The noise spectra of mesoscopic structures

1. The noise spectra of mesoscopic structures Eitan Rothstein With Amnon Aharony and Ora Entin 22.09.10 University of Latvia, Riga, Latvia

3. The desert in Israel

4. Outline • Introduction to mesoscopic physics • Introduction to noise • The scattering matrix formalism • Our results for the noise of a quantum dot • Summary

5. Mesoscopic Physics Meso = Intermidiate, in the middle. Mesoscopic physics = A mesoscopic system is really like a large molecule, but it is always, at least weakly, coupled to a much larger, essentially infinite, system – via phonos, many body excitation, and so on. (Y. Imry, Introduction to mesoscopic physics) A naïve definition: Something very small coupled to something very large.

7. Going down in dimensions (2d) 2DEG Very high mobilty GaAs-AlGaAs at the Heiblum group - PRL 103, 236802 (2009) Si at room temperature

8. Going down in dimensions (1d) Nanowire and QPC Quantum point contact Nanowire Quantized conductance curve

9. Going down in dimensions (1d) Edge states Under certain conditions, high magnetic fields in a two-dimensional conductor lead to a suppression of both elastic and inelastic backscattering. This, together with the formation of edge states, is used to develop a picture of the integer quantum Hall effect in open multiprobe conductors. M. Buttiker, Phys. Rev. B 38, 9375 (1988).

10. Going down in dimensions (0d) Quantum Dots There are different types of quantum dots. A large atom connecting to two ledas A metallic grain on a surface Voltage gates on 2DEG

11. Going down in dimensions (0d) Quantum Dots A theoretical point of view:

12. Going down in dimensions (0d) The pictures are taken from the review by L P Kouwenhoven, D G Austingand S Tarucha

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

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

15. Quantum Noise

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

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

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

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

20. Relations at zero frequency Charge conservation:

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

22. The scattering matrix formalism

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

25. 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

26. 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

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

28. 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

29. Summary “The noise is the signal” R. Landauer, Nature London 392, 658 1998. • A single level dot • At and the noise of a 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. Thank you!!!