Photon-assisted electron-hole shot noise in multi-terminal conductors

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Photon-assisted electron-hole shot noise in
multi-terminal conductors

• Valentin Rychkov

In collaboration with Mikhail Poliansky and
Markus Büttiker
University of Geneva, Switzerland
cond-mat/0507276. To appear in PRB
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Outline

• Motivation
• Scattering formalism
• Electron-hole picture of AC shot noise
• Experimental setup
• Probability game
• Correlation experiment
• HBT-like experiment
• Conclusions

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Motivation

• AC and DC-transport.

Recent review on AC transport G. Platero and R.
Aguado,
Phys. Rep. 395 (1-2) 1 (2004)
Beenakker, Titov, and Trauzettel, Phys. Rev.
Lett. 94, 186804 (2005)
Samuelsson and Buttiker, Phys. Rev. B 71, 245317
(2005)
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L.-H. Reydellet et al. Phys. Rev. Lett. 90,
176803 (2003)
Do electrons and holes produce shot noise
independently?

• HBT-like experiments
• New information about sample?

Possible observation of electron-hole
correlations
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Scattering formalism

• The goal is to calculate shot noise at zero
  frequency
• Scattering matrix describes scattering of
  particles
• Current operator

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Electron-hole picture of transport

• Electrons and holes
• Weak AC-voltage
• Zero temperature

• Scattering matrix is energy independent
  electron-hole symmetry, no interactions.
• Role of interactions, dephasing see Poliansky,
  Samuelson, Buttiker cond-mat/0507336

• Current operator
• Shot noise

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Two terminal geometry
Probability game
,
Not all N attempts are made!
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Correlation experiment
Since pairs come rarely, correlation measurement
show correlations between particles in pairs.
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HBT interferometer
Hanbury Brown, Twiss. Nature 177 (1956)
Van Langen, Buttiker PRB 56 (1997)
HBT-interferometer. Current-current correlations
in DC case
HBT-interferometer. Intensity-intensity
correlations from incoherent sources
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HBT-phase
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1
extrema
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2
RMT Cavity with single channel contacts
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Conclusions

• In the limit of weak AC voltage

• In 2 terminal conductors electron-hole
  correlations coexist with electron-electron and
  hole-hole correlations
• In 3 terminal geometry correlation between
  currents at different leads are pure
  electron-hole correlations
• HBT-like experiments provide complete information
  about exchange interference
• Statistical distribution of exchange interference
  term is found