Computational search for Dirac and Weyl nodes in f-electon antiperovskites

We present the result of an \textit{ab initio} search for new Dirac materials among inverse perovskites. Our investigation is focused on the less studied class of lanthanide antiperovskites containing heavy $f$-electron elements in the cation position. Some of the studied compounds have not yet been synthesized experimentally. Our computational approach is based on density functional theory calculations which account for spin-orbit interaction and strong correlations of the $f$-electron atoms. We find several promising candidates among lanthanide antiperovskites which host bulk Dirac states close to the Fermi level. Specifically, our calculations reveal massive three-dimensional Dirac states in materials of the class A$_3$BO, where A=Sm, Eu, Gd, Yb and B=Sn, Pb. In materials with finite magnetic moment, such as Eu$_3$BO (B=Sn, Pb), the degeneracy of the Dirac nodes is lifted, leading to appearance of Weyl nodes.