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B. Huard & Quantronics group

Interactions between electrons, mesoscopic Josephson effect and asymmetric current fluctuations. B. Huard & Quantronics group. Quantum electronics. Macroscopic conductors. 2 I. I. DC AMPS. DC AMPS. L. L/2. R  L. Mesoscopic conductors. R  L. Quantum mechanics changes the rules.

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B. Huard & Quantronics group

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  1. Interactions between electrons, mesoscopic Josephson effect and asymmetric current fluctuations B. Huard & Quantronics group

  2. Quantum electronics Macroscopic conductors 2 I I DC AMPS DC AMPS L L/2 R  L Mesoscopic conductors R  L Quantum mechanics changes the rules important for L < Lj :phase coherence length

  3. 150 nm Overview of the thesis 1) Phase coherence and interactions between electrons in a disordered metal 2) Mesoscopic Josephson effects 3) Measuring high order current noise superconductor V B I I t d Tool for measuring the asymmetry of I(t) ? I(d) for elementary conductor

  4. 150 nm Overview of the thesis 1) Phase coherence and interactions between electrons in a disordered metal 2) Mesoscopic Josephson effects 3) Measuring high order current noise superconductor V B I I t d Tool for measuring the asymmetry of I(t) ? I(d) for elementary conductor

  5. + le + + + + + + + + 150 nm Electron dynamics in metallic thin films Elastic scattering Grain boundaries Film edges Impurities - Diffusion - Limit conductance Inelastic scattering - Limit coherence (Lj) - Exchange energy Coulomb interaction Phonons Magnetic moments Typically, lF leLj≤ L

  6. How to access e-e interactions ? 1st method : weak localization R(B) measures Lj B In a wire Pierre et al., PRB (2003) B (mT) First measurement: Wind et al. (1986)

  7. U ? eU Diffusion time : (20 ns for 20 µm) How to access e-e interactions ? 2nd method : energy relaxation Occupied states E U=0 f(E)

  8. eU Distribution function and energy exchange rates « weak interactions » U tD tint. E f(E)

  9. eU Distribution function and energy exchange rates « strong interactions » U tD tint. E f(E)

  10. Distribution function and energy exchange rates « weak interactions » « strong interactions » tD tint. tD tint. E E f(E) f(E) f(E) interactions

  11. Understanding of inelastic scattering 1st method Weak localization 2nd method Energy relaxation Interaction stronger than expected OK Coulomb interaction Wind et al. (1986) Pierre et al. (2000) e (µeV) Probed energies : 0.01 0.1 1 10 100 dependence on B as expected OK Magnetic moments Pierre et al. (2003) Anthore et al. (2003)

  12. Understanding of inelastic scattering 1st method Weak localization 2nd method Energy relaxation Interaction stronger than expected OK Coulomb interaction Wind et al. (1986) Pierre et al. (2000) dependence on B as expected OK Magnetic moments Pierre et al. (2003) Anthore et al. (2003) several explanations dismissed (Huard et al.,Sol. State Comm. 2004) Quantitative experiment (Huard et al.,PRL 2005)

  13. Access e-e interactions : measurement of f(E) Dynamical Coulomb blockade (ZBA) R I U=0 mV

  14. U=0.2 mV Measurement of f(E) Dynamical Coulomb blockade (ZBA) R I weak interaction strong interaction U=0 mV

  15. Quantitative investigation of the effects of magnetic impurities 0.65 ppm Mn implantation implanted  bare Left as is Ag (99.9999%) Comparative experiments using methods 1 and 2 Huard et al., PRL 2005

  16. 1st method : weak localization spin-flip Coulomb phonons 0.65 ppm Mn 0.65 ppm consistent with implantation 0.03 ppm compatible with < 1ppm dirt Best fit of Lj(T) for

  17. 2nd method : energy relaxation implanted 0.65 ppm Mn strong interaction U = 0.1 mV B = 0.3 T T= 20 mK bare weak interaction

  18. * rate maximal at Kondo temperature Spin-flip scattering on a magnetic impurity - dephasing - no change of energy At B=0 energy E E f(E) E E

  19. * * Enhanced by Kondo effect Interaction between electrons mediated by a magnetic impurity Virtual state E E-e E’+e E’ f(E) E E-e E’ E’+e Kaminski and Glazman, PRL (2001)

  20. * * Interaction mediated by a magnetic impurity : effect of a low magnetic field (gµBeU) Virtual state E E-e E’+e E-EZ E’ EZ=gµB f(E) E E-e E’ E’+e (e-EZ)-2 Modified rate

  21. Spin-flip scattering on a magnetic impurity : effect of a high magnetic field (gµB eU) Virtual state E E-e eU EZ E’+e E’ E-EZ f(E) Reduction of the energy exchange rate (e-EZ)-2 Modified rate

  22. Experimental data atlowand athighB implanted 0.65 ppm Mn U = 0.1 mV B = 0.3 T (gµBB = 0.35 eU) B = 2.1 T (gµBB = 2.4 eU) Very weak interaction bare U = 0.1 mV T= 20 mK

  23. Various B and U T= 20 mK

  24. Comparison with theory Using theory of Goeppert, Galperin, Altshuler and Grabert PRB (2001) Only 1 fit parameter for all curves : ke-e=0.05ns-1.meV-1/2(Coulomb interaction intensity)

