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• Positive noise correlations in spite of negative crossed conductance• Implications of disorder.
The noise is the signal (R. Landauer)
Johnson-Nyquist noise and Shot noise
information about resistance & temperature … just disturbance
Harry Nyquist (1889-1976: U.S.)
Electrons are emitted by thermal agitation
② Shot noise in a vacuum tube
① Johnson-Nyquist noise for equilibrium circuit
classical picture of current
“simple way to measure the charge of electron”
Annals der Physik (1918)
noise power
Walter Schottky (1886-1976: Germany)
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)
Positive noise correlation in a « NS fork » J.Torrès, T. Martin, EPJB (99)
Noise in Normal metal/Superconducting junctions
Andreev reflection
Positive noise correlation in a « Andreev interferometer » M P Anantram & S. Datta, PRB (1996)
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
(b) Crossed Andreev reflection
-ve correlations
+ve correlations
Motivation: To build a solid state entangler
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
•Non local conductance is enhanced by weak localization
V1 V2
•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.
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