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Quantum Noise Spectra of Mesoscopic Structures - Analytical Study

Explore classical versus quantum noise in mesoscopic structures, with a focus on noise spectrum and scattering matrix formalism. Understand single and two single-level dots, charge conservation, and quantum interference effects.

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Quantum Noise Spectra of Mesoscopic Structures - Analytical Study

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  1. The noise spectra of mesoscopic structures Eitan Rothstein With Amnon Aharony and Ora Entin 02.02.09 Condensed matter seminar, BGU

  2. Outline • Classical vs. quantum noise • The noise spectrum • The scattering matrix formalism • A single level dot • Two single level dots • Summary

  3. Classical Noise Discreteness of charge The Schottky effect (1918)

  4. Classical Noise Thermal fluctuations Nyquist Johnson noise (1928)

  5. Quantum Noise Quantum statistics M. Henny et al., Science 284, 296 (1999).

  6. Quantum Noise Quantum interference I. Neder et al., Phys. Rev. Lett. 98, 036803 (2007).

  7. The noise spectrum L R Sample - Quantum statistical average

  8. Different Correlations Net current: Net charge on the sample: Cross correlation: Auto correlation:

  9. Relations at zero frequency Charge conservation:

  10. The scattering matrix formalism Analytical and exact calculations Single electron picture No interactions M. Buttiker, Phys. Rev. B. 46, 12485 (1992).

  11. The scattering matrix formalism

  12. A single level dot E. A. Rothstein, O. Entin-Wohlman, A. Aharony, PRB (in press).

  13. Unbiased dot • Resonance around • Without bias, is independent of • , parabolic around (In units of )

  14. Unbiased dot • At maximal asymmetry (the red line), , and • Without bias the system is symmetric to the change • The dip in the cross correlations has increased, and moved to • Small dip around

  15. A biased dot at zero temperature • , parabolic around • When , there are 2 steps . • When , there are 4 steps . • For the noise is sensitive to the sign of

  16. A biased dot at zero temperature • The main difference is around zero frequency.

  17. A biased dot at finite temperature • For , the peak around has turned into a dip due to the ‘RR’ process. • The noise is not symmetric to the sign change of also for

  18. Two single level dots

  19. Unbiased dots • Each resonance has one step

  20. Unbiased dot

  21. Unbiased dots • There is a dip at • The dip in is a function of

  22. Finite temperature new • There is a dip at for both cases.

  23. AB flux • The dip in oscillates with AB flux.

  24. e 2 Biased dots • If there is a dip/peak at

  25. Summary • A single level dot • At and the single level quantum dotexhibits a step around . • Finite bias can split this step into 2 or 4 steps, depending on and . • When there are 4 steps, a peak [dip] appears around for [ ]. • Finite temperature smears the steps, but can turn the previous peak into a dip. • 2 single level dots • If , there is a dip / peak at . • This dip oscillates with . Thank you!!!

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