Abstract
It is demonstrated that non-equilibrium vibrational effects are enhanced in molecular devices for which the effective potential for vibrations is sensitive to the charge state of the device. We calculate the electron tunnelling current through a molecule accounting for the two simplest qualitative effects of the charging on the nuclear potential for vibrational motion: a shift (change in the equilibrium position) and a distortion (change in the vibrational frequency). The distortion has two important effects: firstly, it breaks the symmetry between the excitation spectra of the two charge states. This gives rise to new transport effects which map out changes in the current-induced non-equilibrium vibrational distribution with increasing bias voltage. Secondly, the distortion modifies the Franck–Condon factors for electron tunnelling. Together with the spectral asymmetry this gives rise to pronounced nuclear wavefunction interference effects on the electron transport. For instance nuclear-parity forbidden transitions lead to differential conductance anti-resonances, which are stronger than those due to allowed transitions. For special distortion and shift combinations a coherent suppression of transport beyond a bias voltage threshold is possible.
Highlights
This imposes a quasi-selection rule on the Franck-Condon (FC) factors which determine the rates for the electron tunneling. This leads to effects in the intensity of the non-linear conductance resonances which are related to destructive interference of the nuclear wave functions. This is to be contrasted to the blockade [12, 13] and NDC effects [19] discussed previously, which basically follow from classical features of the nuclear motion even though the discrete vibrational excitations are of quantum signature
We have found that non-equilibrium vibrational effects are enhanced in molecular devices for which the effective potential for vibrations is sensitive to the charge state of the device
We modeled this by a change in the vibrational frequency in addition to a shift of the potential minima
Summary
The question how quantized vibrational modes affect the electron transport through a single molecule has recently attracted a lot of interest, both experimentally [1, 2, 3, 4, 5, 6, 7] and theoretically [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. This imposes a quasi-selection rule on the Franck-Condon (FC) factors which determine the rates for the electron tunneling This leads to effects in the intensity of the non-linear conductance resonances which are related to destructive interference of the nuclear wave functions. The FC-factors take into account that the nuclear potential is altered when the molecule becomes charged Their energy dependence through the vibrational numbers m, m′ is typically dominant over that of the rates which we take to be constants Γr = 2π|tr|2ρr with density of states ρr in electrode r = L, R. In contrast to most transport models, here the FC-factors are non-symmetric Fm′m = Fmm′ In general this is the case when the nuclear potentials in the two charge states are not identical up to a shift.
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