The trend to fabricate electrical circuits on nanoscale dimensions has led to
impressive progress in the field of molecular electronics in the last decade. A
theoretical description of molecular contacts as the building blocks of future
devices is challenging though as it has to combine properties of Fermi liquids
in the leads with charge and phonon degrees of freedom on the molecule. Apart
from ab initio schemes for specific set-ups, generic models reveal
characteristics of transport processes. Particularly appealing are descriptions
based on transfer rates successfully used in other contexts such as mesoscopic
physics and intramolecular electron transfer. However, a detailed analysis of
this scheme in comparison with numerically exact data is elusive yet.
It turns out that a formulation in terms of transfer rates provides a
quantitatively accurate description even in domains of parameter space where in
a strict sense it is expected to fail, e.g. for lower temperatures. Typically,
intramolecular phonons are distributed according to a voltage driven steady
state that can only roughly be captured by a thermal distribution with an
effective elevated temperature (heating). An extension of a master equation for
the charge-phonon complex to include effectively the impact of off-diagonal
elements of the reduced density matrix provides very accurate data even for
stronger electron-phonon coupling.Comment: 10 pages, 10 figure
