kondo shuttling - technionqpump/kiselev.pdf · for theoretical physics and workshop on quantum...
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Institut für Theoretische PhysikUniversität Würzburg
M.N.Kiselev
Kondo Shuttling
The Abdus Salam International Centrefor Theoretical Physics
and
Workshop on Quantum Pumping, Haifa, January 8, 2007
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Single orbital level coupled to two leads
Tunneling width
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Single orbital level coupled to two leads
Time-dependent Glazman-Raikh rotation
Gauge potentialTomosuke Aono, 2004
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Adiabatic current and pumped charge per cycle at T=0
Scattering phase shifts
Adiabaticity
at the Fermi level in the leads
M.Büttiker et al, 1994
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Adiabatic pumping at the Kondo regime
Pumped charge
Pumped spin
Nozieres Fermi Liquid regime
Kondo Pump = Resonance Spin Diode
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NanoElectroMechanical Pump = Shuttle
What if is due to a nanomechanics?
H.Park et al, Nature 2000 D.Sheible and R.Blick 2004
Molecular Transistor Nano-Pendulum
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Why do we look for the Kondo effect ?
• The Kondo effect makes it easier for states belonging to the two opposite electrodes to mix
• Reasonably high Kondo temperatures > 1 K
• SETs are highly controllable (by bias, magnetic field etc) devices
in nano-devices ?
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Keeping in mind Pumping …I will speak about Shuttling.
How to make the Kondo effect workin the Nanoelectromechanical devices?
• the nano-device changes its shape in the process of the tunneling
• the nano-devise is nano-machined by external periodic force
How is the KE influenced by the NEM?
K.Kikoin, MK and M.R.Wegewijs, PRL 2006MK, K.Kikoin, R.Shekhter and V.Vinokur, PRB 2006
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Ferrocene ( )5 5 2Fe C H
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Cerocene ( )8 8 2Ce C H
COT = C8H8
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Ytterbocene
Cp* = C5Me5, bipy = (NC5H4)2]
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Fullerenes
H.Park et al, Nature 2000
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Transition metals inside fullerens
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Transport through molecular transistors
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Q: Whether phonons support or destroy Kondo effect?
A: Usually they destroy it due to the energy transfer and the decoherence effects.
Q: Can phonons assist a resonance tunneling?
A: Yes, they can do it through dynamical symmetries.
Phonons + Kondo = “Phondo”
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Effective model
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cage MO = localized cage MO = delocalized
M+
e-
breathing
M+
e-
quadrupolar
M+
e-
dipolar
Triplet Singlet Exchange
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TMOC = Transition Metal + Organic Complex (cage)
Singlet Triplet
s 10
-1R
SO(4) symmetry
Singlet is a ground state
Local phonon can be emitted or absorbed in a co-tunneling processes
Assumption: even electron occupation number
The main source of phonon emission/absorption is the tunneling rate
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Vibration assisted tunneling
single phonon two-phonon
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Phonon assisted processes
single-phonon two-phonon
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Single phonon processes
Summation of “parquet” diagrams
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Single phonon processes
• Single phonon processes assist the Kondo tunneling
• Kondo temperature does not depend on the phonon coupling
• Differential conductance is logarithmically enhanced approaching the Kondo regime
Messages:
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Two-phonon processes
Messages:
• Two-phonon processes also assist the Kondo tunneling, however
• Kondo temperature depends on the phonon coupling
• The two phonon scenario leads to much smaller Kondo temperatures
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Differential Conductance
dIdV
0sdV
Equilibrium Kondo temperature(triplet state)
Non-equilibrium Kondo(S/T transitions)
Strong decoherenceregimes
Log-scaling of peaks is a manifestationof the Kondo effect
S/T splitting
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A resonance condition
… narrows a group of the TMOC with “Phondo”.
What happens if
Fine tuning tool is necessary to control the resonance
?
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Magnetic Field Effects
Magnetic field as a fine tuning tool
M.Pustilnik, Y.Avishai, K.Kikoin, PRL 2000
S=1 Kondo effect S=1/2 Kondo effect
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Single-phonon processes in magnetic field
Messages:
• Single-phonon processes assist the Kondo tunneling, however
• Kondo temperature depends on the phonon coupling
• Magnetic field provides a tool for the fine tuning of the TMOC
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NEM-SET with center-of-mass motion= Mobile Kondo Impurity
Molecular Transistor Nano-Pendulum
D.Sheible and R.Blick 2004H.Park et al, Nature 2000
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Nanotube peapods: C60 @ CNT
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The model
SW transformation
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B EDot
x2/V− 2/V+
Odd-spin Kondo shuttleCompetition between
Breit-Wigner Resonance
Abrikosov-Suhl Resonance
Time-dependent Kondo temperaturesAdiabaticity
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Even-spin Kondo shuttle
B EDot
x2/V− 2/V+
Triplet Kondo Shuttling
Singlet shuttling: No Kondo effect
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Perspectives
A. Pasupathy et al., Science 306,86 (2004)
B: magnetic fieldE: electric field
B EDot
x2/V− 2/V+
• NEM-SET between spin-polarized leads• NEM spin manipulation• Rotating pendulum• Coupled NEM-SET devices (DQD, TQD)
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Conclusions
• Phonon emission/absorption induces the Kondo tunneling
• Dynamical symmetries allow Kondo effect in excited triplet state
• Decoherence due to vibration does not destroy the Kondo effect
L R
Molecular Transistor
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Conclusions
• Phonon emission/absorption induces the Kondo tunneling
• Dynamical symmetries allow Kondo effect in excited triplet state
• Decoherence due to vibration does not destroy the Kondo effect
Molecular Transistor
Kondo shuttle
• Kondo shuttling allows the spin manipulation by NEM motion
• Kondo NEM-SET is a Mobile Quantum Impurity
• Dynamical symmetries influence the Kondo shuttling in S/T setups