  25. Coulomb interaction intensity ke-e energy relaxation weak localization Experiments on 15 different wires: e (µeV) 1 ) -1/2 100 meV -1 10 1 0.1 best fit for ke-e (ns 0.1 0.01 0.02 0.02 0.1 1 -1 -1/2 expected for ke-e (ns meV ) Unexplained discrepancy

  26. Conclusions on interactions spin-flip Coulomb phonons Quantitative understanding of the role played by magnetic impurities but Coulomb interaction stronger than expected

  27. 150 nm Overview of the thesis 1) Phase coherence and interactions between electrons in a disordered metal 2) Mesoscopic Josephson effects 3) Measuring high order current noise superconductor V B I I t d Tool for measuring the asymmetry of I(t) ? I(d) for elementary conductor

  28. Case of superconducting electrodes B I Supercurrent through a weak link ? Unified theory of the Josephson effect Furusaki et al. PRL 1991, …

  29. I V Collection of independent channels t r’ r t’ Conduction channels Coherent Conductor (L«Lj) Landauer Transmission probability

  30. Andreev reflection (1964) S N "e" "h" a(E)e-if "e"  "h" a(E)eif a(E)e-if Andreev reflection probability amplitude

  31. Andreev bound states "e"  "h" → ← t = 1 in a short ballistic channel ( < x ) fR fL a(E)eif a(E)e-if "e" L R "h" E(d) 2 current carrying bound states +D E→ 0 d p 2p E← -D

  32. Andreev bound states fR fL a(E, fL) a(E, fR) "e" "h" "e"  "h" +D E+ in a short ballistic channel ( < x ) t < 1 E(d) 0 d p 2p Central prediction of the mesoscopic theory of the Josephson effect -D E- A. Furusaki, M. Tsukada (1991)

  33. Andreev bound states fR fL a(E, fL) a(E, fR) "e" "h" "e"  "h" in a short ballistic channel ( < x ) t < 1 CURRENT I(d,t) E(d) 0 d p 2p 0 d 2p Central prediction of the mesoscopic theory of the Josephson effect -D A. Furusaki, M. Tsukada (1991)

  34. Quantitative test using atomic contacts . Atomic orbitals I V S S { t1 … tN } A few independent conduction channels of measurable and tunable transmissions J.C. Cuevas et al. (1998) E. Scheer et al. (1998) I-V { t1 … tN } Quantitative test

  35. 3 cm Atomic contact pushing rods sample metallic film pushing rods Flexible substrate insulating layer counter- support counter-support with shielded coil

  36. How to test I(d) theory  V Tunnel junction j Al It Metallic bridge (atomic contact) Ib • Strategy : • Measure {t1,…,tM} • Measure I(d) V>0 V=0

  37. V (circuit breaker) It Ib open circuit : 2D/e>V>0 circuit breaker : Ib>I V>0 stable Switching of a tunnel junction . Ib I 0 2D/e V

  38. Measure {t1,…,tM} V method: Scheer et al. 1997 Transmissions Measure I(V) It AC3 0.992± 0.003 0.089 ±0.06 0.088 ±0.06 Ib AC2 0.957± 0.01 0.185 ±0.05 AC1 0.62± 0.01 0.12 ±0.015 0.115 ±0.01 0.11 ±0.01 0.11 ±0.01

  39. Measure I(d) Ibare I (circuit breaker)  V Ib j It Ib 0 2D/e V d j /f0 + p/2

  40. Measure I(d) 0.992± 0.003 0.957± 0.01 0.62± 0.01

  41. Comparison with theory I(d) 0.992± 0.003 0.957± 0.01 0.62± 0.01 Theory : I(d) + switching at T0

  42. Comparison with theory I(d) 0.992± 0.003 0.957± 0.01 0.62± 0.01 Theory : I(d) + switching at T0 Overall good agreement but with a slight deviation at t 1

  43. 150 nm Overview of the thesis 1) Phase coherence and interactions between electrons in a disordered metal 2) Mesoscopic Josephson effects 3) Measuring high order current noise superconductor V B I I t d Tool for measuring the asymmetry of I(t) ? I(d) for elementary conductor

  44. n 0 t 0 Full counting statistics Vm Average current during t ne/t=It Pt(n) characterizes It pioneer: Levitov et al. (1993) Need a new tool to measure it t

  45. Well known case : tunnel junction Independent tunnel events Poisson distribution n Log scale Pt(n) n Pt(n) is asymmetric Simple distribution detector calibration

  46. Which charge counter ? Tunnel junction Vm It It t

  47. Charge counter: Josephson junction Clarge RlargeClarge 20 µs dIm Im Vm Rlarge Im I G+ Switching rates Im G- -I t Proposal : Tobiska & Nazarov PRL (2004)

  48. Charge counter: Josephson junction dIm Ib dIm+Ib Ib Im Vm G+ dIm -Ib dIm +Ib G- I I Im 0 -I -I t t

  49. Asymmetric current fluctuations G+/ G- -1 |Ib| so that G+ cste (30 kHz) Gaussian noise Im (µA) There is an asymmetry

  50. Asymmetric current fluctuations G+/ G- -1 |Ib| so that G+ cste (30 kHz) Ankerhold (2006) Im (µA) Disagreement with existing theory

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