Weyl semimetal in the rare-earth hexaboride family supporting a pseudonodal surface and a giant anomalous Hall effect

Rare-earth hexaborides offer a rich tapestry for exploring the interplay of topological orders, magnetism, and electron-correlation effects associated with protected quantum phenomena. Here, using first-principles modeling, we identify in cerium hexaboride ($\mathrm{Ce}{\mathrm{B}}_{6}$) a topological state that harbors a pseudonodal surface (PNS) along with double-Weyl fermions. An analysis of the electronic states in the vicinity of the Fermi level reveals the presence of ${M}_{z}$-mirror-symmetry-protected band crossings that involve itinerant ($d$) and localized ($f$) states of Ce. These band crossings are found to remain nearly gapless as one goes away from the mirror plane, driving the formation of PNS states. We also demonstrate the presence of coexisting double-Weyl fermions with chiral charges of $\ifmmode\pm\else\textpm\fi{}2$ on the ${C}_{4z}$ rotational axis. By analyzing the Berry curvature field associated with the topological states, we predict that $\mathrm{Ce}{\mathrm{B}}_{6}$ supports a giant anomalous Hall conductivity of $\ensuremath{-}1840 {\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}{\text{cm}}^{\ensuremath{-}1}$ in the slightly electron-doped regime, which would be larger than the values reported to date in magnetic Weyl semimetals. Our study thus indicates that $\mathrm{Ce}{\mathrm{B}}_{6}$, which combines ferromagnetic order with topological physics in a heavy-fermion matrix, would provide a promising playground for investigating topological magnetic states with giant anomalous Hall responses.