Le bruit d une impureté Kondo

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1 Le bruit d une impureté Kondo T. Kontos Laboratoire Pierre Aigrain, Ecole Normale Supérieure, Paris France Experiment:T. Delattre, C. Feuillet-Palma, L.G. Herrmann J.-M. Berroir, B. Plaçais, D.C. Glattli, G. Fève. Theory: C. Mora, M-S Choi Acknowledgements: A. Cottet, M. Büttiker, K. Le Hur, P. Simon, B. Trauzettel, H. Grabert, P. Hakonen, N. Regnault.

2 Carbon nanotube as building block for hybrid circuits Cooper pair beam splitter L.G. Herrmann et al. Multiterminal nanospinvalve C. Feuillet-Palma et al. Artificial magnetic impurity T. Delattre et al. SWNTs can be used to form various types of hybrid circuits. Quantum dot behavior allow to study Kondo effect in exotic situations

3 Kondo physics J. P. Franck et al. Proc. Roy. Soc. A263, 494 (1961) Magnetic impurity Cu Fe Conduction electrons Resistance of a metal usually decreases as temperature lowered. Increase of resistance in some magnetic alloys explained by Kondo. Antiferromagnetic coupling of spin of electrons with spin of magnetic Impurity.

4 Kondo physics revival H. C. Manoharan et al. Nature 403, 512 (2000) I(t) Co on Cu(111) See also D. Goldhaber-Gordon et al. Nature 98 J. Nygard et al. Nature 00 General property of localized electronic states coupled to continuum (C60, Carbon Nanotubes, semicond. quantum dots, magnetic adatoms) Mostly conductance has been measured so far (average current) What about fluctuations of the current? t

5 Kondo physics in metals vs quantum dots Screening from reservoirs U Increase of resistance of Kondo alloys (e.g. Cu Fe ) at low temperature Increase of conductance up to 2e 2 /h (maximum) in quantum dots In quantum dots, artificial magnetic impurity spin of last electron added charge quantization due to charging (U). Possibility to study Kondo problem in out of equilibrium situations (finite current flows through a single impurity)

6 Kondo physics in metals vs quantum dots Noisy Impurity? Screening from reservoirs U Increase of resistance of Kondo alloys (e.g. Cu Fe ) at low temperature Increase of conductance up to 2e 2 /h (maximum) in quantum dots In quantum dots, artificial magnetic impurity spin of last electron added (charge quantization due to Coulomb blockade) What about fluctuations of the current?

7 The noiseless Fermi sea ( D ) (r) (i) (t) G. Lesovik 89, M. Büttiker 91 Th. Martin, R. Landauer 92 Regularly spaced incident wavepackets (Pauli) Fermionic source naturally noiseless for D~1 Is a Kondo impurity (D~1 also) noisy?

8 Devices and noise setup 2-terminal devices in FET configuration f = 1-2MHz v < 1 mv Cross-correlation measurements Noise measured as a function of V G and V SD

9 Calibration of the setup f=2.221 MHz White noise Calibration using Johnson-Nyquist noise of the 200 Ω resistors (not sample) Several MHz (2.221MHz) band to avoid 1/f noise contribution. Calibration of di/dv dependence of S(Vsd=0) Very important for correcting for non-linearity of device!

10 Nanotubes as quantum dots e - e - Γ L V sd Γ R Reservoir L Reservoir R Vg Discrete levels V sd =0 et V g =0

11 Nanotubes as quantum dots e - e - Γ L V sd Γ R Reservoir L Reservoir R Vg V sd =0 et V g non zero

12 Nanotubes as quantum dots e - e - Γ L V sd Γ R Reservoir L Reservoir R Vg Discrete levels V sd =0 et V g =0

13 Nanotubes as quantum dots e - e - Γ L V sd Γ R Reservoir L Reservoir R V sd Vg V sd non zero et V g =0, resonant transport.

14 Nanotubes as quantum dots e - e - Γ L V sd Γ R Reservoir L Reservoir R V sd Vg V sd non zero et V g =0, resonant transport. Resonances on lignes V sd +αv g =cste

15 Transport spectroscopy of a semiconducting CNT Γ L V sd e - e - Γ R Reservoir L Reservoir R Γ L V sd e - e - Γ R Reservoir L Reservoir R Γ L V sd e - e - Γ R Reservoir L Reservoir R Fabry-Perot regime V ( mv ) SD Vg hv F /L Vg Kondo regime Vg Coulomb blockade di/ d V 0.8 ( h / (4e ( V ) V G Transition from Fabry-Perot to Coulomb blockade as transmission is lowered Kondo regime (horizontal lines in the middle of Coulomb diamonds) in between. More exotic possibilities in SWNTs (SU(4), pure orbital, two particle Kondo) Jarillo-Herrero et al. Nature 05, Makarovski PRL 07

16 Shot noise suppression on resonances Transmission D*4e 2 /h Strong suppression for D~1 Noiseless conductor Fano factor =1- D (fully degenerate case) L. G. Herrmann, T. Delattre, P. Morfin, J.-M. Berroir, B. Plaçais, D.C. Glattli and TK, Phys. Rev. Lett. 99, (2007) See also noiseless character in QPC s : Kumar et al. PRL 96, Reznikov et al. PRL 95, van den Brom and Ruitenbeek PRL 99

17 The Kondo regime in the conductance Sample A Sample B Conductance saturates to 2e 2 /h in the low temperature limit Usual Kondo effect with spin ½ (SU(2)) but more exotic possibilities in CNTs (K-K degeneracy)

