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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.htm. ‘Simple’ and controllable systems can be obtained in nanostructured materials. - PowerPoint PPT Presentation
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Silvano De Franceschi
Laboratorio Nazionale TASC INFM-CNR, Trieste, Italy
Orbital Kondo effect in carbon nanotube quantum dots
http://www.tasc.infm.it/~defranceschis/SilvanoHP.htm
‘Simple’ and controllable systems can be obtained in nanostructured materials.
=> quantum coherent electronics
=> fundamental quantum phenomena
(spintronics, quantum computation, superconducting electronics…)
(quantum coherent dynamics, entanglement, strongly correlated systems,…)
| |
Spin ½ Kondo
| |
Spin ½ Kondo
TK ~ 10 K
TK ~ 1 K
Nygard et al., Nature (2000)
Liang et al. & J. Park et al. Nature (2002)
TK ~ 0.1 - 1 K
Goldhaber-Gordon et al., Nature (1998)Cronenwett et al., Science (1998)Schmid et al., Physica B (1998)
Semiconductor dots
Carbon nanotube dots
Single-molecule dots
In a metal with magnetic impurties:
In a quantum dotwith spin 1/2
| |
Spin ½ Kondo
TK
| |
Spin ½ Kondo
Gate-voltage control:=> Kondo effect in the unitary limit (G → 2e2/h)
[Nature 405, 764 (2000)]
[Science 289, 2105 (2000)]
Magnetic-field control:=> integer-spin Kondo effect at singlet-triplet degeneracy
[ Phys. Rev. Lett. 88, 126803 (2002)]
Bias-voltage control:
[Phys. Rev. Lett. 89, 156801(2002)]
=> Kondo effect out of equilibrium
++
| |
|+ |
+
Spin ½ Kondo
Orbital Kondo
|+, |+,
|, |,
++
++
| |
|+ |
+
Spin ½ Kondo
Orbital Kondo
=
SU(4) Kondo
L. Borda et al., Phys. Rev. Lett. (2003).G. Zaránd et al., Solid State Comm. (2003).
Theory proposals in 2DEG QDs Experiments in 2DEG QDsS. Sasaki et al., Phys. Rev. Lett. (2004)
k||
E (
k ||)
()()
v v
Periodic boundary conditions:
Quantized
momentum around circumference
One-dimensional
subbands
Orbital magnetic moment Orbital magnetic moment
Finite length L
discrete spectrum: 4-fold shell structure at
B=0 (orbital+spin degeneracy)
k||
E (
k ||)
E(1)
E(2)
E(3)
E(1)
E(2)
E(3)
()()
Nanotube quantum dotNanotube quantum dot
Gate
VVG
I
SWNT
v v
Orbital splitting
k||
E (
k ||)
E(1)
E(2)
E(3)
E(1)
E(2)
E(3)
()()
B 0
Nanotube quantum dot
Gate
VVG
I
SWNT
v v
B B
Prediction: Ajiki & Ando, J. Phys. Soc. Jpn (1993)
discrete spectrum: 4-fold is lifted at B0
(orbital splitting >> spin splitting)
[Phys. Rev. Lett. 94, 156802 (2005)]
Kondo effect in a NT QD with 4-fold shell Kondo effect in a NT QD with 4-fold shell structurestructure
Four-fold shell structure at B=0
Each shell has two orbitals with opposite orbital magnetic moment
Orbitals in different shells cross each other at high B
B
E
|+,
|,
|,
|+,gB0
|+, > |, >
| , >|+, >
B = 0
|+, > | , >
| , >|+, >
B = B0
gB
0
Intra-shell 4-fold degeneracy
Inter-shell 2-fold degeneracy
SU(4) Kondo
Orbital Kondo
[Nature 434, 484 (2005)]
2 3 40
1
2
G (e
2/h
)
VG (V)
4
3
2
1
0
B (
T)
n = 3 n = 2 n = 1
half of 1st SHELL
2nd SHELL
3rd SHELL
Linear conductance of a small-band-gap CNT QD
VG(V)
T=8K
UU+
4
3
2
1
0
B (
T)
v v
orb 0.8 meV/T (>> B = 0.06 meV/T)
Consistent with theoretical predictions (Ajiki&Ando J.Phys.Soc. Jpn (1993))
and with recent experiments:Minot et al., Nature (2004); Zaric et al., Science (2004); Coskun et al., ibid.
