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

important for L < Lj : phase coherence length 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

Overview of the thesis d Tool for measuring 1) Phase coherence and interactions between electrons in a disordered metal 150 nm 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

Overview of the thesis d Tool for measuring 1) Phase coherence and interactions between electrons in a disordered metal 150 nm 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

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

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)

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

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

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

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

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 Magnetic moments OK Pierre et al. (2003) Anthore et al. (2003)

several explanations dismissed Quantitative experiment 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 Magnetic moments OK 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)

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

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

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

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

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

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

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

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

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

Experimental data at low and at high B 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

Various B and U T= 20 mK

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

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

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

Overview of the thesis d Tool for measuring 1) Phase coherence and interactions between electrons in a disordered metal 150 nm 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

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

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

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

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

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

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

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

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

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

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

Measure {t1,…,tM} It V Measure I(V) Ib Transmissions AC3 0.992 ± 0.003 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

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

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

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

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

Overview of the thesis d Tool for measuring 1) Phase coherence and interactions between electrons in a disordered metal 150 nm 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

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

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

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

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

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

Asymmetric current fluctuations Ib (µA) so that G G 30 kHz Im (µA)

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

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

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

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 ? Magnetic impurities and 2 level systems cannot explain the discrepancy (bad fits) Slight error at the lowest probed energies would furthermore reduce the intensity ke-e Never been investigated Strong enough if Ag very close to ferromagnetic instability Yes, same result close to equilibrium f(E) 1 Experiment near equilibrium E