Quantum length dependence of conductance in oligomers: First-principles calculations

In recent experiment it was found that for a quantum length dependence of conductance of oligothiophene-CH2 molecules under low bias [Xu et al., Nano Lett. 5, 1491 (2005)], the longer molecule has larger conductance. Due to the experimental motivation, we calculated the conductance of a similar organic compound, oligothiophene, by means of the first-principles method. Our calculations show a similar quantum length dependence of conductance in the low bias region and an oscillated length dependence of conductance in the high bias region. The transport behaviors are determined by the distinct electronic structures of the molecular compounds. The length dependencies of conductance for several other oligomers are calculated to show the diversity in the transport behaviors of molecular wires. The results show that Ohm’s law is not valid for the molecular conductance anymore, and for the low bias region, Magoga’s law is not applicable for some molecular wires, for example, oligothiophene dithiolates.

Figure 1

(Color online) $I\text{−}V$ characteristics of the three oligomers. (a) $\left(n\right)\mathrm{TDTs}$ show the unusual length dependence in the low bias regime, $V<1.2\mathrm{V}$, and the oscillated length dependence under high bias. (b) $\mathrm{PPh}\left(n\right)\mathrm{DTs}$ show a classical-like length dependence. The inset illustrates Magoga’s exponential law under low bias $V=0.4\mathrm{V}$. (c) $\mathrm{PA}\left(n\right)\mathrm{DTs}$ present the classical-like length dependence in low bias regime $V<1.2\mathrm{V}$ and the unusual quantum length dependence under high bias. The inset illustrates Magoga’s exponential law under low bias $V=0.4\mathrm{V}$.

Figure 2

(Color online) DOS as a function of energy of the three oligomers with the gold contacts (shifted vertically for visibility). (a) For $\left(n\right)\mathrm{TDTs}$, the increase in the number of thiophene ring results in an increase of the value of DOS at $E_F$ and a reduction of the HOMO-LUMO gap. (b) For $\mathrm{PPh}\left(n\right)\mathrm{DTs}$, with the increase of benzene ring, DOS at $E_F$ decreases and the HOMO-LUMO gap increases. (c) For $\mathrm{PA}\left(n\right)\mathrm{DTs}$, with the increase of benzene ring, both DOS at $E_F$ and the HOMO-LUMO gap decrease.

Figure 3

(Color online) Transmission spectrum of the three oligomers in equilibrium (shifted vertically for visibility). (a) For $\left(n\right)\mathrm{TDTs}$, the increase in the number of thiophene ring results in an increase of the value of the transmission probability $T$ at $E_F$ and a reduction of the HOMO-LUMO gaps. (b) For $\mathrm{PPh}\left(n\right)\mathrm{DTs}$, with the increase of benzene ring, $T$ at $E_F$ decreases and the HOMO-LUMO gap increases. (c) For $\mathrm{PA}\left(n\right)\mathrm{DTs}$, with the increase of benzene ring, both $T$ at $E_F$ and the HOMO-LUMO gap decrease.