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

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 ). Chernogolovka - June 2012.

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

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  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) Chernogolovka - June 2012

  2. Kondo effect and Mesoscopic physics Increase of the resistance (T<TK) Many body problem kondo normal supra 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 spin In situ control of the parameters new situation (out of equilibrium, orbital Kondo effect)

  3. Kondo effect in quantum dots VS A GL GR reservoir reservoir Quantum dot gate VG U : charging energy; e0: energy level; G=GL+GR : coupling to the reservoirs Kondo effect : dynamical screening of the dot’s spin Under specific conditions: - Odd number of electronsin the dot - Intermediate transparencyof the contacts - Temperature below Kondo temperature TK 3

  4. Kondo resonance in quantum dots Heff = Jeffs.S withJeff = G/n U n:DOS virtual virtual TK = (U G)1/2 exp (-1/ Jeffn) • 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 4

  5. Signature of the Kondo effect on conductance 2TK TK Increase of conductance at low temperature T < TK T > TK What about Kondo dynamics? 5

  6. What about noise? ? VS VG A Out-of-equilibrium Kondo dynamics at frequencies hn~kBTK? TK = 1K, n>20GHz

  7. Noise detection in the Kondo regime Low frequency regime (hn << 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)

  8. Theoretical predictions Signature of the Kondo effect on noise : Logarithmic singularity at V=hn/e RG calculation eV=hn=5kBTK C.P. Moca et al., PRB (2011) • RG calculations at high frequency hn>kBTK and out-of-equilibrium • Prediction of a logarithmic singularity at eV=hn even whenhn>>kBTK High frequency quantum noise detection at frequencies n≥ kBTK/h

  9. Outline Emission n<0 Detector System n>0 Absorption ? A - 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 ? VS VG

  10. Introduction to electronic noise <I> • What is electronic noise? I(t)=<I>+dI(t) Conducting system I(t) Vsd • Why measure noise? Electronic correlations, effective charge, characteristic energy scale, …

  11. Noise in the quantum regime hn >> kBT, hn > eV • energy scales (eV, D, …) and characteristic times • quantum noise : zero point fluctuations Emission n<0 System mesoscopic device Detector Amplifier, Quantum dot, SIS junction,… n>0 Absorption

  12. Noise measurement in the quantum regime Mesoscopic system S I S Source Detector Resonant Circuit 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) T=20 mK

  13. Quantum Noise Detection with a SIS Junction S I S n=30GHz Photo-assisted tunneling current (PAT) ABSORPTION EMISSION Ingold & Nazarov (1992)

  14. Source/detector coupling with a resonant circuit L=1mm a=5µm b=100µm L=nl/4 n odd integer  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)

  15. 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

  16. PAT current due to the tunneling of quasiparticles IPAT measurement as a function of Vsource VD<2D/e Detector bias voltage (VD1 or VD2) : selection of frequency range

  17. Direct measurement of HF emission noise of a Josephson junction Calculated (n=0) 2Δ/e Josephson junction emitting a photon hn=eVS-2D Theory at n Theory at n & finite bandwidth DC current but No emission Noise while eVS<2D+hni

  18. Quantum noise measurement with SIS detector Detection of emission and absorption noise Quantitative measurement of the HFEmission Noise of a Josephson Junction J. Basset et al. PRL 105,166801 (2010) J. Basset et al. PRB85, 085435 (2012) Sensitivity :2 fA² /Hz (1.5mK on 20kW) at 28 GHz, 8 fA² /Hz (5.8mK on 20kW) at 80 GHz Powerful tool to measure HF noise of mesoscopic systems : carbon nanotube quantum dot in the Kondo regime

  19. What about emission noise? ? VS VG A Out-of-equilibrium Kondo dynamics at frequencies hn~kBTK?

  20. 1mm junctions 500nm source NT drain gate Carbon nanotube coupled to the SIS detector VD A R VG R L L A VS Detector biased for emission noise detection 20

  21. Kondo effect in the measured carbon nanotube VG=3.12V 2TK Kondo ridge Zero bias peak Center of the ridge TK=1.4K  n=30GHz What about noise? 21

  22. Recent theoretical predictions Signature of the Kondo effect on noise : Logarithmic singularity at V=hn/e RG calculation eV=hn=5kBTK C.P. Moca et al., PRB (2011) • RG calculations at high frequency hn>kBTK and out-of-equilibrium • Prediction of a logarithmic singularity at eV=hn even whenhn>>kBTK

