quantum pumping and rectification effects in interacting quantum dots francesco romeo in...
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Quantum pumping and rectification effects in
interacting quantum dotsFrancesco Romeo
In collaboration with:Dr Roberta Citro
Prof. Maria Marinaro
University of Salerno,
Dipartimento di Fisica “E. R. Caianiello”
Capri Spring School on Transport in Nanostructures 2009 - Capri, March 29 - April 5
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Quantum pumping techniqueElectron pump in quantum dots (QD):
the finite current problem at zero-phaseFisher-Lee & Brouwer-Wang approachResults for single level interacting and
non-interacting QDConclusions
Outlines
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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)
Quantum Pumping technique
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Adiabatic Quantum Pumping
P. Brouwer, PRB 1998
Current in weak pumping limit
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An Adiabatic Quantum Electron Pump by Switkes et al.
M. Switkes et al., Science 283, 1905 (1999)
QD
Problem: Finite current at zero phase
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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).
Finite zero-phase current
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Hamiltonian of the system
Hamiltonian model
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Current and instantaneous scattering matrix
Instantaneous pumped currents
Time averaged pumped currents
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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)
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Pumping + rectification current
Instantaneous pumped currents in terms of GF
Linewidth and tunneling amplitudes
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The wide band limit is assumed
Pumping through a non-interacting single level QD
Pumping term
Rectification term Effective voltage
Pumping term as in
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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
Pumping through an “interacting” single level QD
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Pumping cycle
Results within the zero-temperature limit
Total charge
Pumping charge
Rectified charge
Energy scale
Rectified charge in the strong interacting limit
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Pumping cycle
Results: time-linear variation of the tunneling phase
Energy scale
Total charge
Rectified charge
Pumping charge
The pumping term (a) presents a sinusoidal behavior with respect to the pumping phase
The rectification term (b) is proportional to the cosine of the pumping phase
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Rectification contribution to the charge (weak pumping approximation)
Analytical dependence of the rectification term vs pumping
phase
Ratchet-like term
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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
Conclusions
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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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We modulate only the interface barriers strength The energy levels on the QD are not modulated
QD-based electron pump
Fermi energy
j-th QD energy level
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Appendix (1): Delta term
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Appendix (2): Pumping Formula
Pumped current
Energy current