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…