Weyl nodes in the bandstructure of bcc iron

Weyl points in 3D bandstructures are receiving increasing attention in connection with topological states of matter. In addition, a controversial suggestion has recently appeared\footnote{Y. Chen \textit{et al.}, Phys. Rev. B \textbf{88}, 125110 (2013).} to the effect that isolated touching points between fully occupied and partially occupied bands, which act as monopole sources of Berry curvature, give a non-quantized, non-Fermi-surface contribution to the intrinsic anomalous Hall conductivity of ferromagnets. With these motivations, we carry out a systematic search for Weyl nodes in the bandstructure of bcc Fe using first-principles calculations. We trace the evolution of the Chern index of the fully occupied 2D bands in the $(k_x,k_y)$ plane as a function of $k_z$, and find several touching events taking place at high-symmetry points and lines in the 2D BZ. The amount of Chern-number transfer is analyzed in terms of the symmetry labels of the crossing bands.\footnote{C. Fang \textit{et al.}, Phys. Rev. Lett. \textbf{108}, 266802 (2012).} In addition to conical intersections with a topological charge $q=1$, we find quadratic touching points with $q=2$ that are protected by $C_4^z$ symmetry, as well as lines of degeneracy carrying a net topological charge.