A theoretical model of a single molecule coupled to many vibronic modes is presented. At low energies, transport is dominated by electron-vibron processes where transfer of an electron through the dot is accompanied by the excitation/emission of quanta (vibrons). Because the frequency of the $n$th mode is taken as an $n$th multiple of the frequency of the fundamental mode, several energetically degenerate or quasi-degenerate vibronic configurations can contribute to transport. We investigate the consequences of strong electron-vibron coupling in a fully emph{symmetric} set-up. Several striking features are predicted. In particular, a gate-asymmetry and pronounced negative differential conductance features are observed. We attribute these features to the presence of slow channels originating from the interplay of Franck-Condon suppression of transport channels and spin/orbital degeneracies.
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