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Quantum pumping and rectification effects in interacting quantum dots

University of Salerno, Dipartimento di Fisica “E. R. Caianiello”. Capri Spring School on Transport in Nanostructures 2009 - Capri, March 29 - April 5. Quantum pumping and rectification effects in interacting quantum dots. Francesco Romeo In collaboration with : Dr Roberta Citro

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Quantum pumping and rectification effects in interacting quantum dots

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  1. University of Salerno, Dipartimento di Fisica “E. R. Caianiello” Capri Spring School on Transport in Nanostructures 2009 - Capri, March 29 - April 5 Quantum pumping and rectification effects in interacting quantum dots Francesco Romeo In collaboration with: Dr Roberta Citro Prof. Maria Marinaro

  2. Outlines • Quantum pumping technique • Electron pump in quantum dots (QD): the finite current problem at zero-phase • Fisher-Lee & Brouwer-Wang approach • Results for single level interacting and non-interacting QD • Conclusions

  3. Quantum Pumping technique • Quantum pump: A device which generates a dc current by a periodic adiabatic variation of the system characteristics; Thouless (83) • Quantization: Integral of current over a period is quantized in system with full bands (robust against disorder and interaction); Niu and Thouless (84) • Mesoscopic systems: typically in quantum dots and semiconductors; Sharma & Brouwer 03 (Theory), Switkes (99), Watson (03) (Experiments)

  4. Adiabatic Quantum Pumping Current in weak pumping limit P. Brouwer, PRB 1998

  5. An Adiabatic Quantum Electron Pump by Switkes et al. QD Problem: Finite current at zero phase M. Switkes et al., Science 283, 1905 (1999)

  6. Finite zero-phase current Possible theoretical explanations: • Rectification of displacement currents • Finite frequency effect (Wang) • Non-equilibrium effect (+ interaction) F. Romeo, R. Citro and M. Marinaro, Phys. Rev. B 78, 245309 (2008).

  7. Hamiltonian model • Hamiltonian of the system

  8. Current and instantaneous scattering matrix • Instantaneous pumped currents • Time averaged pumped currents

  9. Scattering matrix and Fisher-Lee relation (adiabatic theory) • Fisher-Lee relation in adiabatic limit, i.e. • Time derivative of the full Green’s function obtained from the Dyson equation by assuming the uncouple GF as time independent (no time modulation of the QD levels) D. S. Fisher and P. A. Lee, Phys. Rev. B 23, 6851 (1981)

  10. Pumping + rectification current • Instantaneous pumped currents in terms of GF • Linewidth and tunneling amplitudes

  11. Pumping through a non-interacting single level QD Pumping term • The wide band limit is assumed Rectification term Effective voltage Pumping term as in

  12. Pumping through an “interacting” single level QD • A self-consistent treatment of the problem is required • The renormalization of the dot level has been neglected in this approach • The wide band limit is assumed

  13. Results within the zero-temperature limit Rectified charge Pumping charge Total charge • Pumping cycle • Energy scale Rectified charge in the strong interacting limit

  14. Results: time-linear variation of the tunneling phase Pumping charge • Pumping cycle Rectified charge • Energy scale Total charge • The pumping term (a) presents a sinusoidalbehavior with respect to the pumping phase • The rectification term (b) is proportional to the cosine of the pumping phase

  15. Analytical dependence of the rectification term vs pumping phase • Rectification contribution to the charge (weak pumping approximation) Ratchet-like term

  16. Conclusions • We presented a Fisher-Lee based theoretical approach accounting for the finite zero-phase current detected in quantum pump devices. • In this framework the rectification term is naturally included • The proposed approach can be extended directly beyond the linear response regime (i.e. beyond the first order in the pumping frequency) • The interaction effects can be included in the framework of a mean field treatment (slave boson etc) • Energy current and noise can be analyzed within the mentioned theory

  17. Bibliography • F. Romeo, R. Citro, M. Marinaro; Phys. Rev. B 78, 245309 (2008) • R. Citro, F. Romeo; Phys. Rev. B 77, 193309 (2008) • F. Romeo, R. Citro, M. Marinaro; Phys. Rev. B 76, 081301(R) (2007) • R. Citro, F. Romeo; Phys. Rev. B 75, 073306 (2007) • R. Citro, F. Romeo, M. Marinaro; Phys. Rev. B 74, 115329 (2006) • R. Citro, F. Romeo; Phys. Rev. B 73, 233304 (2006) • F. Romeo, R. Citro; Eur. Phys. J. B 50, 483-489 (2006) • R. Citro, F. Romeo; Quantum pumping and rectification effects in • interacting quantum dots, preprint (2009); arXiv:0903.2362v1

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  19. QD-based electron pump j-th QD energy level • We modulate only the interface barriers strength • The energy levels on the QD are not modulated Fermi energy

  20. Appendix (1): Delta term

  21. Appendix (2): Pumping Formula • Pumped current • Energy current

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