We extend the Landauer-Büttiker probe formalism for conductances to the high bias regime and study the effects of environmentally induced elastic and inelastic scattering on charge current in single molecule junctions, focusing on high-bias effects. The probe technique phenomenologically incorporates incoherent elastic and inelastic effects to the fully coherent case, mimicking a rich physical environment at trivial cost. We further identify environmentally induced mechanisms which generate an asymmetry in the current, manifested as a weak diode behavior. This rectifying behavior, found in two types of molecular junction models, is absent in the coherent-elastic limit and is only active in the case with incoherent-inelastic scattering. Our work illustrates that in the low bias-linear response regime, the commonly used “dephasing probe” (mimicking only elastic decoherence effects) operates nearly indistinguishably from a “voltage probe” (admitting inelastic-dissipative effects). However, these probes realize fundamentally distinct I-V characteristics at high biases, reflecting the central roles of dissipation and inelastic scattering processes on molecular electronic transport far-from-equilibrium.
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Numerical simulations28,39–44 and analytical studies (mostly for heat conduction)31,60–62 had demonstrated the emergence of incoherent conduction due to the coupling of local sites to either dephasing or voltage probes. This could be reasoned in terms of the energy eigenstates of the molecule, . The probes scatter electrons in an incoherent manner, elastically or inelastically, between different electronic eigenstates |M〉, introducing an incoherent transport mechanism on top of the coherent (direct left-to-right transmission) contribution. The hybridization of eigenstates to the contacts (at least to one of them) decays exponentially with size in off-resonant situations, leading to small tunneling conduction. The probes however open up a more effective charge transfer pathway between the state |M〉, which is strongly coupled to the left lead, and the state |M′〉, which strongly couples to the right terminal. In long chains of length N, the most effective pathway involves multiple scattering between eigenstates, with the conductance scaling approximately with N−1.28
