  We consider electron transport through a mobile island (i.e., a
nanomechanical oscillator) which can accommodate one or two excess electrons
and show that, in contrast to immobile islands, the Coulomb blockade peaks,
associated with the first and second electrons entering the island, have
different functional dependences on the nano-oscillator parameters when the
island coupling to its leads is asymmetric. In particular, the conductance for
the second electron (i.e., when the island is already charged) is greatly
enhanced in comparison to the conductance of the first electron in the presence
of an external electric field. We also analyze the temperature dependence of
the two conduction peaks and show that these exhibit different functional
behaviors.
