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

Transcription

1 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 11

2 Introduction to electronic noise What is electronic noise? Conducting system I(t) I(t)=<I>+δI(t) V sd <I> Why measure noise? Electronic correlations, effective charge, characteristic energy scale,

3 Noise in the quantum regime hν >> k B T, hν > ev energy scales (ev,, ) and characteristic times quantum noise : zero point fluctuations System mesoscopic device Emission ν< ν> Absorption Detector Amplifier, Quantum dot, SIS junction,

4 Noise measurement in the quantum regime Source Detector Mesoscopic S system I S Resonant Circuit Carbon nanotube in the Kondo regime SIS junction Noise detection with SIS junction : Kouwenhoven s group, Science (3) P.M. Billangeon et al.,prl (6) T= mk

5 Quantum Noise Detection with a SIS Junction I D (na) ν=3ghz EMISSION ABSORPTION I PAT < hν/e hν/e I PAT >... /e Photo-assisted tunneling current VD(mV) (PAT) EMISSION ABSORPTION S I S Ingold & Nazarov (199)

6 Resonant coupling betwen a Carbon nanotube and a SIS detector A V D 1µm junctions A R R L L V G source L=nλ/ n odd integer 5nm NT V S superconductor gate drain ¼ wavelength resonant circuit Independent DC polarisations of the source and the detector Coupling at eigen frequencies of the resonator (3 GHz and harmonics) Coupling proportional to the quality factor (J. Basset et al. PRL 1)

7 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 7

8 Kondo resonance in quantum dots H eff = J eff σ.s with J eff = Γ/ν U ν: DOS virtual virtual T K = (U Γ) 1/ exp (-1/ J eff 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 8

9 Signature of the Kondo effect on conductance T K T K T < T K Increase of conductance at low temperature T > T K What about Kondo dynamics? 9

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

11 Carbon nanotube coupled to the SIS detector 1µm V D A junctions R V G V S A R L L source 5nm NT Detector biased for emission noise detection gate drain 11

12 Kondo effect in the measured carbon 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.K ν=3ghz What about noise? 1

13 Recent theoretical predictions Signature of the Kondo effecton 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

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

15 dsi/dv S ds I /dv S - - High frequency noise in the Kondo regime data theory hν 1 /e hν 3 /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 ANY EXPLANATIONS?? Coll. with C.P.Moca, G.Zarand and P.Simon 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.K T RG K =.38K - - asymmetry a=.67 hν~.5 k B T - U=.5meV, Γ=.51meV K - Theoretical - predictions approximately times higher than experimental result V S (mv)

16 High frequency noise in the Kondo regime dsi/dv S - - 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 - hν 3 /e 8 GHz hν~.5 k B T K V S (mv) 16

17 High frequency noise in the Kondo regime dsi/dv S ds I /dv S 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 17

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 α, β : fitting parameters Spin lifetime in the dot reduces with applied voltage bias V S 18 Coll. with C.P.Moca, G.Zarand and P.Simon

19 Single decoherence rate function reproduce the data dsi/dv S - - 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=1, β=.15 ds I /dv S V S (mv) 8 GHz hν~.5 k B T K 19

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

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

22 Conclusions High frequency noise in the Kondo regime Singularity due to Kondo effect for hν ~ k B T K No singularity for hν ~.5 k B T K Consistent with theory with decoherence due to the bias voltage arxiv: