Sign change of the anomalous Hall effect and the anomalous Nernst effect in Weyl semimetal CeAlSi

We report the anomalous Hall effect (AHE) and the anomalous Nernst effect (ANE) data for the non-collinear Weyl semimetal CeAlSi. The anomalous Hall conductivity ({\sigma}_ij^A) was measured for two different orientations of the magnetic field (B), namely {\sigma}_yz^A for B II a and {\sigma}_xy^A for B II c, where a and c denote the crystallographic axes. We find that {\sigma}_xy^A and {\sigma}_yz^A are of opposite sign and both are large below the Curie temperature (T_C). In the paramagnetic phase, {\sigma}_xy^A raises even more and goes through a maximum at T ~ 170 K, whereas the absolute value of {\sigma}_yz^A decreases with increasing temperature. The origin of the sign difference between {\sigma}_xy^A and {\sigma}_yz^A was attributed to the reconstruction of the band structure under the variation of the spin orientation. Further, in a system where humps in the AHE are present and scalar spin chirality is zero, we show that the k-space topology plays an important role to determine the transport properties at both low and high temperatures. We also observed the anomalous contribution in the Nernst conductivity ({\alpha}_xy^A) measured for B II c. {\alpha}_xy^A/T turns out to be sizeable in the magnetic phase and above T_C slowly decreases with temperature. We were able to recreate the temperature dependences of {\sigma}_xy^A and {\alpha}_xy^A/T in the paramagnetic phase using a single band toy-model assuming a non-zero Berry curvature in the vicinity of the Weyl node. A decisive factor appears to be a small energy distance between the Fermi level and a Weyl point.