Orbital magnetic moment
VG(V)
Orbital magnetic momentOrbital magnetic moment
Colour scale x100
3
4
5
7
1
2
6
500
600
Vg (m
V)
700
800
B (T)0 3.6
E. Minot et al. Nature 428, 536 (2004)
0.3 0.4 0.5
-30
30
Vsd
(m
V)
0
Vg (V)
1 2 3 4
0.6
G (e2/h)
0
0.2
No 4-fold degeneracy No link between spectrum & B-evolution of QD states
They measured large orbital magnetic moments orb = DevF/4 ~ 0.7meV/T ~ 12 B
Problems:
Small band gap semic. nanotube
4
3
2
1
0
B (
T)
v v
orb 0.8 meV/T (>> B = 0.06 meV/T)
Consistent with theoretical predictions (Ajiki&Ando J.Phys.Soc. Jpn (1993))
and with recent experiments:Minot et al., Nature (2004); Zaric et al., Science (2004); Coskun et al., ibid.
Orbital magnetic moment
VG(V)
4
3
2
1
0
B(T
)
x20
IV I II III IV I II
A B C D E F
B1 C1
C2
D1
D2
E1
E2
F1
F2
G1
A’ B’ C’ D’ E’ F’
01/2 0
1
1/20
1
1/2
1/2 1/2
0
13.0 3.5 4.0VG(V)2.5
QD orbital & spin configurationQD orbital & spin configuration
k||
E (
k ||)
E(1)
E(2)
E(3)
E(1)
E(2)
E(3)
k||
E (
k ||)
E(1)
E(2)
E(3)
E(1)
E(2)
E(3)
k||
E (
k ||)
E(1)
E(2)
E(3)
E(1)
E(2)
E(3)
k||
E (
k ||)
E(1)
E(2)
E(3)
E(1)
E(2)
E(3)
k||
E (
k ||)
E(1)
E(2)
E(3)
E(1)
E(2)
E(3)
k||
E (
k ||)
E(1)
E(2)
E(3)
E(1)
E(2)
E(3)
4
3
2
1
0
B(T
)
x20
IV I II III IV I II
A B C D E F
B1 C1
C2
D1
D2
E1
E2
F1
F2
G1
A’ B’ C’ D’ E’ F’
01/2 0
1
1/20
1
1/2
1/2 1/2
0
13.0 3.5 4.0VG(V)2.5
QD orbital & spin configurationQD orbital & spin configuration
B
E
(AA’):
(CC’):
(DD’):
(EE’):
(FF’):
AA’
(BB’):BB1 B1B’
,
CC1 C2C’
,C1C2,
,DD1 D2D’,D1D2
,EE1E2E’
,E1E2
,FF1 F2F’
,F1F2
–orb(2) – – gB
12
orb(2) – – gB
12 –orb
(2) + – gB12
–orb(2) + – gB
12
orb(2) – – gB
12 –orb
(1) – – gB12
orb(2) + – gB
12
–orb(1) – – gB
12
orb(2) – – gB
12
–orb(1) – – gB
12
orb(2) + – gB
12
–orb(1) + – gB
12
orb(1) – – gB
12 –orb
(1) + – gB12
orb(2) + – gB
12
E(3)
E(2)
E(1)
E+(3)
E+(2)
E+(1)
E
B
+,1+,2
+,3
,3,2
,1
[Phys. Rev. Lett. 94, 156802 (2005)]
3 electrons 1 electron
4
3
2
1
0
B(T
)
x20
IV I II III IV I II
A B C D E F
B1 C1
C2
D1
D2
E1
E2
F1
F2
G1
A’ B’ C’ D’ E’ F’
01/2 0
1
1/20
1
1/2
1/2 1/2
0
13.0 3.5 4.0VG(V)2.5
QD orbital & spin configurationQD orbital & spin configuration
B
E
