Quantum Dots – Past, Present and Open Questions Yigal Meir
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Transcript of Quantum Dots – Past, Present and Open Questions Yigal Meir
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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
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Quantum dot – an artificial device, small enough so that quantization of energy levels and electron charge
are important
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vertical quantum dots
Single molecules
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Tarucha et al.
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Vg
L
R
Transmission resonance when
)0()0(
1)0()0(
1
)0()0(11 )1(
NNggNN
gNgNNN
EEeVeVEEeNVEVNeEEE
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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
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Coulomb Blockade
eUCeV
CeNCQV
g
g
//
//
UV
eVUNEE
NeVNN
UE
g
gNN
gN
1
2
)1(
charging of a capacitor
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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.
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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
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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)
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McEuen et al.
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Spin flips
Kouwenhoven et al.
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NNg UV 1
Level statistics and random matrix theory
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Artificial molecules
Dynamics
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R
L
Probes the excited states
Nonlinear transport
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Foxman et al.
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Correlation between excited state of N electrons and the ground states of N+1 electrons
Marcus et al.
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B
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Is transport through a quantum dot coherent ?
Yacoby, Heiblum
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CosBABA
eABBABeA ii
2
Re2
22
*222
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Checking quantum measurement theory
Aleiner, Wingreen, Meir
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Buks et al.
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The Kondo effect
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Relevant to transport through quantum dots
Ng and Lee
Glazman and Raikh
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chemical potential
Conductance (2e2/h)
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Goldhaber-Gordon, Kastner (1998)Cronenwett et al. (1998)
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Kouwenhoven et al.
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ond
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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.
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The Kondo effect out of equilibriumMeir, Wingreen, Lee
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The two-impurity Anderson model
Georges & Meir
chang
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Kondo vs. RKKY
Marcus et al.
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The two-channel Kondo effect
Non- Fermi liquid ground state
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Oreg & Goldhaber-Gordon
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More open questions
Phase of transmission amplitude
Heiblum
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eV=E
Inelastic process ?
Ensslin
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Noise measurements and electron bunching
Heiblum
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Thomas et al. (1996,1998,2000)
The “0.7 anomalyThe “0.7 anomaly””
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Rejec and Meir
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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.
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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: