LAUSR

$\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnAl}$ has been predicted to have Weyl points near the Fermi level in $L{2}_{1}$-ordered structure, which is expected to give rise to exotic transverse transport properties such as large anomalous Hall (AHE) and Nernst effects (ANE) due to large Berry curvature. In this study, the effects of Fermi level position and atomic ordering on AHE and ANE in $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnA}{\mathrm{l}}_{1\ensuremath{-}x}\mathrm{S}{\mathrm{i}}_{x}$ were studied systematically. The $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnAl}$ film keeps $B2$-disordred structure regardless of annealing temperature, which results in much smaller anomalous Hall conductivity ${\ensuremath{\sigma}}_{xy}$ and transverse Peltier coefficient ${\ensuremath{\alpha}}_{xy}$ than those calculated for $L{2}_{1}$-ordered $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnAl}$. Our newly performed calculation of ${\ensuremath{\sigma}}_{xy}$ with taking $B2$ disordering into account well reproduces the experimental result; thus it was concluded that Berry curvature originating from the Weyl points is largely reduced by $B2$ disordering. It was also revealed Al substitution with Si shifts the position of the Fermi level and greatly improves the $L{2}_{1}$ atomic ordering, leading to strong enhancement of ${\ensuremath{\alpha}}_{xy}$, which also agreed with our theoretical calculation. The highest thermopower of ANE of 5.7 \ensuremath{\mu}V/K, which is comparable to the recent reports for $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnGa}$, was observed for $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnA}{\mathrm{l}}_{0.63}\mathrm{S}{\mathrm{i}}_{0.37}$ because of dominant contribution of ${\ensuremath{\alpha}}_{xy}$. This study clearly shows the importance of both Fermi level tuning and high atomic ordering for obtaining the effect of topological features in Co-based Heusler alloys on transverse transport properties.