Quantum Noise of a Carbon Nanotube Quantum Dot in the Kondo Regime

Exp : J. Basset, A.Yu. Kasumov, H. Bouchiat and R. DeblockLaboratoire de Physique des Solides – Orsay (France)

Theory : P. Simon (LPS), C.P. Moca and G. Zarand (Budapest)

Chernogolovka - June 2012

Kondo effect : - model system for electronic correlations- screening of a localized magnetic moment in a conductor

- nanophysics (quantum dots (Goldhaber-Gordon et al. Nature (1998), Cronenwett et al.

Science (1998); carbon nanotube (Nygard et al. Nature (2000))

Kondo effect on a single spinIn situ control of the parameters new situation (out of equilibrium, orbital Kondo effect)

Many body problem

Kondo effect and Mesoscopic physics

supra

normal

kondo

Increase of the resistance (T<TK)

3

Kondo effect in quantum dots

U : charging energy; 0: energy level; LR : 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

L R

reservoir reservoir

Quantum dotVS

A

VG

gate

4

Kondo resonance in quantum dots

TK = (U )1/2 exp (-1/ Jeff )

- 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 .S with Jeff = / U : DOS

5

2TK

T < TK

T > TK

TK

Signature of the Kondo effect on conductance

What about Kondo dynamics?

Increase of conductance at low

temperature

What about noise?

A

?

VS

VG

Out-of-equilibrium Kondo dynamics at frequencies h~kBTK?

TK = 1K, >20GHz

Noise detection in the Kondo regime

Low frequency regime (h << kBTK) and low bias voltage (eVsd < kBTK) :- semiconductor quantum dots (SU2) : Influence of Kondo correlations on the Fano factor

O. Zarchin et al. Phys. Rev. B (2008) Y. Yamauchi et al., Phys.Rev.Lett. (2011)

- carbon nanotube quantum dots : Signature of orbital and spin effect T. Delattre et al., Nature Phys. (2009)

Theoretical predictions

C.P. Moca et al., PRB (2011)

Signature of the Kondo effect on noise :

Logarithmic singularity at V=h/eRG calculation

eV=h=5kBTK

- RG calculations at high frequency h>kBTK and out-of-equilibrium

- Prediction of a logarithmic singularity at eV=heven when h>>kBTK

High frequency quantum noise detection at frequencies ≥ kBTK/h

Outline

- Introduction to noise measurement in the quantum regime

- Resonant coupling circuit and SIS detector :- Emission noise of a Josephson junction

- High frequency noise detection of a carbon nanotube in the Kondo regime

System Detector

Emission<0

>0Absorption

?

?

VS

VG

A

• What is electronic noise?

Introduction to electronic noise

I(t)=<I>+I(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,…

Emission<0

>0Absorption

h >> kBT, h > eV

Source Detector

Mesoscopic system S SI

Noise measurement in the quantum regime

Josephson Junction-

Carbon nanotube in the Kondo regime

Superconductor / Insulator / Superconductor (SIS) junction

Noise detection with SIS junction : Kouwenhoven’s group, Science (2003)

P.M. Billangeon et al.,PRL (2006)

Resonant Circuit

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

h/e

h/e

ABSORPTION

I D

(nA

)

VD(mV)2/e

EMISSION

Quantum Noise Detection with a SIS Junction

EMISSION ABSORPTIONPhoto-assisted tunneling current

(PAT)

=30GHz

S SI

Ingold & Nazarov (1992)

Source/detector coupling with a resonant circuit

¼ wavelength resonant circuit as in T.Holst et al. PRL(1994)

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 (Q~10)

L=1mm

a=5µm

b=100µm

L=n/4

n odd integer

Source and detector coupled via the resonant circuit

Source

=

Josephson

Junction

• AC Josephson effect : « on-chip » calibration of the coupling

• Measurement of the quasi-particle high frequency noise

PAT current due to the tunneling of quasiparticlesIPAT measurement as a function of Vsource

Detector bias voltage (VD1 or VD2) : selection of frequency range

VD<2/e

Direct measurement of HF emission noise of a Josephson junction

DC current but No emission Noise while eVS<2+hi

Josephson junction emitting a photon

h=eVS-2

2Δ/e

Calculated (=0)

Theory at

Theory at & finite bandwidth

Quantum noise measurement with SIS detector

Detection of emission and absorption noise

Quantitative measurement of the HF Emission Noise of a Josephson Junction J. Basset et al. PRL 105,166801 (2010)

J. Basset et al. PRB 85, 085435 (2012)

Sensitivity : 2 fA² /Hz (1.5mK on 20k) at 28 GHz, 8 fA² /Hz (5.8mK on 20k) at 80 GHz

Powerful tool to measure HF noise of mesoscopic systems :

carbon nanotube quantum dot in the Kondo regime

What about emission noise?

A

?

VS

VG

Out-of-equilibrium Kondo dynamics at frequencies h~kBTK?

20

LL

VG

AVD

R

A

VS

R

source

draingate

NT

500nm

1m

junctions

Carbon nanotube coupled to the SIS detector

Detector biased for emission noise detection

21

-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 =30GHz

2TK

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=h/e

RG calculation

eV=h=5kBTK

- RG calculations at high frequency h>kBTK and out-of-equilibrium

- Prediction of a logarithmic singularity at eV=heven when h>>kBTK

-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

dS

I/dV

S(p

A².

