Silvano De Franceschi

1
Orbital Kondo effect in carbon nanotube quantum
dots
Silvano De Franceschi
Laboratorio Nazionale TASC INFM-CNR, Trieste,
Italy
http//www.tasc.infm.it/defranceschis/SilvanoHP.h
tm
2
Simple and controllable systems can be obtained
in nanostructured materials.
gt quantum coherent electronics
(spintronics, quantum computation,
superconducting electronics)
gt fundamental quantum phenomena
(quantum coherent dynamics, entanglement,
strongly correlated systems,)
3
Spin ½ Kondo
??
??
4
Spin ½ Kondo
??
??
Goldhaber-Gordon et al., Nature (1998)
Cronenwett et al., Science (1998)
Schmid et al., Physica B (1998)
TK 0.1 - 1 K
Semiconductor dots
Nygard et al., Nature (2000)
TK 1 K
Carbon nanotube dots
Liang et al. J. Park et al. Nature (2002)
TK 10 K
Single-molecule dots
5
Spin ½ Kondo
??
??
In a metal with magnetic impurties
In a quantum dot with spin 1/2
6
Spin ½ Kondo
??
??
Gate-voltage control
gt Kondo effect in the unitary limit (G ? 2e2/h)
Science 289, 2105 (2000)
Magnetic-field control
gt integer-spin Kondo effect at singlet-triplet
degeneracy
Nature 405, 764 (2000)
Phys. Rev. Lett. 88, 126803 (2002)
Bias-voltage control
gt Kondo effect out of equilibrium
Phys. Rev. Lett. 89, 156801(2002)
7
Spin ½ Kondo
??
??
Orbital Kondo

?
??
8
Spin ½ Kondo
??
??
?
Orbital Kondo

?
??

,??
,??
SU(4) Kondo
?,??
?,??
Experiments in 2DEG QDs
Theory proposals in 2DEG QDs
S. Sasaki et al., Phys. Rev. Lett. (2004)  
L. Borda et al., Phys. Rev. Lett. (2003). G.
Zaránd et al., Solid State Comm. (2003).
9
Orbital magnetic moment
Periodic boundary conditions ? Quantized
momentum around circumference ? One-dimensional
subbands
E (k)
k
(?)
(?)
10
Nanotube quantum dot
E (k)
k
E?(1)
E-(1)
(?)
(?)
E?(2)
E-(2)
E?(3)
E-(3)
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Nanotube quantum dot
discrete spectrum 4-fold is lifted at B?0
(orbital splitting gtgt spin splitting) Phys.
Rev. Lett. 94, 156802 (2005)
Prediction Ajiki Ando, J. Phys. Soc. Jpn (1993)
12
Kondo effect in a NT QD with 4-fold shell
structure
Nature 434, 484 (2005)

• Four-fold shell structure at B0
• Each shell has two orbitals with opposite orbital
  magnetic moment
• Orbitals in different shells cross each other at
  high B

E
gmB0
B
B 0
B B0
gmB0
?, gt
, gt
?, gt
, gt
?, gt
, gt
?, gt
, gt
Intra-shell 4-fold degeneracy
Inter-shell 2-fold degeneracy
SU(4) Kondo
Orbital Kondo
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Linear conductance of a small-band-gap CNT QD
3rd SHELL
T8K
2nd SHELL
UD
U
half of 1st SHELL
n 3
n 2
n 1
4
3
B (T)
2
1
0
VG(V)
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Orbital magnetic moment
?orb ? 0.8 meV/T (gtgt ?B 0.06 meV/T)
Consistent with theoretical predictions
(AjikiAndo J.Phys.Soc. Jpn (1993))
and with recent experiments Minot et al., Nature
(2004) Zaric et al., Science (2004) Coskun et
al., ibid.
4
3
B (T)
2
1
0
VG(V)
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Orbital magnetic moment
E. Minot et al. Nature 428, 536 (2004)
They measured large orbital magnetic moments ?orb
DevF/4 0.7meV/T 12 ?B
Problems

