Time-Dependent View of Sequential Transport through Molecules with Rapidly Fluctuating Bridges

Molecules in junctions often fluctuate considerably, especially when subject to the influence of solvent molecules. These fluctuations in site energies and couplings can be sampled, for example, by using molecular dynamics simulations, and can lead to incoherent effects in charge transport. To this end, a popular snapshot-averaged Landauer approach is compared to a time-dependent Green’s function scheme. Since sequential transport dominates in systems with rapidly varying bridges, schemes not taking the time order of conformations into account, such as the Landauer approach, are inappropriate.

Figure 1

TD-NEGF current $I(t)$ through a seven-site DNA molecule compared to the Landauer current. (a) Currents based on a 20-ps MD trajectory using a 1-fs time step. The heavily fluctuating time-resolved TD-NEGF current is displayed in light blue, whereas the dark-blue curve shows its running average over 2000 frames. The lower curve (red) denotes the Landauer results. The average values over the complete trajectory are $I_{\mathrm{TD}\mathrm{\text{−}}\mathrm{NEGF}}=73.52\mathrm{nA}$ and $I_{\mathrm{Landauer}}=0.0739\mathrm{nA}$. (b) Currents computed using a coarse-grained version of the MD trajectory. The corresponding energies and couplings of 500 snapshots have been averaged to coarse-grained time points. The inset shows the first 100 fs of the seven site energies.

Figure 2

A two-site system with a site energies switching time of 40 fs. (a) The TD-NEGF current through the device is shown in blue, compared to the Landauer current, shown in red (lower curve). The inset shows the site energy of the first site as a function of time for different values of the switching parameter $s$. (b) The occupation number of both sites as a function of time.

Figure 3

A two-site system with a site energies switching time of 500 fs. (a) The TD-NEGF currents for three values of the switching parameter $s$ compared to the Landauer currents. (b) Population dynamics for both sites. The filled regions indicate the fast oscillations not resolved on the present scale.