18 The Kondo regime in the conductance Sample A Sample B Transport measurements on these Kondo ridges Conductance saturates to 2e 2 /h in the low temperature limit Usual Kondo effect with spin ½ (SU(2)) but more exotic possibilities in CNTs (K-K degeneracy)

19 Anomalous temperature dependence of the noise Johnson-Nyquist formula S I =4k B TdI/dV Decrease Increase Non monotonic temperature dependence of equilibrium noise Maximum around T K Fluctuation-dissipation theorem still holds! (as expected)

20 Current noise in the Kondo regime Two channel resonant tunneling picture Non-interacting theory explains neither the conductance nor the noise Two channels needed as expected for SWNTs

21 Noise in non-interacting quantum coherent conductors Landauer formula Johnson-Nyquist type noise Ya.M. Blanter and M. Büttiker, Phys. Rep. 336, 1 (2000) Shot noise term Two channels for SWNTs due to K-K degeneracy of graphene Expect noiseless situation for D~1 Energy dependent D in general but no explicit dependence on V sd In some cases, effective D for interactions

22 Current noise in the Kondo regime Two channel resonant tunneling picture Non-interacting theory explains neither the conductance nor the noise Two channels needed as expected for SWNTs

23 Current noise in the Kondo regime Two channel resonant tunneling picture Non-interacting theory explains neither the conductance nor the noise Two channels needed as expected for SWNTs

24 SU(2) The two limiting cases SU(4) Interactions (charge quantization) lock the phase of the many-body resonance (Friedel sum rule) Noise can discriminate between SU(4) and SU(2) symmetry

25 Slave Boson Mean Field Theory Determination of parameters Γ, ε for the SU(4) symmetry : ~ ~ Interaction taken into account self-consistently Keep non-interacting formula for current and noise Description valid at V< T K, Γ 0 when V >>T K Interpolation with resonant tunneling at high bias

26 Current noise in the Kondo regime

27 Current noise in the Kondo regime SBMFT accounts quantitatively for the data SU(4) symmetry taken as minimal model Kondo impurities noisy! T. Delattre, C. Feuillet-Palma, L.G. Herrmann, P. Morfin, J.-M. Berroir, G. Fève, B. Plaçais, D.C. Glattli, M.S. Choi, C. Mora and TK, Nature Physics (2009).

28 Scaling of conductance in the Kondo regime Scaling of conductance (T K and assymmetry determined from SBMF) Similar slope as a function of T as Sasaki et al. (attributed SU(4) Kondo) but higher than Jarillo-Herrero et al. or Makarovski et al. T. Delattre, C. Feuillet-Palma, L.G. Herrmann, P. Morfin, J.-M. Berroir, G. Fève, B. Plaçais, D.C. Glattli, M.S. Choi, C. Mora and TK, Nature Physics (2009).

29 Scaling of noise in the Kondo regime Reference values Scaling of conductance also found in noise! Slope of (0.45+/- 0.05)*2eδI Noise invariant very close to ½ predicted by SBMF at T=0 T. Delattre, C. Feuillet-Palma, L.G. Herrmann, P. Morfin, J.-M. Berroir, G. Fève, B. Plaçais, D.C. Glattli, M.S. Choi, C. Mora and TK, Nature Physics (2009).

30 Conclusion Measurements of noise in SWNT devices Noise suppression in the Fabry-Perot regime Current noise enhancement within the Kondo resonance as a consequence of e-e interactions Quantitative understanding with slave boson mean field theory Scaling of the noise similar to that of conductance (only single energy scale T K ) with invariant close to 1/2. Noisy Kondo impurities Test bench for Kondo theory in out of equilibrium situations

31 Direct measurement of K-K degeneracy lifting Sample B Noise oscillates but not the conductance Direct measurement of transmission eigenvalues Mode coupling (leads, weak disorder) L. G. Herrmann, T. Delattre, P. Morfin, J.-M. Berroir, B. Plaçais, D.C. Glattli and TK, Phys. Rev. Lett. 99, (2007)

32 The weak backscattering regime Noise smaller than simple non-interacting picture Difficult to explain with decoherence only Signature of electron electron interactions? L. G. Herrmann, T. Delattre, P. Morfin, J.-M. Berroir, B. Plaçais, D.C. Glattli and TK, Phys. Rev. Lett. 99, (2007).

33 The noiseless Fermi sea V Gate 2-D electron gas Gate Quantum point contact QPC (photo Y. Jin LPN CNRS Marcoussis) 1 rst mode 2 nd mode Fano reduction factor ,0 0,8 0,6 0,4 0,2 0,0 ( T ) ( ) Kumar 1 1et al. PRL (1996) T 1 T 1+ T Conductance 2e² / h 2 Kumar et al. PRL 96, Reznikov et al. PRL 95

34 Fabrication of SWNTs devices Au alignment markers Nanotube CVD growth (methane process) Localization with AFM or SEM Pd contacts

35 Energy independent transmission limit Mesoscopic P.I.N. code {D n } Johnson-Nyquist type noise Shot noise term Ya.M. Blanter and M. Büttiker, Phys. Rep. 336, 1 (2000) Two channels for SWNTs due to K-K degeneracy of graphene Expect noiseless situation for D~1 Direct determination of D 1 and D 2 Fano=S I /2eI

Coupling quantum dot circuits to microwave cavities

Coupling quantum dot circuits to microwave cavities Matthieu Delbecq To cite this version: Matthieu Delbecq. Coupling quantum dot circuits to microwave cavities. Quantum Physics [quant-ph]. Université