Despite its mathematical complexity, the nonequilibrium
Green's function method has gained a
great popularity in recent years in the computation
of transport across molecular junctions, mostly
because of the elegant way in which, at least in
principle, electron-phonon and electron-electron interactions
can be treated in a unied and systematic
way [1], [2], [3].
In most cases the system Hamiltonian is described
within a single particle DFT approach.
The advantage is the possibility to include several
hundreds of atoms which are normally necessary in
order to describe both contacts and molecule. The
main problem of DFT is related to the description of
the unkown exchange-correlation potential, usually
approximated as that of a free electron gas. This
tends to overestimate the metallic characteristics of
the molecular states, producing among the others,
an underestimation of the HOMO-LUMO gap, with
relevant consequences to transport.
Therefore a batter correlation potential is a central
issue in order to achieve not only quantitative
predictions of tunneling currents, but also correct
qualitative trends. In order to improve this aspect
many groups have tried to improve the DFT formalisms
either using hybrid functionals, or including
correlated transport [4], [5] and self-interaction
corrections [6].
In this paper we present a different approach
based on the GW approximation technique, related
to Green's function theory [7], [8]. The system
Hamiltonian is obtained within the spirit of a DFTbased
tight-binding approach called DFTB [9]. The
implementation of the GW method over DFTB in
the plasmon-pole approximation is a fast and flexible
scheme [10]. This scheme is quite accurate in
predicting correction to HOMO and LUMO states,
in good agreement with the experimental workfunction
and affinities. Unfortunately the quasiparticle
energies degrade for energy levels of the molecule
far from the gap. This is due to the approximations
of our GW implementation and the use of
a minimal basis set. However this lack of accuracy
becomes problematic in transport calculations.
Numerical artifacts have been observed, producing
large broadering of the energy levels tailing in the
energy gap considerably enlarging the transmission.
We expect however the off-resonant transmission to
be dominated by the position and broadening of the
HOMO and the LUMO energies only, with little
effect of the other levels. For these reasons we have
worked around the problem by using the GW correction
as a first step for the energy gap correction
and implemented a simple scissor operator which
rigidly shifts the valence and conduction set of
molecular orbitals according to the GW prediction.
This scheme was applied to calculations of various
polymeric chains. Here we show results relative to
poly-phenylene molecules represented in Figure 1.
Figure 2 shows the complex band structure calculated
for an infinite poly-phenylene chain. The
imaginary part of the complex bandstructure represents
the tunneling decay for vanishing states and
is related to off-resonant tunneling. The plot shows
the difference between the full GW renormalization
in comparison to the shissor operator.
Figure 3 shows the coherent tunneling across
phenylene chains of varying lengths. The figure
shows a significant increase of the HOMO-LUMO
gap with a consequent decrease of tunneling probability
at the Fermi level of the Cu-Molecule-Cu
system used in our calculations.
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Despite its mathematical complexity, the nonequilibrium
Green's function method has gained a
great popularity in recent years in the computation
of transport across molecular junctions, mostly
because of the elegant way in which, at least in
principle, electron-phonon and electron-electron interactions
can be treated in a unied and systematic
way [1], [2], [3].
In most cases the system Hamiltonian is described
within a single particle DFT approach.
The advantage is the possibility to i...
»