Misc,
A Generalized Landauer Approach for Electron Transport in a Single Molecule
(2014)cite arxiv:1408.1066Comment: 31 pages, 5 figures.
Abstract
We present a quaternion-inspired formalism specifically developed to evaluate
the electric current that traverses a single molecule subjected to an
externally applied voltage. The molecule of interest is covalently connected to
two small metallic clusters, forming an extended molecule complex. The
quaternion approach allows for an integrated treatment of the charge transport
in single molecules where both ballistic and co-tunneling (coherent) mechanisms
are taken on equal footing, although only in the latter case the presence of
eventual transient charged states of the system needs to be considered. We use
a Dyson series to obtain a generalized Fermi golden rule, from which we derive
an expression for the net current the two electrodes: in doing this, we take
into account all possible transitions between electronic states localized at
the electrodes and levels in the extended molecule complex. In fact, one can
apply the method to the entire range of coupling regimes, not only in the weak
or strong cases, but also in intermediate situations, where ballistic and
co-tunneling processes compete with each other. We also discuss initial results
of the application of this formalism to the description of the electronic
transport in two small organic molecules representative of two different limit
situations. In the first case, a conjugated molecule (where spatially
delocalized molecular orbitals favor ballistic contributions) is considered,
and in the second, the current traverses a saturated hydrocarbon (whose
structure should contain more localized molecular orbitals). In both cases, we
fully describe the field-induced self-adjustment of the electronic levels of
the extended molecule complex at an ab initio quantum chemical level, using
density functional theory.
