Charge transport in molecular junctions: From tunneling to hopping with the probe technique

Abstract

We demonstrate that a simple phenomenological approach can be used to simulate electronic conduction in molecular wires under thermal effects induced by the surrounding environment. This "Landauer-Büttiker's probe technique" can properly replicate different transport mechanisms, phase coherent nonresonant tunneling, ballistic behavior, and hopping conduction. Specifically, our simulations with the probe method recover the following central characteristics of charge transfer in molecular wires: (i) the electrical conductance of short wires falls off exponentially with molecular length, a manifestation of the tunneling (superexchange) mechanism. Hopping dynamics overtakes superexchange in long wires demonstrating an ohmic-like behavior. (ii) In off-resonance situations, weak dephasing effects facilitate charge transfer, but under large dephasing, the electrical conductance is suppressed. (iii) At high enough temperatures, kBT/ϵB > 1/25, with ϵB as the molecular-barrier height, the current is enhanced by a thermal activation (Arrhenius) factor. However, this enhancement takes place for both coherent and incoherent electrons and it does not readily indicate on the underlying mechanism. (iv) At finite-bias, dephasing effects may impede conduction in resonant situations. We further show that memory (non-Markovian) effects can be implemented within the Landauer-Büttiker's probe technique to model the interaction of electrons with a structured environment. Finally, we examine experimental results of electron transfer in conjugated molecular wires and show that our computational approach can reasonably reproduce reported values to provide mechanistic information.

Thermopower of molecular junctions: Tunneling to hopping crossover in DNA

“…(19). At high temperatures (room temperature in our case), the tail of the Fermi function enhances the ballistic contribution-even beyond hopping conduction 57 . Indeed, in panel (a2) with T =200 K we observe that the ballistic component is enhanced over the hopping contribution at small γ d .…”

“…To compute the electrical conductance, we use the voltage probe as implemented in Ref. 57 . To simulate a thermal gradient and compute the thermopower, however, we have also to selfconsistently set the temperature of the thermal environment, which we compute via the voltage-temperature probe method 61,64 .…”

“…4(a), with the conductance showing a typical crossover from an activationless to an activated form as we increase the temperature, even when environmental effects are turned off completely with γ d = 0, see also Ref. 57 . Temperaturedependent conductance measurements can thus be quite confusing to interpret.…”

“…Particularly, in Ref. 57 we demonstrated that the LBP method can capture different transport regimes in molecular wires: tunneling conduction, ballistic motion, and incoherent hopping. In Refs.…”

Inelastic effects in molecular transport junctions: The probe technique at high bias

“…A central advantage of the probe technique is the ability to craft different types of incoherent scattering processes following certain conditions. These conditions manifest in the "dephasing" and "voltage" probes, which respectively allow only elastic or inelasticdissipative scattering 26,27 .…”