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.