  To understand the unexpectedly high thermoelectric performance observed in
the thin-film Heusler alloy Fe$_2$V$_{0.8}$W$_{0.2}$Al, we study the magnon
drag effect, generated by the tungsten based impurity band, as a possible
source of this enhancement, in analogy to the phonon drag observed in FeSb$_2$.
Assuming that the thin-film Heusler alloy has a conduction band integrating
with the impurity band, originated by the tungsten substitution, we derive the
electrical conductivity $L_{11}$ based on the self-consistent t-matrix
approximation and the thermoelectric conductivity $L_{12}$ due to magnon drag,
based on the linear response theory, and estimate the temperature dependent
electrical resistivity, Seebeck coefficient and power factor. Finally, we
compare the theoretical results with the experimental results of the thin-film
Heusler alloy to show that the origin of the exceptional thermoelectric
properties is likely to be due to the magnon drag related with the
tungsten-based impurity band.
