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

Abstract: 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.