Theory%20of%20vibrationally%20inelastic%20electron%20transport%20through%20molecular%20bridges

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Theory of vibrationally inelastic electron
transport through molecular bridges

• Martin Cížek
• Charles University Prague
• Michael Thoss, Wolfgang Domcke
• Technical University of Munich

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Motivation I Molecular electronics as ultimate
solution for miniaturization of electronic
devices

• Experiments conduction properties of individual
  molecules
• M. A. Reed et al. Science 278 (1997) 252
• Conductance of a molecular junction.
• H. Park et al. Nature 407 (2000) 57
• Nanomechanical oscillations in a single-C60
  transistor.
• R. H. M. Smit et al. Nature 419 (2002) 906
• Measurement of the conductance of a hydrogen
  molec.

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Motivation II
A.Nitzan, M.A.Ratner, Science 300 (2003) 1384

• Goal of this work To understand role of the
  molecular vibrations in the transmission of
  electrons through a molecular bridge

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Motivation III
B.Y.Gelfand, S.Schmitt-Rink, A.F.J.Levi Phys.
Rev. Lett. 62 (1989) 168 Tunneling in the
presence of phonons A solvable model.
W.Domcke, C. Mundel Phys.
Rev. A 18 (1985) 4491 Calculation of cross
sections for vibrational excitation and
dissociative attachment in HCl and DCl

• Goal II To apply methods developed for
  electron-molecule scattering in gas phase (if
  possible)

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Theoretical model outline
GL(E)
GR(E)
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Separation of vibrations to system and bath
degrees of freedom
M. Thoss and W. Domcke, J. Chem. Phys. 109 (1998)
6577.
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Theoretical model single particle description

• H HS HB HSB

System Hamiltonian Bath Hamiltonian System-
bath coupling
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Model Electronic degrees of freedom
ß ß v
v ß ß
µL µL µL
?d µR
µR µR
Exactly solvable model Tight-binding
(Huckel-type Hamiltonian) Conduction band in
leads µa-2ß lt E lt µa2ß Energy dependent
width Selfenergy function (level shift)
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Transmission through molecular bridge
1) Elastic case (frozen vibrations) Exact
analytic solution
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Transmission through molecular bridge
Including vibrations (no bath) Exact numerical
solution
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Transmission through molecular bridge
Including vibrations and bath Perturbation
expansion in HSB
Can be summed to all orders for symmetric bridge
under zero bias (unitarity).
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Calculation of the current
CAUTION MANY BODY PROBLEM
tR?L (?f,?i)
eF
eF
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Results weakly coupled case
vibrations
Elastic
dissipation
Transmission
v 0.2 ß
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Results strongly coupled vibrations
vibrations
Elastic
dissipation
Transmission
v 0.2 ß
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Convergence of the expansionin the system-bath
coupling
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Results strongly coupled leads
Elastic Vibrations dissipation
Transmission
v ß
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Results strongly coupled leads
Elastic Vibrations dissipation
Transmission
v ß
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Wide-band approximation G(E)const.
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Conclussions and outlook

• We have demonstrated ability of our approach to
  describe inelastic effects in molecular
  conduction within single particle (tunneling
  electron) approximation.
• Our approach is capable to treat anharmonic
  vibrations and dissociation of the bridge
  molecule. The wide band limit is not assumed
  ability to describe semiconductors.
• Generalization to full many particle description
  is necessary nonequilibrium Greens function
  techniques. First step self-consistent Born
  approximation.
• Determination of the model parameters for
  realistic molecular systems employing ab initio
  quantum chemistry methods.

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Acknowledgements

• Wolfgang Domcke, Michael Thoss
• Financial support
• Alexander von Humboldt foundation
• The detailed description of this work can be
  found in
• http//arxiv.org/abs/cond-mat/0312080
• Phys. Rev. B (2004) in press

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Narrow resonances in VE on H2 e- H2(J22-27)
? G10-7 eV e- D2(J30-39) ? G10-11 eV
G03.210-7eV
Long lived states H-2(J27) ? t
ns D-2(J38) ? t 10µs