  The demand for green energy increases day by day due to environmental concern
and thermoelectric (TE) materials are one of the eco-friendly energy resources.
Few authors reported high TE performance in TmCu$_3$Ch$_4$, reaching the figure
of merit (ZT) above 2 at 1000K, from first-principles calculations neglecting
electron-phonon scattering, spin-orbit coupling effect (SOC), and
energy-dependent carrier lifetime. Here, thermoelectric transport properties of
TmCu$_3$Ch$_4$ are reinvestigated through considering these parameters, and
significant discrepancies are found. The ZT of p-type TaCu$_3$Te$_4$ can reach
~3 at 1000K among these compounds due to its low lattice thermal conductivity
($\kappa_l$) (0.38 W m-1 K-1). Interestingly, the value of $\kappa_l$ is
reduced to 0.17 W m-1 K-1 through 1 GPa pressure while the power factor is
slightly improved due to bandgap reduction, leading to an extraordinary ZT~5.5
at 1000K. Although the substitution of Se causes a slight reduction of
$\kappa_l$ to ~0.3 W m-1 K-1, the power factor is reduced significantly due to
the dramatic reduction of DOS near Fermi level, which leads to lower the
Seebeck coefficient largely and increase electrical conductivity slightly.
