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Quantum Noise of a Carbon Nanotube Quantum Dot in the Kondo Regime
Exp : J. Basset, A.Yu. Kasumov, H. Bouchiat, and R. Deblock
Laboratoire de Physique des Solides – Orsay (France)
Theory : P. Simon (LPS), C.P. Moca and G. Zarand (Budapest)
Workshop: « Charge and heat dynamics in nano-systems »
Orsay 2011
• What is electronic noise?
Introduction to electronic noise
I(t)=<I>+δδδδI(t)
Vsd
I(t)
Conducting system
•Why measure noise?
Electronic correlations, effective charge, characteristic energy
scale, …
<I>
Noise in the quantum regime
• energy scales (eV, ∆, …) and characteristic times
• quantum noise : zero point fluctuations
System
mesoscopic device
Detector
Amplifier, Quantum dot, SIS junction,…
Emissionν<0
ν>0
Absorption
hν >> kBT, hν > eV
Source Detector
Mesoscopic system
S SI
Noise measurement in the quantum regime
Carbon nanotube in
the Kondo regime
SIS junctionNoise detection with SIS junction :
Kouwenhoven’s group, Science (2003)
P.M. Billangeon et al.,PRL (2006)
ResonantCircuit
T=20 mK
0.0 0.2 0.4 0.6 0.8 1.0
0
10
20
30
40
50
IPAT
<0
IPAT
>0
hνννν/e
hνννν/e
ABSORPTION
I D(n
A)
VD(mV)
2∆∆∆∆/e
EMISSION
Quantum Noise Detection with a SIS Junction
EMISSION ABSORPTIONPhoto-assisted tunneling current
(PAT)
ν=30GHz
S SI
Ingold & Nazarov (1992)
superconductor
source
draingate
NT
500nm
1µm
junctions
LL
VG
A
VD
R
A
VS
R
Resonant coupling betwen a Carbon nanotube and a SIS detector
� ¼ wavelength resonant circuit
� Independent DC polarisations of the source and the detector
� Coupling at eigen frequencies of the resonator (30 GHz and harmonics)
� Coupling proportional to the quality factor (J. Basset et al. PRL 2010)
L=nλλλλ/4n odd integer
7
Kondo effect in quantum dots
U : charging energy; εεεε0: energy level; Γ=ΓL+ΓR : coupling to the reservoirs
Under specific conditions:- Odd number of electrons in the dot- Intermediate transparency of the contacts- Temperature below Kondo temperature TK
Kondo effect : dynamical screening of the dot’s spin
ΓL ΓR
reservoir reservoir
Quantum
dotVS
A
VG
gate
8
Kondo resonance in quantum dots
TK = (U Γ)1/2 exp (-1/ Jeff ν)
- Transport through second order spin flip events
- Formation of a many body spin singlet (spin of the dot + conduction electrons)
- Peak in the DOS of the dot at the Fermi energy of the leads � Kondo resonance
virtual
virtual
Heff = Jeff σ.S with Jeff = Γ/ν U ν: DOS
9
TK
T < TK
T > TK
TK
Signature of the Kondo effect on conductance
What about Kondo dynamics?
Increase of conductance at low
temperature
What about emission noise?
A
?
VS
VG
Out-of-equilibrium Kondo dynamics at frequencies hν~kBTK?
11
LL
VG
A
VD
R
A
VS
R
source
drain
gate
NT
500nm
1µm
junctions
Carbon nanotube coupled to the SIS detector
Detector biased for emission noise detection
12
-2 -1 0 1 2
0.2
0.4
0.6
0.8
1.0
1.2
dId
V(e
²/h
)
VS(mV)
Kondo effect in the measured carbon nanotube
Kondo ridge
Center of the ridge � TK=1.4K � ν=30GHz
TK
VG=3.12V
Zero bias peak
What about noise?
Recent theoretical predictions
C.P. Moca et al., PRB (2011)
Signature of the Kondo effect on
noise :
Logarithmic singularity at V=hν/e
RG calculation
eV=hν=5kBTK
- RG calculations at high frequency hν>kBTK and out-of-equilibrium
- Prediction of a logarithmic singularity at eV=hν even when hν>>kBTK
-2
0
2
4
-4
-2
0
2
4
0
2
/dV
S(p
A².
Hz
-1.V
-1)
data
dS
I/d
VS(p
A².
Hz
-1.V
-1)
dI/dV
(e²/
h)
14
High frequency noise in the Kondo regime
30 GHzhν~kBTK
2hν1/e
2hν3/e
No emission noise
if |eVS| < hν
Small singularity related to the Kondo resonance at
hν~kBTK
hν~kBTK :
- Absence of emission noise if |eVS| < hν- Singularity at |eVS| = hν qualitatively consistent with
predictions
15
High frequency noise in the Kondo regime
30 GHzhν~kBTK
80 GHzhν~ 2.5 kBTK
ANY EXPLANATIONS??
