|
We have presented a theoretical study of the electrical
conductance properties of molecular wires in the context of
one-electron theory. A numerical method has been developed for
the study of transport in molecular wires which solves for the
transmission coefficients using Schroedinger's equation. It
allows for the study of multimode leads attached to a molecule.
We then proceeded to present a simple analytically solvable
model which highlighted the interesting phenomena of
antiresonances. A formula was derived that predicts Fermi
energies for which a molecule with a given set of molecular
energy levels should display antiresonances. It predicts two
mechanisms by which antiresonances arise: one due to
interference between the molecular orbitals and the other due
to a cancellation of the effective hopping parameter.
As an application of our numerical method studied the
conductance of BDT. We examined the role of coupling by
considering both the strong and weak regimes. For strong
coupling it was found that the MW has regions of strong
transmission. These regions occur at energies which differ
from the isolated molecule's energy levels because of state
hybridization with the surface states of the gold tips. The
conductance found for the strong coupling case was orders of
magnitude greater than that found experimentally, although
qualitatively it shared common features. In the weak coupling
study the transmission displayed resonances at energies
corresponding to those of the isolated molecule. The magnitude
was also significantly down. This resulted in a conductance
curve that was of the magnitude found in the experiment.
Future work will need to focus on the electrostatic problem of
the molecule within an applied electric field and the
consequences of this in the context of Landauer theory,
many-electron and possible polaronic effects within the MW.
Using our analytic formula for antiresonances, we were able to
predict the occurrence of an antiresonance within a more
sophisticated numerical study utilizing a molecule attached
bridging a metal wire break junction. The model should also be
of interest for future MW work since it introduces the idea of
``filter'' molecules. Our numerical studies showed that  conjugated chain molecules act as effective mode filters to
electrons incident from the metallic leads. The filter chains
in our model reduced the number of propagating modes down to
one, which was then coupled to the ``active'' molecule. Our
formula was derived on the assumption of only a single
propagating mode, and for the ``active'' molecule considered it
was able to successfully predict the energy at which the
antiresonance occurred. The antiresonance was charaterized by
a drop in the differential conductance.
Next: Bibliography
Up: Electrical Conductance of Molecular
Previous: Antiresonance Calculations
Eldon Emberly
1998-10-14
|