Electron transport through molecules

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Electron transport through molecules

• 1) Molecular conductors/Kondo effect
• 2) Holstein mode
• 3) Phonon in barriers
• 4) Shuttle mode (center of mass)
• 5) future work....

Group C.A. B?sser K.A.
Al-Hassanieh E. Dagotto at
Department of Physics University of Tennessee
and Oak Ridge National Laboratory
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Transport in organic molecules
W. Liang et al, Nature Vol. 417, 725 (2002)
Leads
Small gap (1 nm) between the metal tips
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Characteristic of the molecular conductors

• Small size

gt strong electronic correlations / many body
effects (Coulomb blockade, Kondo).
gt easier to see phonon effects.
Conductance
Just the elastic terms !!!!!!
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Coulomb Blockade vs Kondo
Kondo regime (TltTk)
CB regime (TgtTk)
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Exact diagonalization Dyson Eq.
1) Divide the system in two parts (cutting two
connections)
2) Solve the many-body cluster using exact
diagonalization technique (ground state
calculation)
3) re-establish the cuted connections using a
Dyson equation
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Holstein mode
Electron-phonon coupling terms are derived from
an expansion of first order in the electron-ion
interaction when the ions are displaced from the
equilibrium position x.
The displacement can be quantized as the Harmonic
oscillator.
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Some systems
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Effective Hamiltonian
Canonical transformation
Anderson impurity Hamiltonian with effective
parameters
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1 Quantum dot
P. Cornaglia et al, PRL 93 147201 (2004) NRG.
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2QDs - Kondo regime
Exact diagonalization calculations
H. Jeong, Science Vol 293, 2221 (2001)
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2QD ED embedding
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Barriers modulated by phonon
gt Shuttle mode
Holstein mode
Phonon assisted tunneling
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Conductance
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Future work....
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