Quantum Noise Measurement of a Carbon Nanotube Quantum dot in the Kondo Regime

Transcription

1 Quantum Noise Measurement of a Carbon Nanotube Quantum dot in the Kondo Regime J. Basset, 1 A.Yu. Kasumov, 1 C.P. Moca, G. Zarand,, 3 P. Simon, 1 H. Bouchiat, 1 and R. Deblock 1 1 Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 85, F-9145 Orsay Cedex, France. BME-MTA Exotic Quantum Phase Group, Institute of Physics, Budapest University of Technology and Economics, H-151 Budapest, Hungary. 3 Freie Universit at Berlin, Fachbereich Physik, Arnimallee 14, D Berlin, Germany. GDR Physique mésoscopique Jeudi 8 Décembre 11

2 Introduction to electronic noise What is electronic noise? Conducting system I(t) I(t)=<I>+δI(t) V sd <I>=G.V sd Why noise measurement? Electronic correlations, effective charge, characteristic energy scales E c,

3 Noise: from classical to quantum regime S I (ν) Low Frequency (hν<<ev,k B T) High Frequency (hν~ev; hν>>k B T) (Quantum regime) Thermal Noise (Johnson-Nyquist) (ev<k B T): S I =4k B TG Shot Noise (ev>k B T): S I =ei.f with F: Fano factor - Noise Photons (microwave) Emission Absorption White Noise Strong frequency dependence 3

4 Ex: resistor R at thermal equilibrium Emission and Aborption noise S I (ν) SV (a.u.) T=.1K T=1K Emission k B TR Absorption hνr High Frequency (hν~ev; hν>>k B T) (Quantum Regime) - Noise Photons (microwave) ν(ghz) Emission Absorption Quantum noise detection scheme needed 4

5 Detecting noise at high frequency -HF Electronics R.J. Schoelkopf et al.prl (1997), E. Zakka-Bajjani et al. PRL(7), Gabelli et al PRL(8), - On-chip Quantum Detectors SIS junction = Good quantum detector This experiment : R.Deblock et al.science (3), P.-M. Billangeon et al. PRL (6), Source Resonant Circuit Capacitive coupling Detector Mesoscopic S system I S GDR PhD Defense Physique Julien mésoscopique BASSET 5

6 Outline 1. Principle of the SIS junction as a quantum noise detector. Source/detector coupling and preliminary results 3. Emission Noise of a carbon nanotubequantum dot in the Kondo regime Signature of Kondo screening dynamics and decoherence 4. Conclusions and perspectives 6

7 Outline 1. Principle of the SIS junction as a quantum noise detector. Source/detector coupling and preliminary results 3. Emission Noise of a carbon nanotubequantum dot in the Kondo regime Signature of Kondo screening dynamics and decoherence 4. Conclusions and perspectives 7

8 SIS Junction as a quantum noise detector 5 S I S 4 I D (na) /e VD(mV) 8

9 SIS Junction as a quantum noise detector 5 4 ν=3ghz EMISSION (by source) S I S I D (na) 3 1 hν/e I PAT >...4 /e VD(mV) 9

10 SIS Junction as a quantum noise detector 5 4 ν=3ghz ABSORPTION (by source) S I S I D (na) 3 I PAT < hν/e /e VD(mV) 1

11 5 4 SIS Junction as a quantum noise detector ν=3ghz ν =6GHz EMISSION ABSORPTION I D (na) 3 1 hν'/e hν'/e...4 /e VD(mV) Photo-assisted tunneling current (PAT) EMISSION ABSORPTION 11 G.L.Ingold and Yu V.Nazarov, in Single charge tunneling (Plenum, New-York,199)

12 Outline 1. Principle of the SIS junction as a quantum noise detector. Source/detector coupling and preliminary results 3. Emission Noise of a carbon nanotubequantum dot in the Kondo regime Signature of Kondo screening dynamics and decoherence 4. Conclusions and perspectives 1

13 Source/detector coupling through a resonant circuit L=1mm a=5µm b=1µm L=nλ/4 n odd integer ν 1 ~3 GHz ¼ wavelength resonant circuit Independent DC polarisations of the source and the detector eigen frequencies of the resonator Coupling proportional to the quality factor 13

