  We discuss the thermoelectric properties assisted by the Fano effect of a
parallel double quantum dot (QD) structure. By adjusting the couplings between
the QDs and leads, we facilitate the nonresonant and resonant channels for the
Fano interference. It is found that at low temperature, Fano lineshapes appear
in the electronic and thermal conductance spectra, which can also be reversed
by an applied local magnetic flux with its phase factor $\phi=\pi$. And, the
Fano effect contributes decisively to the enhancement of thermoelectric
efficiency. However, at the same temperature, the thermoelectric effect in the
case of $\phi=\pi$ is much more apparent, compared with the case of zero
magnetic flux. By the concept of Feynman path, we analyze the difference
between the quantum interferences in the cases of $\phi=0$ and $\phi=\pi$. It
is seen that in the absence of magnetic flux the Fano interference originates
from the quantum interference among infinite-order Feynman paths, but it occurs
only between two lowest-order Feynman paths when $\phi=\pi$. The increase of
temperature inevitably destroys the electron coherent transmission in each
paths. So, in the case of zero magnetic field, the thermoelectric effect
contributed by the Fano interference is easy to weaken by a little increase of
temperature.
