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

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Presentation transcript:

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

Noise: An Introduction Noise and entanglement: Historical perspective 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. 2

The noise is the signal (R. Landauer)

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

classical picture of current 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.

QUANTUM TRANSPORT: scattering approach Reservoirs + S matrix

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)

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)

Why do positive cross-correlations imply entanglement 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

Noise correlations: BTK approach

Noise correlations: Greens function approach

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

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)]

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

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

Transmission: Two barrier case

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

Classical result

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

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.