Absence of Weyl nodes in EuCd_2As_2 revealed by the carrier density dependence of the anomalous Hall effect

The antiferromagnetic layered compound EuCd_2As_2 is widely considered as a leading candidate of ideal Weyl semimetal, featuring a single pair of Weyl nodes in its field-induced ferromagnetic (FM) state. Nevertheless, this view has recently been challenged by an optical spectroscopy study, which suggests that it is a magnetic semiconductor. In this study, we have successfully synthesized highly insulating EuCd_2As_2 crystals with carrier density reaching as low as 2× 10^15 cm^-3. The magneto-transport measurements revealed a progressive decrease of the anomalous Hall conductivity (AHC) by several orders of magnitude as the carrier density decreases. This behavior contradicts with what is expected from the intrinsic AHC generated by the Weyl points, which is independent of carrier density as the Fermi level approaches the charge neutrality point. In contrast, the scaling relationship between AHC and longitudinal conductivity aligns with the characteristics of variable range hopping insulators. Our results suggest that EuCd_2As_2 is a magnetic semiconductor rather than a topological Weyl semimetal.