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 The Schottky effect (1918) Discreteness of charge

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 LR - Quantum statistical average Sample

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

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 There is a dip at for both cases. new

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

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

25. Summary A single level dot At and the single level quantum dot exhibits 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!!!