Charge Transport in Strongly Coupled Molecular Junctions: "In-Phase" and "Out-of-Phase" Contribution to Electron Tunneling

We report a first-principles study on the evolution of nonequilibrium charge transport in a two-terminal molecular-scale device with the increase in the length of the molecular wire built out of cubane oligomers. In particular, for wires of three different lengths, we look into the relative contribution of the "in-phase" and the "out-of-phase" components of the total electronic current under the influence of an external bias. In the low-bias regime, the "out-of-phase" contribution to the total current is minimal and the "in-phase" elastic tunneling of the electrons is responsible for the net electronic current. This is true, irrespective of the length of the molecular spacer. In this regime, the current-voltage characteristics follow Ohm's law and the conductance of the wires is found to decrease exponentially with the increase in length, which is in agreement with experimental results. However, after a certain "offset" voltage, the current increases nonlinearly with bias and the "out-of-phase" tunneling of electrons reduces the current substantially. This behavior is attributed to the reduction in constructive interference due to phase randomization at the resonant tunneling regime, and thus, the height of the transmission peak is reduced. We subsequently studied the interaction of conduction electrons with the vibrational modes as a function of external bias in the three different oligomers since they are one of the main sources of phase-breaking scattering. The number of vibrational modes that couple strongly with the electronic levels is found to increase with the length of the spacer, which is consistent with the existence of the lowest "offset" voltage for the longest wire under study.