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Pumping in Interacting Systems

Pumping in Interacting Systems. Yuval Oreg Department of Condensed Matter Physics. http://www.weizmann.ac.il/condmat/oreg_group.html. With Eran Sela. Outline. What are pumps? What are electron pumps? Phase Coherent Pumps Non coherent Pumps General formula for interacting systems

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Pumping in Interacting Systems

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  1. Pumping in Interacting Systems Yuval Oreg Department of Condensed Matter Physics http://www.weizmann.ac.il/condmat/oreg_group.html

  2. With Eran Sela

  3. Outline • What are pumps? • What are electron pumps? • Phase Coherent Pumps • Non coherent Pumps • General formula for interacting systems • The two channel Kondo system • Topological quantization of spin current • Effective magnetic field and Non Fermi liquid behavior at finite T • Conclusions

  4. Heat pumps • Sadi Nicholas Leonard Carnot 1796-1832 • Work= Area P V

  5. Single Electron Pumps –Electron Turnstile

  6. N+1 N+1 N N N+1 N N+1 N+1 N+1 N N N N+1 N

  7. Single Electron Pumps

  8. BPT [non interacting] Hartree X2 δX X0 X1 Pumps formulae T Brouwer BPT EC Interaction

  9. Pumps formulae T Brouwer BPT Non coherent pumps (Sela and YO PRB 2005) EC Rate equations Quantum - interacting (Sela and YO PRL 2006) Interaction

  10. Adiabatic limit Non Coherent PumpsWith geometric interpretation(Sela and YO PRB2005) aAsymmetry coefficient Q charge on one of the capacitor plates τ>RC

  11. y δX X0 x

  12. Pure Spin Pumps

  13. For 2DEG with area A

  14. Prefers polarization A=1μm2

  15. L γ δU With dephasing (using Buttiker’s model) Classical non coherent result With DOS ->1/C and Transmission ->1/R When non coherent pumps formula applies? IClass/ICoherent= L kF =L/λF

  16. Pumps formulae T Brouwer BPT Non coherent pumps (Sela and YO PRB 2005) EC Rate equations ? Interaction

  17. Pumps (with interaction) at low temp Kubo Formula • Aleiner and Matveev: Open dots (1998) • Sharma and Shamon: Lut-Liq (2001, 2003) • Citro et al: Lut – Liq (2003) • Cohen (2003): Applied to non interacting systems Keldysh • J. Splettstoesser et al. (Average time ) approximation

  18. Central area may depend on parameters X1, X2 Left Lead Right Lead All parts (including leads) may have interactions X2 δX X0 BPT (non interacting) X1

  19. X2 δX X0 X1 Adiabatic Limit Curvature O(δX2) Relaxation time

  20. Geometric/Topologic interpretation

  21. Application to Dots c d d c c d Average time Aprox.

  22. G εd dQd=Adεd -#U2/(T2Γ) A=#U2/(T2Γ)+U2/T3 Infinite order in Γ second order in U, Assume: U and Γ «T

  23. Application to repulsive quantum critical points y x

  24. Spin pumps in the two channel Kondo x=Δ=J1-J2, y=h At x=y=0 NFL point T1/2 sing.

  25. Emery Kivelson Line hГ Δ=(J1 -J2)/Г=Cos( θ) Kondo Temp

  26. Concentrated around r=1 • Integral over B=ћ

  27. h0 L2 Δ Δ0 1

  28. Conclusions • Non coherent pumps at high temp. • A generic pumping formula for interacting systems, with a geometric interpretation. • Application to two channel Kondo physics with anomalous exponents and interesting topology

  29. Dziękuje どうもありがとう спасибо 감사합니다

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