Quantum Dots

1
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
2
Quantum dot an artificial device, small enough
so that quantization of energy levels and
electron charge are important
3
vertical quantum dots
4
Tarucha et al.
5
Vg
mR
mL
Transmission resonance when
6
Example 2d harmonic oscillator
7
(No Transcript)
8
Coulomb Blockade
charging of a capacitor
9
Coulomb blockade peaks
Single electron transistor
Kastner et al.
10

• Now include quantum effects
• energies

• wavefunctions
• The peak amplitude depends on the wavefunction
  the electron tunnels into

11

• Example - Quantum Hall effect
• All states within a landau level are degenerate,
  except edge states, En(n1/2)hwc
• The radii are quantized pr2nf0 (n Landau
  level index)

n1
n0
12
McEuen et al.
13
(No Transcript)
14
Spin flips
Kouwenhoven et al.
15
Level statistics and random matrix theory
16
Artificial molecules
17
Nonlinear transport
mL
mR
Probes the excited states
18
Foxman et al.
19
Correlation between excited state of N electrons
and the ground states of N1 electrons
Marcus et al.
20
(No Transcript)
21
Is transport through a quantum dot coherent ?
22
(No Transcript)
23
(No Transcript)
24
Checking quantum measurement theory
Aleiner, Wingreen, Meir
25
Buks et al.
26
The Kondo effect
27
(No Transcript)
28
Conductance (2e2/h)
chemical potential
29
Goldhaber-Gordon, Kastner (1998) Cronenwett et
al. (1998)
30
Kouwenhoven et al.
31
Kondo scaling
Temperature K
Goldhaber-Gordon et al.
32
The Kondo effect out of equilibrium
Meir, Wingreen, Lee
33
The two-impurity Anderson model
Georges Meir
34
Kondo vs. RKKY
Marcus et al.
35
The two-channel Kondo effect
Non- Fermi liquid ground state
36
Oreg Goldhaber-Gordon
37
More open questions
38
(No Transcript)
39
Ensslin
Inelastic process ?
40
Noise measurements and electron bunching
Heiblum
41
The 0.7 anomaly
42
Rejec and Meir
43
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.

44
Theory Experiment

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