We consider electronic transport through break-junctionsbridged by a single molecule in the Kondo regime. We de-scribe the system by a two-channel Anderson model. We takethe tunneling matrix elements to depend on the position of themolecule. It is shown, that if the modulation of the tunnelingby displacement is large, the potential confining the moleculeto the central position between the leads is softened and theposition of the molecule is increasingly susceptible to externalperturbations that break the inversion symmetry. In this regime,the molecule is attracted to one of the leads and as a conse-quence the conductance is small. We argue on semi-classicalgrounds why the softening occurs and corroborate our findingsby numerical examples obtained by Wilson's numerical renor-malization group and Schonhammer-Gunnarsson's Variationalmethod. Sketch of the model device. The overlap integrals between themolecular orbital and the leads (V_L, V_Rfor left, right lead, re-spectively) are modulated by the position of the molecule. Theenergy of the molecular level ∈is determined by the gate volt-age.
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