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Quantum Dots – Past, Present and Open Questions
Yigal Meir
Department of Physics &The Ilse Katz Center for Meso- and Nano-scale
Science and Technology
Beer Sheva, ISRAEL
Quantum dot – an artificial device, small enough so that quantization of energy levels and electron charge
are important
00, )2/1()2/1( yxnn nnyx
NNNNg EEeV 1
)(
otherwise
NEEEEVe NNNNNg 0
,...12,6,2)()( 011
)0,0(0
)0,1(),1,0(2 0
)1,1(),0,2(),2,0(3 0
)2,1(),1,2(),0,3(),3,0(4 0
)(2
1),( 22
0 yxmyxV
N
iiNE
1
Example: 2d harmonic oscillator
0.08
0.06
0.04
0.02
0
g (e
2 /h)
-300 -280 -260 -240 -220Vg (mV)
(a) B = 30 mTT ~ 100 mK
Coulomb blockade peaks
Single electron transistor
Kastner et al.
Now include quantum effects:
• energies
NNg
gNNN
g
N
iiN
UV
eVUNEE
NeVNN
UE
1
11
12
)1(
• wavefunctions
The peak amplitude depends on the wavefunction the electron tunnels into
n=1
n=0
Example - Quantum Hall effect:• All states within a landau level are degenerate, except edge states, En=(n+1/2)hc
• The radii are quantized r2=n0 (n – Landau level index)
Correlation between excited state of N electrons and the ground states of N+1 electrons
Marcus et al.
arX
iv:c
ond
-mat/
98
072
33
v1
15
Ju
l 1
99
8arX
iv:c
ond
-mat/
98
072
33
v1
15
Ju
l 1
99
8
Vds I
Vg
(b)
-140 -130 -120 -110 -100 -90 -80 -7 00
0.1
0.2
0.3
0.4
0.5
100mK 200mK 300mK 500mK 800mK 1000mK 1500mK 2200mK 3000mK 3800mK
-140 -130 -120 -110 -100 -90 -80 -7 00
0.1
0.2
0.3
0.4
0.5 -4 -2 0 2 4 6 8 10 12
0 2 40
5
10
15
20
25
102
103
104
0
0.1
0.2
0.3
0.4
0.5(a) = -0.91
= -1.26 = -1.60 = -1.95 = -3.67
102
103
104
(b) = -0.74 = -0.48 = -0.22 = 0.12 = 0.47 = 1.50
10-2
10-1
100
101
0
0.2
0.4
0.6
0.8
1
= -0.74, = 280 eV= -0.91= -1.08
= -0.98, = 215 eV
= -1.00, NRG results
= 0.00
h
eG
22
Temperature [K]
Kondo scaling
Goldhaber-Gordon et al.
conclusions• Quantum dots are controllable miniaturized devices,
which can be instrumental in our understanding of mesoscopic and strongly correlated systems.
• May be the basic ingredient in applications of quantum computing.
• In spite of their apparent simplicity, still many open questions.
P. A. Lee P. Nordlander M. Kastner
N. S. Wingreen M. Pustilnik U. Meirav
J. Kinaret A. Golub P. McEuen
B. L. Altshuler Y. Avishai E. Foxman
X.-G. Wen A. Auerbach D. Goldhaber-Gordon
A.-P. Jauho P. Rojt L. Kouwenhoven
A. L. Aleiner O. Entin-Wohlman R. Ashoori
E. Shopen A. Aharony M. Heiblum
A. Georges T. Aono A. Yacoby
D. C. Langreth Y. Dubi C. Marcus
K. Hirose T. Rejec K. Ensslin
Y. Gefen T. Ihn
Theory: Experiment:
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