� Dynamics of the Kondo effect ?
Not predicted by theory
C.P. Moca et al. PRB 10
2hν1/e
2hν3/e
-2 -1 0 1 2-4
-2
0
2
4
-4
-2
0
2
4
0
2
dS
I/dV
S(p
A².
Hz
-1.V
-1)
VS (mV)
data
theory
dS
I/d
VS(p
A².
Hz
-1.V
-1)
dI/dV
(e²/
h)
Singularity related to the
Kondo resonance at hν~kBTK
� Qualitatively consistent but not quantitatively
Coll. with C.P.Moca, G.Zarand and P.Simon
- Theoretical comparison takes into account experimental data with no fitting parameter!
- Kondo temperature TK=1.4K � TKRG=0.38K
- asymmetry a=0.67
- U=2.5meV, Γ=0.51meV - Theoretical predictions approximately 2 times higher than experimental result
16
High frequency noise in the Kondo regime
30 GHzhν~kBTK
80 GHzhν~ 2.5 kBTK
Singularity related to the
Kondo resonance at hν~kBTK
� Qualitatively consistent but not quantitatively2hν1/e
2hν3/e
-2 -1 0 1 2-4
-2
0
2
4
-4
-2
0
2
4
0
2
dS
I/dV
S(p
A².
Hz
-1.V
-1)
VS (mV)
data
theory
dS
I/d
VS(p
A².
Hz
-1.V
-1)
dI/dV
(e²/
h)
No singularity at hν~2.5 kBTK!� Not consistent with theory
17
High frequency noise in the Kondo regime
30 GHzhν~kBTK
80 GHzhν~ 2.5 kBTK
Singularity related to the
Kondo resonance at hν~kBTK
� Qualitatively consistent but not quantitatively2hν1/e
2hν3/e
-2 -1 0 1 2-4
-2
0
2
4
-4
-2
0
2
4
0
2
dS
I/dV
S(p
A².
Hz
-1.V
-1)
VS (mV)
data
theory
dS
I/d
VS(p
A².
Hz
-1.V
-1)
dI/dV
(e²/
h)
No singularity at hν~2.5 kBTK!� Not consistent with theory
ANY EXPLANATIONS??
� Decoherence at high VS ?
Monreal et al. PRB 05
Van Roermund et al. PRB 10
De Franceschi et al. PRL 02
Fit with additional spin decoherence rate
18
Decoherence due to voltage bias
- External decoherence rate
� Form similar to the intrinsic rate (C.P. Moca et al. PRB 11)� Consistent with the differential conductance� Consistent with the noise power for both frequencies
Spin lifetime in the dot reduces with applied voltage bias VS
Coll. with C.P.Moca, G.Zarand and P.Simon
α, β : fitting parameters
19-2 -1 0 1 2-4
-2
0
2
4
-4
-2
0
2
4
dS
I/dV
S(p
A².
Hz
-1.V
-1)
VS (mV)
data
theory with
decoherence
theory
dS
I/d
VS(p
A².
Hz
-1.V
-1)
Single decoherence rate function reproduce the data
30 GHzhν~kBTK
80 GHzhν~ 2.5 kBTK
Fits OK using a single bias dependent spin decoherence
rate function
with α=14, β=0.15
20
-2 -1 0 1 2-4
-2
0
2
4
-4
-2
0
2
4
dS
I/dV
S(p
A².
Hz
-1.V
-1)
VS (mV)
dS
I/d
VS(p
A².
Hz
-1.V
-1)
Logarithmic singularity and decoherence effects
• eV increases � Kondo peaks in the density of states (attached to the leads)
split and vanish due to decoherence
• Decoherence already pointed out
Exp. : De Franceschi et al. PRL 02, Leturcq et al. PRL 05
Th. : Monreal et al. PRB 05, Van Roermund et al. PRB 10
Many photons
emitted at eV=hν1
Few photons
emitted at eV=hν3
21
High frequency Fano like factor in the Kondo regime
30 GHz
80 GHz
• Subpoissonian Noise F§1
• F decreases whenconductance increases
� Consistent with a highly
transmitted channel
0 1
N.B. : Energy independent transmission
� Fano factor
Conclusions
High frequency noise in the Kondo regime
• Singularity due to Kondo effect for hν ~ kBTK
• No singularity for hν ~ 2.5 kBTK
• Consistent with theory with decoherence due to the bias voltage
arXiv:1110.1570
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