Orbital crossing at B=3T
Orbital Kondo Effect Orbital Kondo Effect
0.90 0.95
10
8
6
4
2
0VG (V)
B (
T)
0
1
0
1/2 1/2
1/21/2
IIIII IV I II III
B = B0 6T
Orbital flip
B
E
|+,
|,
|,
|+,gB0
B
B
|,
|+,
|+,
|,
E
B0
Orbital Kondo EffectOrbital Kondo Effect
B
E
|+,
|,
|,
|+,gB0
0.90 0.95
10
8
6
4
2
0VG (V)
B (
T)
0
1
0
1/21/2
1/21/2
IIIII IV I II III
B = B0 6T
Orbital flipOrbital flip at eV=B
B = B0 6T
-1 0 1 20.7
1.4
dI/d
V (e
2/h
)
V (mV)
2gB0
2B
1.1
1.2
0.1 1 T (K)
dI/d
V (
e2 /h)
B = B0 6T
-1 0 1 20.7
1.4
dI/d
V (e
2/h
)
V (mV)
2gB0
2B
1.1
1.2
0.1 1 T (K)
dI/d
V (
e2 /h)
B = B0 6T
Low-impedance bipolar spin Low-impedance bipolar spin filterfilter
B
VG
I II IIIIV
I II III
Switch VG switch filter polarityOrbital Kondo effect low impedance
4
3
2
1
0
B(T
)
IV I II III IV I II
G1
01/2 0
1
1/20
1
1/2
1/2 1/2
0
13.0 3.5 4.0VG(V)2.5
Orbital+Spin Degeneracy => Strong Kondo Orbital+Spin Degeneracy => Strong Kondo (multilevel)(multilevel)
4
2
0
-2
-4
V (
mV
)
B = 0T
I II III0 IV
2.50 2.75 3.00 3.25 3.50VG (V)
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)]
4
2
0
-2
-4
V (
mV
)
2.50 2.75 3.00 3.25 3.50
4
2
0
-2
-4
V (
mV
)
VG (V)
B = 0T
B = 1.5T
I II III0 IV
Multiple splitting @ finite Multiple splitting @ finite B B !!
The Kondo resonance for 1 electron splits in 4 peaks
V (
mV
)
-2 -1 0 1 2
2
1
0
-1
-2
B (T)
Four-fold splitting Four-fold splitting SU(4)- SU(4)-KondoKondo
Zeemansplitting
Orbitalsplitting
[Theory: Choi, Lopez and Aguado, cond-mat/0411665]
I
B
dI/dV
V
-1.21 -1.19
2
0
-2
VG (V)
V (
mV
)
Inelastic cotunneling spectroscopyInelastic cotunneling spectroscopy[PRL 86, 878 (2001)]
Step in dI/dV at V=level spacing
E
eV= +E
eV= -E
0 1 2 3
0.8
0.4
0
-0.4
-0.8
B (T)
V (
mV
)
B=0.7T
0.04
0.08
dI/
dV
(e2
/h)
0.5 0 -0.5
0.04
0.08
V (mV)
dI/
dV
(e2
/h)
B=80mT
0 1 2 3B (T)
0 1 2 3
-0.8
-0.4
0.0
0.4
0.8
V (
mV
)
B (T)
2gBB
gBB
4orbB
Zeeman, orbital, orbital + ZeemanZeeman, orbital, orbital + Zeeman
References
Pablo Jarillo-HerreroJing Kong Herre van der ZantCees DekkerLeo Kouwenhoven
Orbital Kondo effect [Nature 434, 484 (2005)]Magneto-transport spectroscopy [Phys. Rev. Lett. 94, 156802 (2005)]
Collaborators