  We present a comprehensive study of thermoelectric transport properties of a
quantum nanoelectromechanical system (NEMS) described by a
single-electron-transistor (SET) coupled to a quantum nanomechanical resonator
(NR). The effects of a quantum NR on the electronic current are investigated
with special emphasis on how the SET-NR coupling strength plays a role in such
a NEMS. We find that the SET-NR coupling is not only able to suppress or
enhance the thermoelectric current but can also switch its direction. The
effect of the NR on the thermoelectric coefficients of the SET are studied and
we find that even a small SET-NR coupling could dramatically suppress the
figure of merits ZT . Lastly, we investigate the backaction of electronic
current on the NR and possible routes of heating or cooling the NR are
discussed. We find that by appropriately tuning the gate voltage the backaction
can be eliminated, which could find possible applications to enhance the
sensitivity of detection devices.
