Quantum Interference in Coherent Molecular Conductance

Coherent electronic transport through individual molecules is crucially sensitive to quantum interference. We investigate the zero-bias and zero-temperature conductance through $\pi$-conjugated annulene molecules weakly coupled to two leads for different source-drain configurations, finding an important reduction for certain transmission channels and for particular geometries as a consequence of destructive quantum interference between states with definite momenta. When translational symmetry is broken by an external perturbation we find an abrupt increase of the conductance through those channels. Previous studies concentrated on the effect at the Fermi energy, where this effect is very small. By analyzing the effect of symmetry breaking on the main transmission channels we find a much larger response thus leading to the possibility of a larger switching of the conductance through single molecules.

Figure 1

Schematic representation of the molecules studied numerically in the presence of a gate voltage $V_g$, small hybridization to the leads $t^{\prime }$ and two source-drain lead geometries.

Figure 2

Top: Transmittance through a benzene molecule for the para ($A$ substitution in Fig. 1) (broken line) and meta ($B$ substitution in Fig. 1) (full line) configurations as a function of the gate voltage measured from the Fermi energy. Here $t^{\prime }=0.4$. Bottom: Same for the meta configuration in the presence of different on-site potentials which break the translational invariance. Here a finite Lorentzian width $\eta =0.03$ and $t^{\prime }=0.1$ have been taken for visualization purposes. Inset: evolution of the area under the transmission peak through the HOMO as a function of local energy.

Figure 3

Same as Fig. 2, for $N=10$ annulene.

Figure 4

Top: Transmittance through an [8]-annulene molecule for the $A$ (broken line) and $B$ (full line) configurations as a function of the gate voltage measured from the Fermi energy. Here $t^{\prime }=0.4$. Bottom: Transmittance for the $B$ configuration in the presence of a local perturbation of the hopping of the form $t(1-\phi )$ which breaks the translational invariance ($\eta =0.03$ and $t^{\prime }=0.1$). Inset: evolution of the HOMO integral as a function of $\phi$.

Figure 5

Top: HOMO integral of a [12]-annulene molecule for the $A$ (broken line) and $B$ (full line) configurations as a function of the locally perturbed hopping $t(1-\phi )$ (left panel) and the dimerization parameter $\delta$ (right panel). Bottom: Transmittance for the $B$ configuration in the presence of dimerization.