Origins of the anomalous Hall conductivity in the symmetry enforced Fe3GeTe2 nodal-line ferromagnet

Abstract: Fe$_3$GeTe$_2$ has gained attention in the condensed matter community for its potential to be exfoliated into thin films with ferromagnetic (FM) order, thanks to its van der Waals layered structure and significant intrinsic anomalous Hall conductivity (AHC). In this work, we analyze the electronic structure and show that, contrary to prior claims, the bulk of the AHC cannot arise from gapped nodal lines. By studying the material's symmetry properties, both with and without spin-orbit coupling (SOC) and across paramagnetic and FM phases, we find that Fe$_3$GeTe$_2$ hosts mirror-symmetry-protected nodal lines, which support surface drumhead states. Additionally, we identify three key sources of AHC: nodal lines in the paramagnetic phase gapped by the FM order, Weyl points within specific energy ranges, and gaps between spin-up and spin-down bands caused by SOC. Finally, our calculations suggest that electron doping could increase the AHC up to four times compared to its value at the computed Fermi level.