Electron transport through ribbonlike molecular wires calculated using density-functional theory and Green’s function formalism

We study the length dependence of electron transport through three families of rigid, ribbonlike molecular wires. These series of molecules, known as polyacene dithiolates, polyphenanthrene dithiolates, and polyfluorene dithiolates, represent the ultimate graphene nanoribbons. We find that acenes are the most attractive candidates for low-resistance molecular-scale wires because the low-bias conductance of the fluorene- and phenanthrene-based families is shown to decrease exponentially with length, with inverse decay lengths of $\beta =0.29{\text{Å}}^{-1}$ and $\beta =0.37{\text{Å}}^{-1}$, respectively. In contrast, the conductance of the acene-based series is found to oscillate with length due to quantum interference. The period of oscillation is determined by the Fermi wave vector of an infinite acene chain and is approximately $10\text{Å}$. Details of the oscillations are sensitive to the position of thiol end groups and in the case of “para” end groups, the conductance is found initially to increase with length.

Figure 1

The molecules: (a) fluorenes and (b) phenanthrenes, and two types of acenes, which we will call (c) para and (d) Meta. The molecules consist of $n=2$, 3, and 4 fused benzene rings. Length of unit cell: $a_{uc}=8.295\text{Å}$, $4.3567\text{Å}$, and $2.44\text{Å}$.

Figure 2

(Color online) Length dependence of the room-temperature conductance. ${\beta }_{flu}=-0.29$ and ${\beta }_{phe}=-0.37$. The number of benzene rings $n$ in fluorenes are [2:4], for phenanthrenes [2:6], and for the acenes are [2:7]. The 7-acene is the longest acene molecule that can be synthesized.

Figure 3

(Color online) Length dependence of the room-temperature conductance. The number of benzene rings $n$ in fluorenes are [2:12], for phenanthrenes [2:17], and for the acenes are [2:23].

Figure 4

(Color online) Comparison between hollow and top contacts.

Figure 5

(Color online) Band structure of infinite fluorene, acene, and phenanthrene as a function of the wave vector parallel to the backbone of the chains.

Figure 6

(Color online) HL gaps of fluorenes, acenes, and phenanthrenes plotted as a function of the length of the molecules. The gaps for the infinitely long molecules is also shown.

Figure 7

(Color online) Energy dependence of $T\left(E\right)$ for fluorenes and phenanthrenes.

Figure 8

(Color online) Energy dependence of $T\left(E\right)$ for para- and meta-acenes.

Figure 9

A simplified model of the acene molecule attached to 1D leads. $ϵ$ and $\gamma$ are the on-site and hopping parameters of the lead, ${\gamma }_{L-S}$ connects the molecule to the leads, ${ϵ}_S$ is the on-site energy of the two atoms at the ends of the molecule, ${ϵ}_C$ is the on-site energy of the sites of the ladder, ${\gamma }_1$ is the longitudinal hopping parameter between the ladder sites, and ${\gamma }_{\alpha }$ the transverse hopping element.

Figure 10

(Color online) Comparison between DFT calculation of 11-acene in para position and the ladder model with the parameters of ${ϵ}_0=0.0$, ${\gamma }_0=1.0$, ${\gamma }_{L-S}=0.26$, ${ϵ}_S=0.066$, ${ϵ}_C=-0.47$, ${\gamma }_1=0.505$, and ${\gamma }_{\alpha }=0.366$.