• No 4-fold degeneracy
• No link between spectrum
• B-evolution of QD states

Small band gap semic. nanotube
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Orbital magnetic moment
?orb ? 0.8 meV/T (gtgt ?B 0.06 meV/T)
Consistent with theoretical predictions
(AjikiAndo J.Phys.Soc. Jpn (1993))
and with recent experiments Minot et al., Nature
(2004) Zaric et al., Science (2004) Coskun et
al., ibid.
4
3
B (T)
2
1
0
VG(V)
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QD orbital spin configuration
F
C
D
E
A
B
x20
4
3
II
IV
I
IV
II
I
III
B(T)
2
1
0
D
E
F
B
C
A
3.0
3.5
4.0
2.5
VG(V)
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QD orbital spin configuration
F
C
D
E
A
B
x20
4
3
II
IV
I
IV
II
I
III
B(T)
2
1
0
D
E
F
B
C
A
3.0
3.5
4.0
2.5
VG(V)
B
E
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B
E?(1)
E(1)
AA
(AA)
?,3
E?(2)
E(2)
?,2
1
?orb(2) g?B
2
?,1
E?(3)
E(3)
,1
,3
BB1
B1B
,2
,
(BB)
1
?orb(2) g?B
1
E
?orb(2) g?B
D12
D23
2
2
,
CC1
C1C2
C2C
,
(CC)
1
1
?orb(2) g?B
?orb(2) g?B
1
?orb(1) g?B
2
2
2
DD1
D1D2
D2D
,
,
(DD)
1
1
1
?orb(2) g?B
?orb(2) g?B
?orb(1) g?B
2
2
2
E2E
EE1
E1E2
,
,
(EE)
1
1
1
?orb(1) g?B
?orb(2) g?B
?orb(1) g?B
2
2
2
FF1
F1F2
F2F
,
,
(FF)
1
?orb(1) g?B
1
1
?orb(2) g?B
?orb(1) g?B
2
2
2
Phys. Rev. Lett. 94, 156802 (2005)
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QD orbital spin configuration
F
C
D
E
A
B
x20
4
3
II
IV
I
IV
II
I
III
B(T)
2
1
0
D
E
F
B
C
A
3.0
3.5
4.0
2.5
VG(V)
B
E
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Orbital Kondo Effect
10
0
1/2
8
1/2
B (T)
6
1
4
1/2
0
1/2
2
I
III
III
II
IV
II
0
0.90
0.95
VG (V)
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Orbital Kondo Effect
E
10
0
gmB0
1/2
8
1/2
B (T)
6
1
4
1/2
0
1/2
2
I
III
III
II
IV
II
0
0.90
0.95
VG (V)
B
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Low-impedance bipolar spin filter
II
II
III
III
I
I
IV
B
Switch VG ? switch filter polarity
VG
Orbital Kondo effect ? low impedance
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OrbitalSpin Degeneracy gt Strong Kondo
(multilevel)
4
3
IV
II
IV
I
II
I
III
B(T)
2
1
0
3.0
3.5
4.0
VG(V)
2.5
4
II
I
III
0
2
IV
V (mV)
0
-2
B 0T
-4

• Strong Kondo effect for 1 and 3 electrons in the
  shell

• Strong triplet-singlet inelastic cotunneling
  peaks for 2 electrons in the shell S. Sasaki,
  S. DF et al. Nature (2000)

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Multiple splitting _at_ finite B !
4
II
I
III
0
IV
2
V (mV)
B 0T
0
-2
-4
4
2
B 1.5T
V (mV)
0
-2
-4
2.50
2.75
3.00
3.25
3.50
VG (V)
The Kondo resonance for 1 electron splits in 4
peaks
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Four-fold splitting ? SU(4)-Kondo
Orbital splitting
dI/dV
2
I
1
Zeeman splitting
V (mV)
0
B
V
-1
-2
-2
-1
0
1
2
B (T)
Theory Choi, Lopez and Aguado,
cond-mat/0411665
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Inelastic cotunneling spectroscopy
PRL 86, 878 (2001)
DE
Step in dI/dV at Vlevel spacing
2
V (mV)
0
-2
-1.21
-1.19
VG (V)
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References

• Orbital Kondo effect Nature 434, 484 (2005)
• Magneto-transport spectroscopy Phys. Rev. Lett.
  94, 156802 (2005)

Collaborators
Pablo Jarillo-Herrero Jing Kong Herre van der
Zant Cees Dekker Leo Kouwenhoven