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Mesoscopic Capacitors

Mesoscopic Capacitors. Mesoscopic Capacitors. Markus B ü ttiker. University of Geneva. Haifa, Jan. 12, 2007. Mesoscopic physics = Wave nature of electrons is important. The elementary system. Mesoscopic physics focuses on a few elementary geometries

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Mesoscopic Capacitors

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  1. Mesoscopic Capacitors Mesoscopic Capacitors Markus Büttiker University of Geneva Haifa, Jan. 12, 2007

  2. Mesoscopic physics = Wave nature of electrons is important The elementary system Mesoscopic physics focuses on a few elementary geometries which illustrate best the effect we are interested in: Closed rings Persistent currents Aharonov-Bohm effect Rings with leads Quantum point contacts Conductance quantization . . . . . . Cavity connected to one lead RC-time

  3. The mesoscopic capacitor Buttiker, Thomas, Prêtre, Phys. Lett. A 180, 364 (1993) single potential U geometrical capacitance C What is the RC-time? Gabelli, Fève, Berroir, Plaçais, Cavanna, Etienne, Jin, Glattli, Science 313, 499 (2006).

  4. Classical versus quantum charge relaxation Classical circuit Mesoscopic capacitor is universal !! For a single, spin-polarized channel Buttiker, Thomas, Pretre, Phys. Lett. A 180, 364 (1993)

  5. 7 Dynamic external and internal response Buttiker, Thomas, Pretre, Phys. Lett. A 180, 364 (1993) single potential U geometrical capacitance C External response Internal response Invariance under arbitrary potential shift

  6. Capacitance and Charge Relaxation Buttiker, Thomas, Pretre, Phys. Lett. A180, 364 (1993) charge relaxation resistance electrochemical capacitance Eigen channels of s; Universal for n =1;

  7. Quantized charge relaxation resistances 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) Brouwer and M. B., Europhys. Lett. 37, 441 (1997). Chaotic cavity coupled to two QPC (one channel) Pedersen, van Langen, M. B., Phys. Rev. B 57, 1838 (1998).

  8. Experimentalists model Gabelli (thesis), Gabelli et al, Science 313, 499 (2006) density of states assumption 1: uniform level spacing assumption 2: voltage dependence of transmission through QPC

  9. Mesoscopic Capacitor: Experiment Gabelli, Feve, Berroir, Placais, Cavanna, Etienne, Jin, Glattli Science 313, 499 (2006).

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 Role of coherence: S. Nigg and M. Buttiker, (unpublished)

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 Role of coherence: S. Nigg and M. Buttiker, (unpublished)

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

  13. Role of Interactions S. E. Nigg, R. Lopez and M. Buttiker, PRL 97, 206804 (2006) For poarized spin channel for “arbitrary” interactions!!

  14. S. E. Nigg, R. Lopez, MB, Phys. Rev. Lett. 97, 206804 (2006) Coulomb blockade and spin degeneracy two levels low magnetic fields coupling strongly blockaded weakly blockaded

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

  16. Summary Quantized charge relaxation resistance 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 Role of dephasing Role of charge quantization Role of inetractions Quantized dynamic charge emission and absorption

  17. Works on pumping

  18. 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 Transport M. 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)

  19. 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)

  20. 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)

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