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

The desert in Israel

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

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.

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

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

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).

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 surfaceVoltage gates on 2DEG

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

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

Classical Noise The Schottky effect (1918) Discreteness of charge

Classical Noise Thermal fluctuations Nyquist Johnson noise (1928)

Quantum Noise

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

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

The noise spectrum LR - Quantum statistical average Sample

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

Relations at zero frequency Charge conservation:

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

The scattering matrix formalism

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

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

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

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

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

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