The noise spectra of mesoscopic structures

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

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

Classical Noise Discreteness of charge The Schottky effect (1918)

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, 036803 (2007).

The noise spectrum L R Sample - Quantum statistical average

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

Relations at zero frequency Charge conservation:

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

The scattering matrix formalism

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

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

Two single level dots

Unbiased dots • Each resonance has one step

Unbiased dot

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

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

AB flux • The dip in oscillates with AB flux.

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

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!!!

The noise spectra of mesoscopic structures