Electronic transport decay rule for junction of oligophenylene molecules sandwiched between phosphorene nanoribbons

We study the influence of electrodes on the exponential transport rule for the junction of oligophenylene-linked and oligoacene-linked molecules between two zigzag phosphorene nanoribbons (ZPNRs), where molecules consisting of one, two and three benzene rings are considered, respectively. We find by ab initio calculations that the amplitude of current through the junction is dependent on both the molecular length and the molecule-ZPNR coupling manner. In specification, the current through the single-bond coupled junction with the molecular plane perpendicular to the ZPNRs is almost two times that with parallel configuration due to the greater number of transport channels provided by the p(y) orbital in the former case. In contrast, the current of the junction with double-bond coupling is nearly two orders of magnitude larger because of the stronger coupling strength. Nevertheless, in any case the ZPNR-electrode junction, like metal-electrode junctions, also obeys the exponential decaying rule in transport with the variation of molecular length. Importantly, the relationship between the resistance and the molecular length, regardless of the coupling details, can be fitted by a linear line in the semilog coordinate but with different slopes determined by the coupling manner. This indicates that the exponential rule of transport under small bias voltages is electrode-material-independent for molecular junctions with any electrode. But the value of the decaying factor, importantly, is heavily dependent not only on the molecule itself but also on the electrode materials as well as the molecule-electrode coupling method.