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Antiresonance Calculations

We now look at a MW system that displays antiresonances that are predicted by the formula derived in Sec. II. Eq. (8) was derived for an idealized MW system where there was only one incident electron mode on the molecule. Thus in designing the MW system for the numerical study we tried to approximate the ideal system as closely as possible. The MW system we suggest consists of left and right $\pi $ conjugated chain molecules attached to what we will call the ``active'' molecule. The purpose of these conjugated chains is to act as filters to the many modes that will be incident from the metallic leads. For appropriate energies they will restrict the propagating electron mode to be only $\pi $ like. This $\pi $ backbone will only interact with the $\pi $ orbitals of the molecule if they are bonded in an appropriated fashion.

Figure 4: Atomistic diagram of leads attached to filter molecules and active molecule. The filter molecules consist of C8H8 chains. The active molecule contains 2 $\pi $ levels which interact with the filter molecules. The leads are (111) gold.
\includegraphics[bb= 35 237 600 470

An atomic diagram of our system is shown in Fig. 4. The leads are oriented in the (111) direction. The chain molecules are bonded to clusters of gold atoms that form the tips of the leads. The carbon atom nearest to the gold tip binds over the hollow site of the tip. The chains each have eight CH groups, which for the energies considered will only admit a $\pi $ like state to propagate along them. This gives rise to the filtering process mentioned above. The active molecule is chosen to have two $\sigma$ states and two $\pi $ states. The chain's $\pi $ like orbitals will only couple to the two $\pi $ states of the active molecule.

The Fermi energy for our gold leads is around -10 eV which lies within the $\pi $ band. We would like an antiresonance to occur somewhere near this energy. The parameters entering Eq. 8 (i.e. the molecular orbital energies and their overlaps with the chains) are chosen so that one of the roots of the equation yields a value near -10 eV. The numerically calculated electron transmission probability for this model is shown in Fig. 5a; an antiresonance is seen in the plot at the predicted energy of -10.08 eV. The differential conductance at room temperature was calculated using Eq. (1). Two different conductance calculations are shown in Fig. 5b. The solid curve corresponds to a choice of Fermi energy of -10.2 eV. Because it lies to the left of the antiresonance in a region of strong transmission, the conductance is strong at 0 V. It then drops at around 0.2 V when the antiresonance is crossed. The dashed curve was calculated using a Fermi energy of -10.0 eV. It starts in a region of lower transmission and thus the antiresonance suppresses the increase in current. After 0.2 V the large transmission to the left of the antiresonance is sampled and the current rises sharply. So in both cases the antiresonance has lowered the conductance. It is conceivable to think of utilizing more antiresonances in a narrow energy range to create a more pronounced conductance drop.


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