14 Preliminary results published in PRL 15,16681 (1) Equilibrium Noise of the transmission line resonator Noise asymmetry at very low temperature ν 1 ~3 GHz; ν 3 ~8 GHz SV(T) (nv²/hz) hν 3 Re[Z(ν 3 )] hν 1 Re[Z(ν 1 )] Absorption Noise Sv(+ν 3 ) Absorption Noise Sv(+ν 1 ) Emission Noise Sv(-ν 1 ) T(K) Out of Equilibrium Emission Noise of a Josephson junction Frequency dependence of quasiparticles shot noise 14

15 Outline 1. Principle of the SIS junction as a quantum noise detector. Source/detector coupling and preliminary results 3. Emission Noise of a carbon nanotubequantum dot in the Kondo regime Signature of Kondo screening dynamics and decoherence 4. Conclusions and perspectives 15

16 Kondo effect and mesoscopic physics - Kondo effect in bulk materials (dilute magnetic alloys) Screening of localized magnetic moments by conduction electrons Model system to study electronic correlations Many-body problem Resistance increase in bulk materials (T<T K ) Kondo Normal Supra 16

17 Kondo effect and mesoscopic physics - Kondo effect in bulk materials (dilute magnetic alloys) Screening of localized magnetic moments by conduction electrons Model system to study electronic correlations Many-body problem Resistance increase in bulk materials (T<T K ) Kondo Normal Supra - In nanophysics Kondo effect at a single spin level and in out-of-equilibrium situations In-situ control of many parameters (voltage bias, dot s occupation, T K ) 17

18 Kondo effect in quantum dots Γ L Γ R reservoir reservoir V S gate Quantum dot A V G U : charging energy; ε : energy level; Γ=Γ L +Γ R : coupling to the reservoirs Kondo effect : dynamical screening of the dot s spin Under specific conditions: - Odd number of electrons in the dot - Intermediate transparency of the contacts - Temperature below Kondo temperature T K 18

19 H eff = J eff σ.s Kondo resonance in quantum dots with J eff = Γ/ν U ν: DOS virtual virtual T K = (U Γ) 1/ exp (-1/ J eff ν) - Transport through multiple 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 19

20 Signature of the Kondo effect on conductance T K T K Universal scaling with temperature and bias voltage T < T K T > T K Kondo plateau when odd numbers of e - + T<T K If T< T K, zero bias conductance can increase up toe /h T K and barrier asymmetry are the only relevant parameters What about Kondo dynamics?

21 What about emission noise?? V S A V G Out-of-equilibrium Kondo dynamics at frequencies hν~k B T K? 1

22 Carbon nanotube coupled to the SIS detector Z Z 1 1µm V D A junctions R V G V S A R l l source 5nm NT CVD home-grown nanotube Kasumov et al. Appl. Phys. A 7 + Miguel Monteverde superconductor gate drain

23 Kondo effect for the nanotube didv(e²/h) V G =3.1V T K V S (mv) Kondo ridge Zero bias peak Center of the ridge T K =1.4K ν=3ghz What about noise? 3

24 Recent theoretical predictions Signature of the Kondo effect on noise : Logarithmic singularity at V=hν/e RG calculation ev=hν=5k B T K C.P. Moca et al., PRB (11) - RG calculations at high frequency hν>k B T K and out-of-equilibrium - Prediction of a logarithmic singularity at ev=hν even when hν>>k B T K 4

25 dv /dv S (pa².hz -1.V -1 S (pa².hz -1.V -1 ) dsi/ ) High frequency noise in the Kondo regime data predictions 3 GHz hν~k B T K hν 1 /e hν 3 /e V S (mv) hν~k B T K : di I/dV (e²/h) Small singularity related to the Kondo resonance at hν~k B T K No emission noise if ev S < hν Absence of emission noise if ev S < hν - Singularity at ev S = hν qualitatively consistent with

