2 10-4 s
LBT
12
When we polarize nuclear spins in a magnetic field,we change the energy of the nuclear spin system!
IBEZ
Spin temperature A.Redfield, Phys.Rev.98, 1787 (1955)
nm
nn
nnm k
k
/exp/exp
0 0
n
For semiconductors:M.I.Dyakonov, V.I.Perel, JETP 41,759 (1975); D.Paget et al, PRB 15, 5780 (1977)
Spin temperature
22
1~)1(
3
LNNB BB
SBSSIk
Optical cooling of the nuclear spin system by oriented electrons. Magnetic field dependences of reciprocal spin-temperature (1) and mean spin of nuclei (2)
V.K.Kalevich et al, JETP Lett. 35, 20 (1982):
KN610
B
S
NB
V.K.Kalevich et al, JETP Lett. 35, 20 (1982):
KN610
NB
B
Phase transition into a magnetically ordered state
cooling
N =-10-8 K
N =5.10-7 K
P=85%
P=55%
Merkulov, Papava, Ponomarenko, Vasiliev, Can.J.Phys. 66, 135 (1988)antiferromagnetic
Theory for GaAs (laboratory frame):
Experiment and theory (rotating frame, CaF2, LiH):Abragam group, 1970s
Ferromagnetic or antiferromagnetic
Nuclear spin ordering
V. L. Korenev, PRL 99, 256405 (2007).
PN max=65%
<BN>
BNf
S0<S(t)>
I.A.Merkulov, G.Alvarez, D.R.Yakovlev, T.C.Schultess, PRB 81, 115107 (2010)
<BN>
BNf
S0<S(t)>
Mean nuclear spin grows at the expenseof nuclear spin fluctuations.At the same time, fluctuations are suppressed
1
2
TNT
Summary
1) Dynamical polarization of nuclei in semiconductorsproduces very strong, classical magnetic fields affectingelectron spins. This can be directly observed in optical spectraof individual quantum dots.2) Shifts of electron spin levels in nuclear fields result in nonlinear effects and a theoretical possibility of self-polarization.3) The nuclear spin system can be cooled down to microkelvins.If we manage to cool it further down, we could freeze nuclear spinsand obtain a nuclear antiferromagnet with strongly reduced fluctuations .4) To do this, we have to reach high nuclear polarization, which isnot so easy…