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A molecular wire (MW)in its simplest definition consists of a molecule connected between two reservoirs of electrons. The molecular orbitals of the molecule when they couple to the leads provide favourable pathways for electrons. Such a system was suggested in the early '70's by Aviram and Ratner to have the ability to rectify current[1]. Experimental research on MW has increased over the past few years looking into the possibility of rectification and other phenomena[2,3,4,5,6,7,8,9]. There has also been an increase in the theoretical modeling of MW systems[10,11,12,13,14,15]. For a comprehensive overreview of the current status of the molecular electronics field see [16].

Theoretical studies of the electronic conductance of a MW bring together different methods from chemistry and physics. Quantum chemistry is used to model the energetics of the molecule. It is also incorporated into the study of the coupling between the molecule and the metallic reservoirs. Once these issues have been addressed it is possible to proceed to the electron transport problem. Currently, Landauer theory[17,18] is used which relates the conductance to the electron transmission probability.

A molecule of current experimental interest as a MW is 1,4 benzene-dithiolate (BDT)[3]. It consists of a benzene molecule with two sulfur atoms attached, one on either end of the benzene ring. The sulfurs bond effectively to the gold nanocontacts and the conjugated $\pi $ ring provides delocalized electrons which are beneficial for transport. Two major unknowns of the experimental system are the geometry of the gold contacts and the nature of the bond between the molecule and these contacts. This paper attempts to highlight these important issues by showing how the differential conductance varies with bond strength.

For mesoscopic systems with discrete energy levels (such as MW) connected to continuum reservoirs, the transmission probability displays resonance peaks. Another potentially important transport phenomenon that has been predicted is the appearance of antiresonances[14,19]. These occur when the transmission probability is zero and correspond to the incident electrons being perfectly reflected by the molecule. We derive a simple condition controlling where the antiresonances occur in the transmission spectrum. We apply our formula to the case of a MW consisting of an ``active'' molecular segment connected to two metal contacts by a pair of finite $\pi $ conjugated chains. In this calculation we show how an antiresonance can be generated near the Fermi energy of the metallic leads. The antiresonance is characterized by a drop in conductance. We find that for this calculation our analytic theory of antiresonances has predictive power.

In Sec. II, we describe the scattering and transport theory used in this work. The first subsection deals with Landauer theory. The second subsection outlines a method for evaluating the transmission probability for MW systems. The last subsection outlines our derivation of the antiresonance condition. In Sec. III, we present some calculations on BDT for different lead geometries and different binding strengths. Sec. IV describes a numerical calculation for a system displaying antiresonances which are predicted by the formula in Sec. II. Finally we conclude with some remarks in Sec. V.

Next: Transport Theory Up: Electrical Conductance of Molecular Previous: Electrical Conductance of Molecular
Eldon Emberly

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