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Positive HBT/noise cross-correlations in superconducting hybrids: Role of disorder

Positive HBT/noise cross-correlations in superconducting hybrids: Role of disorder. R. Melin, C. Benjamin and T. Martin, Phys. Rev. B 77, 094512 (2008). Talk outline:. Noise: An Introduction Noise and entanglement: Historical perspective NSN junctions: CAR and EC

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Positive HBT/noise cross-correlations in superconducting hybrids: Role of disorder

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  1. Positive HBT/noise cross-correlations in superconducting hybrids: Role of disorder R. Melin, C. Benjamin and T. Martin, Phys. Rev. B 77, 094512 (2008)

  2. Talk outline: Noise: An Introduction Noise and entanglement: Historical perspective NSN junctions: CAR and EC Positive noise correlations in spite of negative crossed conductance Implications of disorder.

  3. The noise is the signal (R. Landauer)

  4. Johnson-Nyquist noise and Shot noise ① Johnson-Nyquist noise for equilibrium circuit Harry Nyquist (1889-1976: U.S.) information about resistance & temperature … just disturbance ② Shot noise in a vacuum tube Electrons are emitted by thermal agitation

  5. noise power “simple way to measure the charge of electron” Annals der Physik (1918) Walter Schottky (1886-1976: Germany) classical picture of current Electrons are emitted Independently from each other: Poissonian process.

  6. QUANTUM TRANSPORT: scattering approach Reservoirs + S matrix

  7. Hanbury Brown and Twiss experiment Bunching effect: positive correlations Fermions: Negative correlations (T. Martin & R. Landauer M. Buttiker, PRB ’s 92) Exp: Schonenberger 99, Yamamoto 99 (Science)

  8. Noise in Normal metal/Superconducting junctions Andreev reflection Positive noise correlation in a « Andreev interferometer » M P Anantram & S. Datta, PRB (1996) Positive noise correlation in a « NS fork » J.Torrès, T. Martin, EPJB (99)

  9. Motivation: To build a solid state entangler Why do positive cross-correlations imply entanglement • +ve cross-correlations in a fermionic system • Reason for this anomaly: correlations between fermions (a)Electron co-tunneling -ve correlations (b) Crossed Andreev reflection +ve correlations

  10. Noise correlations: BTK approach

  11. Noise correlations: Greens function approach

  12. Noise cross-correlations: The half metallic case • Anti-parallel alignment: completely positive (crossed Andreev processes) • Parallel alignment: completely negative (elastic co-tunneling) • At Vb=+Va (P/AP) noise vanishes due to Pauli blocking For fermions: f=f 2

  13. Noise cross-correlations: NSN • Transparent interfaces: Noise cross-correlations +ve • Semi-transparent interfaces: Noise cross-correlations –ve • Tunneling limit: -ve for EC and +ve for CAR [Bignon, et. al., EPL(2004)]

  14. Novelty of our work (1) • In NSN systems: Crossed conductance = CAR-EC • Negative crossed conductance does not imply negative cross-correlations!

  15. Novelty of our work (2) • Interpretation: (a) double Andreev reflection (b) double non-local Andreev process

  16. Transmission: Two barrier case

  17. Weak localization: Three barriers F. Marquardt, Lecture notes on weak localization

  18. Classical result

  19. V1 V2 • Non local conductance is enhanced by weak localization Noise cross correlations enhanced by weak localization

  20. Perspective • Probing interesting physics in the weak localization regime • Probing entanglement in nanophysics-This study constitutes what is the next generation in the evolving project to detect the splitting of cooper pairs into different leads.

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