Transcript Nanocrystals

Single exciton spectroscopy in a
semimagnetic nanocrystal
J. Fernández-Rossier
Institute of Materials Science, University of Alicante, SPAIN
CdTe nanocrystal+ 1Mn
CdTe nanocrystal
PL
PL
S=5/2
2S+1=6
L. Besombes et al., PRL93, 207403, 2004
Absorption
6N
Mn
Spin
relaxation
Emission
Goal: Calculate PL and quantum information
Talk available in: www.ua.es/jfrossier/personal
4x6N
4
-1
-1
+1
 ()
+2
 ( )
1
Exciton States Manifold
(XSM)
6N
Ground State Manifold
(GSM)
Method :
1) Calculation of one-body wave
functions (for a given dot)
2) Evaluation of many body excitonMn spin Hamiltonian
3) Exact diagonalization of GSM
4) Exact diagonalization of XSM
5) Linear reponse theory
NMn
1
2
3
4
GSM Qbits
6
2
36
5
216 7
1296 10
FORMALISM
Ground State Manifold (GSM)
 


H 0   J I , I ' M I  M I '  gB B   M I
I ,I '
I
(S1,...,SN )  S1 ... SN
H0 G  EG G
6N
Exciton States Manifold (XSM)
e
4 6N
h
H0  H1  X
  
H1  H  J e  M I  S e ( xI )  Heisenberg
I
  
VB
 H  J h  M I  S h ( xI )
Ising
CB
I
 EX X
SPIN ORBIT
INTERACTION
  
M I  S h ( xI ) 
z
z 
M I S ( xI )
Valence band Spin orbit: Ising coupling
SHAPE MATTERS:
Quenching of transverse Hole-Mn exchange
  
M I  S h ( xI ) 
M I z S z ( xI )
GSM and XSM spectrum
H0  H1  X
 EX X
H0  H1  X
 EX X
Magnetic Field (0,0,5)
1 Mn
NG=6
NX=24
2 Mn
NG=36
NX=244
3Mn
NG=216
NX=864
E(meV)
E(meV)
Photoluminescence
(PL) Theory
PL: results
PL, theory
PL, experiment
Spontaneous Emission from X to G
2
X 


X p G  E X  EG   
2
 ( )
G
Optical
Selection rules
SPIN BLOCKADE
Energy
conservation
 ()
PL SPECTRUM
e  E X / k BT
PL( )   P( E X )X  
X
ZX
X
X
Energy (meV)
Occupation
of excited state
Thermal like
occupation
OPTICAL SPIN BLOCKADE
2


X p G  E X  EG   
2
G
X pG
2
 G ( S1 ,...,S N ) S ( S1 ,...,S N )
2
g pX
2
Standard
Franck Condon= optical selection
rule
Spin Blockade
24*6=144 XSM to GSM
Only 12 are allowed
GSM
X 
Photon measurement=
SPIN
MEASUREMENT
XSM
N=3. Narrowing and shift
PL, experiment
0T
2T
4T
6T
8T
10T
 ()
 ( )
P. S. Dorozhkin,
Phys. Rev. B 68,
195313 (2003)
Conclusions
• Model Hamiltonian gives good account of PL experiments:
– Single Mn
– Broadening and narrowing of lines
– Voigt wider than Faraday
• Optical detection of quantum state of N=1,..4 spin S=5/2 in
semiconductor nanocrystal.
Related papers:
1) JFR, in preparation
2) JFR, L. Brey, Phys. Rev. Lett. 93 117201 (2004)
3) G. Chiappe, JFR, et al, Condmat/0407639