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

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

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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 150 nm V I Tool for measuring the asymmetry of I(t) ? I B superconductor I( ) for elementary conductor t

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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 150 nm V I Tool for measuring the asymmetry of I(t) ? I B superconductor I( ) for elementary conductor t

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Electron dynamics in metallic thin films + + + + + + + + + lele Grain boundaries Film edges Impurities Elastic scattering - Diffusion - Limit conductance Coulomb interaction Phonons Magnetic moments Inelastic scattering - Limit coherence ( L ) - Exchange energy Typically, F l e L ≤ L 150 nm

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

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

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U E eU f(E) Distribution function and energy exchange rates « weak interactions » D int.

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U E eU f(E) « strong interactions » Distribution function and energy exchange rates D int.

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f(E) interactions E f(E) « weak interactions » E f(E) « strong interactions » Distribution function and energy exchange rates D int. D int.

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Understanding of inelastic scattering Coulomb interaction Magnetic moments Interaction 1 st method Weak localization 2 nd method Energy relaxation OK Wind et al. (1986) OK stronger than expected Pierre et al. (2003) dependence on B as expected Anthore et al. (2003) Pierre et al. (2000) µeV 0.010.1110100 Probed energies :

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

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

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

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

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

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

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

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

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Interaction mediated by a magnetic impurity : effect of a low magnetic field (gµB eU) f(E) E E-E- E’+ E’ E’+ E’E E-E- Virtual state E Z =gµB Modified rate ** E Z E-EZE-EZ

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Spin-flip scattering on a magnetic impurity : effect of a high magnetic field (gµB eU) f(E) E E-EZE-EZ EZEZ Reduction of the energy exchange rate eU E-E- E Z Modified rate E’+ E’ Virtual state

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B = 0.3 T (gµ B B = 0.35 eU) B = 2.1 T (gµ B B = 2.4 eU) Very weak interaction Experimental data at low and at high B implanted 0.65 ppm Mn bare U = 0.1 mV T= 20 mK

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Various B and U T= 20 mK

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

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Coulomb interaction intensity e-e 0.020.11 0.02 0.1 1 energy relaxation weak localization best fit for e-e (ns meV -1/2 ) expected for e-e (ns meV -1/2 ) Unexplained discrepancy µeV 0.01 0.1 1 10 100 Experiments on 15 different wires:

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

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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 150 nm V I Tool for measuring the asymmetry of I(t) ? I B superconductor I( ) for elementary conductor t

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

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

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a(E)e -i "e" "h" "e" N S Andreev reflection probability amplitude Andreev reflection (1964) a(E)e i a(E)e -i

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E( ) 22 ++ -- 0 2 current carrying bound states LL RR "e" "h" "e" = 1 Andreev bound states in a short ballistic channel ( < ) E→E→ E←E← a(E)e -i R a(E)e i L ← →

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LL RR a(E, L )a(E, R ) "e" "h" "e" < 1 -- 0 E-E- 22 E( ) ++ E+E+ Central prediction of the mesoscopic theory of the Josephson effect A. Furusaki, M. Tsukada (1991) Andreev bound states in a short ballistic channel ( < )

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LL RR a(E, L )a(E, R ) "e" "h" "e" < 1 -- 0 22 E( ) Central prediction of the mesoscopic theory of the Josephson effect A. Furusaki, M. Tsukada (1991) Andreev bound states in a short ballistic channel ( < ) CURRENT I( ) 22 0

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I S S V { 1 … N } A few independent conduction channels of measurable and tunable transmissions J.C. Cuevas et al. (1998) E. Scheer et al. (1998) Atomic orbitals Quantitative test using atomic contacts. Quantitative test I-V { 1 … N }

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

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Al Metallic bridge (atomic contact) Tunnel junction IbIb ItIt V How to test I( ) theory Strategy : 1)Measure { 1,…, M } 2)Measure I( ) V>0 V=0

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IbIb V 0 I 2 /e Switching of a tunnel junction. ItIt V IbIb circuit breaker : I b >I V>0 stable (circuit breaker) open circuit : 2 /e >V>0

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IbIb ItIt V Measure { 1,…, M } Measure I(V) method: Scheer et al. 1997 0.957 ± 0.01 0.992 ± 0.003 AC3 AC2 AC1 Transmissions 0.089 ±0.06 0.185 ±0.05 0.12 ±0.015 0.115 ±0.01 0.088 ±0.06 0.11 ±0.01 0.11 ±0.01 0.62 ± 0.01

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IbIb ItIt V Measure I( ) (circuit breaker) V 0 2 /e I I bare IbIb

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Measure I( ) 0.957 ± 0.01 0.992 ± 0.003 0.62 ± 0.01

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

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

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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 150 nm V I Tool for measuring the asymmetry of I(t) ? I B superconductor I( ) for elementary conductor t

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0 n Full counting statistics P (n) characterizes Average current during VmVm ne/ =I II t pioneer: Levitov et al. (1993) Need a new tool to measure it

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Independent tunnel events Poisson distribution P (n) is asymmetric P (n) n nn Well known case : tunnel junction Simple distribution detector calibration Log scale

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Which charge counter ? VmVm II II t Tunnel junction

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Charge counter: Josephson junction t VmVm ImIm ImIm ImIm ImIm I R large C large R large C large 20 µs -I Switching rates Proposal : Tobiska & Nazarov PRL (2004)

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Charge counter: Josephson junction t VmVm ImIm I m I m +I b 0 I m -I b IbIb t ImIm I -I I I m +I b IbIb

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Asymmetric current fluctuations I m (µA) I b (µA) so that 30 kHz

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Asymmetric current fluctuations I m (µA) cste (30 kHz) There is an asymmetry |I b | so that Gaussian noise

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Asymmetric current fluctuations I m (µA) Disagreement with existing theory Ankerhold (2006) cste (30 kHz) |I b | so that

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Conclusions Decoherence and interactions in disordered metals Quantitative experiments Open : Coulomb intensity Unified theory of Josephson effect Quantitative agreement with fundamental relation Persp. : spectro and manip. of Andreev states Tool for measuring high order current noise Tool sensitive to high order noise OK Open : Interpretation ? I (nA)

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Coulomb interaction discrepancy explanations - Extrinsic energy exchange processes ? - Quasi-1D model inappropriate ? - Diffusive approximation invalid ? - Hartree term stronger than expected ? - Theory valid at equilibrium only ? Experiment near equilibrium E f(E) 0 1 Magnetic impurities and 2 level systems cannot explain the discrepancy (bad fits) Slight error at the lowest probed energies would furthermore reduce the intensity e-e Never been investigated Strong enough if Ag very close to ferromagnetic instability Yes, same result close to equilibrium

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