Hz-1

.V-1)

dI/d

V (

e²/h

)

23

High frequency noise in the Kondo regime

30 GHzh~kBTK

2h1/e

2h3/e

No emission noise if |eVS| < h

Small singularity related to the Kondo resonance at

h~kBTK

h~kBTK :- Absence of emission noise if |eVS| < h - Singularity at |eVS| = h qualitatively consistent with

predictions

0 1-1 2-2VS (mV)

24

High frequency noise in the Kondo regime

30 GHzh~kBTK

80 GHzh~ 2.5 kBTK

ANY EXPLANATIONS??

Dynamics of the Kondo effect ? Not predicted by theory

C.P. Moca et al. PRB 10

2h1/e

2h3/e

-2 -1 0 1 2-4

-2

0

2

4

-4

-2

0

2

4

0

2

dSI/d

VS(p

A².

Hz-1

.V-1)

VS (mV)

data theory

dSI/d

VS(p

A².

Hz-1

.V-1)

dI/d

V (

e²/h

)

Singularity related to the Kondo resonance at h~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, =0.51meV

- Theoretical predictions approximately 2 times higher than experimental result

25

High frequency noise in the Kondo regime

30 GHzh~kBTK

80 GHzh~ 2.5 kBTK

Singularity related to the Kondo resonance at h~kBTK

Qualitatively consistent but not quantitatively

2h1/e

2h3/e

-2 -1 0 1 2-4

-2

0

2

4

-4

-2

0

2

4

0

2

dSI/d

VS(p

A².

Hz-1

.V-1)

VS (mV)

data theory

dSI/d

VS(p

A².

Hz-1

.V-1)

dI/d

V (

e²/h

)

No singularity at h~2.5 kBTK! Not consistent with theory

26

High frequency noise in the Kondo regime

30 GHzh~kBTK

80 GHzh~ 2.5 kBTK

Singularity related to the Kondo resonance at h~kBTK

Qualitatively consistent but not quantitatively

2h1/e

2h3/e

-2 -1 0 1 2-4

-2

0

2

4

-4

-2

0

2

4

0

2

dSI/d

VS(p

A².

Hz-1

.V-1)

VS (mV)

data theory

dSI/d

VS(p

A².

Hz-1

.V-1)

dI/d

V (

e²/h

)

No singularity at h~2.5 kBTK! Not consistent with theory

ANY EXPLANATIONS??

Decoherence at high VS ? Monreal et al. PRB 05

Van Roermund et al. PRB 10De Franceschi et al. PRL 02

Fit with additional spin decoherence rate

27

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

, : fitting parameters

28-2 -1 0 1 2-4

-2

0

2

4

-4

-2

0

2

4

dSI/d

VS(p

A².

Hz-1

.V-1)

VS (mV)

data theory with

decoherence theory

dSI/d

VS(p

A².

Hz-1

.V-1)

Single decoherence rate function reproduce the data

30 GHzh~kBTK

80 GHzh~ 2.5 kBTK

Fits OK using a single bias dependent spin decoherence

rate function

with =14, =0.15

29

-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/dV

S(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=h1

Few photons emitted at eV=h3

-2 -1 0 1 2-4

-2

0

2

4

-4

-2

0

2

4

0

2

data theory

dS

I/dV

S(p

A².

Hz-1

.V-1)

VS (mV)

data theory

dS

I/dV

S(p

A².

Hz-1

.V-1)

dI/d

V (

e²/h

)

• Real time Renormalization Group technique• Systematic expansion in the reservoir-system coupling

S. Andergassen et al., Nanotechnology (2010)

• Kondo system out of equilibrium

• Relaxation and decoherence included

Other theoretical approach

Good agreement with experiment with no fit parameter

S. Mülher and S. Andergassen

31

High frequency Fano like factor in the Kondo regime

30 GHz

80 GHz

• Subpoissonian Noise F1• F decreases when

conductance 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 h ~ kBTK

• No singularity for h ~ 2.5 kBTK

• Consistent with theory with decoherence due to the bias voltage

J. Basset et al. Phys. Rev. Lett. 108, 046802 (2012).

Quantum Noise of the resonant circuit

No source bias Detector only sensitive to Quantum Noise of the resonator at

equilibrium

Real part of the impedance seen by the detector

Low quality factor due to direct connection Even peaks due to finite value of impedance

mismatch

AC Josephson effect : calibration

IC : critical current

Dynamical Coulomb blockade Ingold et Nazarov (1992)

T~0.9K

Resonator

Resonator

Photons exchange

Resonator

T~0.02K

0.3 0.4 0.5 0.6 0.7 0.8 0.9

020406080

100120140160

Absorption

T=0.95K

T=0.88K

T=0.58K

80GHz 28GHz

dI D

/dV

D(µ

S)

VD(mV)

Emission

28GHz

T=0.02K

T~0.5K

S

SS I

SS I

SS I

Signal due to the resonant circuit Voltage Noise

Real part of the impedance of the resonant circuit.

Extracted from calibration.

• T=0 : No Emission noise but Absorption Zero Point fluctuations• T increases : Emission appears & Absorption increases

Crossover from Quantum to thermal Noise

crossover from quantum to thermal noise

1=28 GHz

38

-100 -50 0 50 100

0

1

2

3

4

+28GHz

2kBTR

Absorption

T=0.01K T=0.5K T=1K

SV

(a.u

.)

(GHz)

Emission

-28GHz

• T=0 : No Emission noise but Absorption Zero Point fluctuations

• T increases : Emission appears & Absorption increases

Thermal Noise

Noi

se @

T=0

(ZPF

)

Noise spectrum of a resistor R

Josephson junction as signal source2 operating modes : • Cooper pairs tunneling : AC Josepshon effect

• Quasiparticle tunneling :

and

Symmetric spectrum with peaks at frequencies

• Only absorption noise• Singularities at

• Emission and absorption noise • Singularity in emission at • Singularity in absorption at

emission absorption