  23. High frequency noise in the Kondo regime 30 GHz hn~kBTK Small singularity related to the Kondo resonance athn~kBTK 2hn1/e No emission noise if |eVS| < hn -2 -1 0 1 2 2hn3/e VS (mV) hn~kBTK : - Absence of emission noise if |eVS| < hn - Singularity at |eVS| = hn qualitatively consistent with predictions 23

  24. High frequency noise in the Kondo regime 30 GHz hn~kBTK 80 GHz hn~ 2.5 kBTK Singularity related to the Kondo resonance athn~kBTK  Qualitatively consistent but not quantitatively 2hn1/e • ANY EXPLANATIONS?? • Dynamics of the Kondo effect ? Not predicted by theory • C.P. Moca et al. PRB 10 Coll. with C.P.Moca, G.Zarand and P.Simon 2hn3/e - Theoretical comparison takes into account experimental data withno fitting parameter! - Kondo temperature TK=1.4K  TKRG=0.38K - asymmetry a=0.67 - U=2.5meV, G=0.51meV - Theoretical predictions approximately 2 times higher than experimental result 24

  25. High frequency noise in the Kondo regime 30 GHz hn~kBTK 80 GHz hn~ 2.5 kBTK Singularity related to the Kondo resonance athn~kBTK  Qualitatively consistent but not quantitatively 2hn1/e No singularity athn~2.5 kBTK!  Not consistent with theory 2hn3/e 25

  26. High frequency noise in the Kondo regime 30 GHz hn~kBTK 80 GHz hn~ 2.5 kBTK Singularity related to the Kondo resonance athn~kBTK  Qualitatively consistent but not quantitatively 2hn1/e No singularity athn~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 2hn3/e Fit with additional spin decoherence rate 26

  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 a, b : fitting parameters Spin lifetime in the dot reduces with applied voltage bias VS 27 Coll. with C.P.Moca, G.Zarand and P.Simon

  28. Single decoherence rate function reproduce the data 30 GHz hn~kBTK 80 GHz hn~ 2.5 kBTK Fits OK using a single bias dependent spin decoherence rate function with a=14, b=0.15 28

  29. Logarithmic singularity and decoherence effects Many photons emitted at eV=hn1 Few photons emitted at eV=hn3 • 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 29

  30. Other theoretical approach • 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 Good agreement with experiment with no fit parameter S. Mülher and S. Andergassen

  31. High frequency Fano like factor in the Kondo regime 80 GHz 0 1 30 GHz N.B. : Energy independent transmission  Fano factor • Subpoissonian Noise F1 • F decreases when conductance increases  Consistent with a highly transmitted channel 31

  32. Conclusions • High frequency noise in the Kondo regime • Singularity due to Kondo effect for hn ~ kBTK • No singularity for hn ~ 2.5 kBTK • Consistent with theory with decoherence due to the bias voltage J. Basset et al. Phys. Rev. Lett. 108, 046802 (2012).

  33. Quantum Noise of the resonant circuit No source bias Detector only sensitive to Quantum Noise of the resonator at equilibrium

  34. Real part of the impedance seen by the detector AC Josephson effect :calibration Dynamical Coulomb blockade Ingold et Nazarov (1992) IC : critical current • Lowquality factor due to direct connection • Even peaksdue to finite value of impedance mismatch

  35. Signal due to the resonant circuit Voltage Noise S S S S S S I I I Photons exchange Resonator S T~0.9K Resonator T~0.5K Resonator T~0.02K

  36. Crossover from Quantum to thermal Noise Real part of the impedance of the resonant circuit. Extracted from calibration. n1=28 GHz crossover from quantum to thermal noise • T=0 : No Emissionnoise but Absorption  Zero Point fluctuations • T increases : Emission appears& Absorption increases

  37. Noise spectrum of a resistor R Noise @ T=0 (ZPF) Thermal Noise • T=0 : No Emissionnoise but Absorption  Zero Point fluctuations • T increases : Emission appears& Absorption increases 38

  38. Josephson junction as signal source • 2 operating modes : • Cooper pairs tunneling : AC Josepshon effect • Quasiparticle tunneling : and Symmetric spectrum with peaks at frequencies absorption emission • Only absorption noise • Singularities at • Emission and absorption noise • Singularity in emission at • Singularity in absorption at

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