26 dsi/dv S (pa².hz -1.V -1 ) ds I /dv S (pa².hz -1.V -1 ) High frequency noise in the Kondo regime data theory hν 1 /e hν 3 /e 3 GHz hν~k B T K V S (mv) di/dv (e²/h) Singularity related to the Kondo resonance at hν~k B T K Qualitatively consistent but not quantitatively Calculations by C.P. Moca, G. Zarand (Budapest) and P. Simon (Orsay) ANY EXPLANATIONS?? Dynamics of the Kondo effect? - Theoretical comparison takes into account experimental Not data predicted with no by fitting theory parameter! C.P. Moca et al. PRB 1 - Kondo temperature T 8 GHz K =1.4K T RG K =.38K - - asymmetry a=.67 hν~.5 k B T - U=.5meV, Γ=.51meV K - Theoretical -4 predictions approximately times higher than experimental result V S (mv)

27 High frequency noise in the Kondo regime dsi/dv S (pa².hz -1.V -1 ) data theory hν 1 /e 3 GHz hν~k B T K di/dv (e²/h) Singularity related to the Kondo resonance at hν~k B T K Qualitatively consistent but not quantitatively No singularity at hν~.5 k B T K! Not consistent with theory ds I /dv S (pa².hz -1.V -1 ) - hν 3 /e 8 GHz hν~.5 k B T K V S (mv) ANY EXPLANATIONS??? 7

28 dsi/dv S (pa².hz -1.V -1 ) ds I /dv S (pa².hz -1.V -1 ) High frequency noise in the Kondo regime data theory hν 1 /e hν 3 /e 3 GHz hν~k B T K 8 GHz hν~.5 k B T K V S (mv) di/dv (e²/h) Singularity related to the Kondo resonance at hν~k B T K Qualitatively consistent but not quantitatively No singularity at hν~.5 k B T K! Not consistent with theory ANY EXPLANATIONS?? Decoherence at high V S? Monreal et al. PRB 5 Van Roermund et al. PRB 1 De Franceschi et al. PRL Fit with additional spin decoherence rate 8

29 Additional voltage bias induced decoherence - External decoherence rate : criteria Form similar to the intrinsic rate (C.P. Moca et al. PRB 11) Consistent with conductance Consistent with noise power for both frequencies α and β : fitting parameters Spin lifetime in the dot reduces with applied bias V S Calculations by C.P. Moca, G. Zarand (Budapest) and P. Simon (Orsay) 9

30 Single decoherence rate function reproduce the data dsi/dv S (pa².hz -1.V -1 ) data theory with decoherence theory 3 GHz hν~k B T K Fits OK using a single bias dependent spin decoherence rate function with α=14, β=.15 4 ds I /dv S (pa².hz -1.V -1 ) V S (mv) 8 GHz hν~.5 k B T K 3

31 Logarithmic singularity and decoherence effects ds -1.V -1 ) dsi/dv S (pa².hz -1.V -1 I /dv S (pa².hz ) V S (mv) Many photons emitted at ev=hν 1 Less photons emitted at ev=hν 3 DOS DOS ev increases Kondo peaksin the density of states (attached to the leads) split and vanish due to decoherence Decoherence already pointed out Exp. : De Franceschi et al. PRL, Leturcq et al. PRL 5 31 Th. : Monreal et al. PRB 5, Van Roermund et al. PRB 1

32 High frequency Fano like factor in the Kondo regime 1 3 GHz N.B. : Energy independent transmission Fano factor 3 GHz Subpoissonian Noise F 1 F decreaseswhen conductance increases Consistent with a highly transmitted channel 8 GHz 8 GHz 3 3

33 Outline 1. Principle of the SIS junction as a quantum noise detector. Source/detector coupling and preliminary results 3. Emission Noise of a carbon nanotubequantum dot in the Kondo regime Signature of Kondo screening dynamics and decoherence 4. Conclusions and perspectives 33

34 Conclusions and perspectives CONCLUSIONS High frequency emission noise of a carbon nanotube in the Kondo regime Singularity due to Kondo effect for hν ~ k B T K No singularity for hν ~.5 k B T K Explained by strong decoherence effects (submitted arxiv: v1) PERSPECTIVES Carbon nanotube quantum dots in other transport regimes Coulomb Blockade Coulomb gap Ec? Fabry-Pérot nanotube length L via hv F /L? Superconducting contacts phase dynamics vs T K, MAR signature 34

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