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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 
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
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
1998-10-14
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