Markus BüttikerUniversity of GenevaUniversity of Geneva

Haifa, Jan. 12, 2007 Haifa, Jan. 12, 2007

Mesoscopic CapacitorsMesoscopic Capacitors

The elementary system

Mesoscopic physics focuses on a few elementary geometries which illustrate best the effect we are interested in:

Closed rings Persistent currents

Rings with leads Aharonov-Bohm effect

Quantum point contacts Conductance quantization

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.Cavity connected to one lead RC-time

Mesoscopic physics = Wave nature of electrons is important

The mesoscopic capacitor

single potential U geometrical capacitance C

Buttiker, Thomas, Prêtre, Phys. Lett. A 180, 364 (1993)

Gabelli, Fève, Berroir, Plaçais, Cavanna, Etienne, Jin, Glattli, Science 313, 499 (2006).

What is the RC-time?

Classical versus quantum charge

relaxationClassical circuit

Mesoscopic capacitor

For a single, spin-polarized channel is universal !!Buttiker, Thomas, Pretre, Phys. Lett. A 180, 364 (1993)

Dynamic external and internal response

Internal response

Invariance under arbitrary potential shift

single potential U

geometrical capacitance C

Buttiker, Thomas, Pretre, Phys. Lett. A 180, 364 (1993)

External response

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Capacitance and Charge Relaxation

electrochemical capacitance charge relaxation resistance

Eigen channels of s;

Universal for n =1;

Buttiker, Thomas, Pretre, Phys. Lett. A180, 364 (1993)

Universal for n =1; For k degenerate channels

Spin less electrons

Spin degenerate channel

Ideally coupled Carbon Nanotube

Chaotic cavity coupled to two QPC (N channel)

Chaotic cavity coupled to two QPC (one channel)

Quantized charge relaxation resistances

Brouwer and M. B., Europhys. Lett. 37, 441 (1997).

Pedersen, van Langen, M. B., Phys. Rev. B 57, 1838 (1998).

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Experimentalists model

density of states

assumption 1: uniform level spacing

Gabelli (thesis), Gabelli et al, Science 313, 499 (2006)

assumption 2: voltage dependence of transmission through QPC

Gabelli, Feve, Berroir, Placais, Cavanna, Etienne, Jin, Glattli Science 313, 499 (2006).

Mesoscopic Capacitor: Experiment

Role of coherence:S. Nigg and M. Buttiker, (unpublished)

Role of coherence:S. Nigg and M. Buttiker, (unpublished)

Role of charge quantizationM. Buttiker and S. E. Nigg , Nanotechnolgy 18, 044029 (2007)[S. E. Nigg , R. Lopez and M. Buttiker, PRL 97, 206804 (2006)]

Role of Interactions S. E. Nigg, R. Lopez and M. Buttiker, PRL 97, 206804 (2006)

For poarized spin channel for “arbitrary” interactions!!

Coulomb blockade and spin degeneracyS. E. Nigg, R. Lopez, MB, Phys. Rev. Lett. 97, 206804 (2006)

two levels

low magnetic fields

coupling

strongly blockaded

weakly blockaded

Quantized dynamic charge injection G. Feve, Thesis, ENS, Paris, Dec. 23, 2006

Summary

For a single spin-polarized channel, self-consistent scattering theory predicts a universal charge relaxation resistance of half a resistance quantum

A seminal experiment by Gabelli et al. supports this prediction

Quantized dynamic charge emission and absorption

Role of dephasing

Quantized charge relaxation resistance

Role of charge quantization

Role of inetractions

Works on pumping

Pumping (w. M. Moskalets)Time-resolved noise of adiabatic quantum pumps

M. Moskalets, M. Buttiker, Phys. Rev. B 75, 035315 (2007)

● Multiparticle correlations of an oscillating scatterer M. Moskalets and M. Büttiker, Phys. Rev. B 73, 125315 (2006)

Magnetic-field symmetry of pump currents of adiabatically driven mesoscopic structures M. Moskalets and M. Büttiker, Phys. Rev. B 72, 035324 (2005)

Scattering Theory of Dynamic Electrical TransportM. Buttiker, M. Moskalets, Lect. Notes Phys. 690, 33 (2006)

Floquet scattering theory for current and heat noise in large amplitude adiabatic pumps M. Moskalets and M. Büttiker, Phys. Rev. B 70, 245305 (2004)

Adiabatic quantum pump in the presence of external ac voltages M. Moskalets and M. Büttiker, Phys. Rev. B 69, 205316 (2004)

Quantum pumping: Coherent rings versus open conductors M. Moskalets and M. Büttiker, Phys. Rev. B 68, 161311 (2003)

Pumping (w. M. Moskalets)

Hidden quantum pump effects in quantum coherent rings M. Moskalets and M. Büttiker, Phys. Rev. B 68, 075303 (2003)

Floquet states and persistent-current transitions in a mesoscopic ring M. Moskalets and M. Büttiker, Phys. Rev. B 66, 245321 (2002)

Floquet scattering theory of quantum pumps M. Moskalets and M. Büttiker, Phys. Rev. B 66, 205320 (2002)

Dissipation and noise in adiabatic quantum pumps M. Moskalets and M. Büttiker, Phys. Rev. B 66, 035306 (2002)

Effect of inelastic scattering on parametric pumping M. Moskalets and M. Büttiker, Phys. Rev. B 64, 201305 (2001)

Pumping

● Leggett-Garg Inequality with a Kicked Quantum Pump A. N. Jordan, A. N. Korotkov, and M. Büttiker, Phys. Rev. Lett. 97, 026805 (2006)

Shot noise of photon-excited electron-hole pairs in open quantum dots M. L. Polianski, P. Samuelsson, and M. Büttiker, Phys. Rev. B 72, 161302 (2005)

● Dynamic generation of orbital quasiparticle entanglement in mesoscopic conductors P. Samuelsson and M. Büttiker, Phys. Rev. B 71, 245317 (2005)

● Photon-assisted electron-hole shot noise in multiterminal conductors V. S. Rychkov, M. L. Polianski, and M. Büttiker, Phys. Rev. B 72, 155326 (2005)

Noise-assisted classical adiabatic pumping in a symmetric periodic potential O. Usmani, E. Lutz, and M. Büttiker, Phys. Rev. E 66, 021111 (2002)

Scattering theory of photon-assisted electron transport M. H. Pedersen and M. Büttiker, Phys. Rev. B 58, 12993 (1998)