  Recent progress in the field of molecular electronics has revealed the
fundamental importance of the coupling between the electronic degrees of
freedom and specific vibrational modes. Considering the examples of a molecular
dimer and a carbon nanotube double quantum dot, we here theoretically
investigate transport through a two-site system that is strongly coupled to a
single vibrational mode. Using a quantum master equation approach, we
demonstrate that, depending on the relative positions of the two dots,
electron-phonon interactions can lead to negative differential conductance and
suppression of the current through the system. We also discuss the experimental
relevance of the presented results and possible implementations of the studied
system.
