Magnetically tunable Dirac and Weyl fermions in the Zintl materials family

Abstract

Recent classification efforts encompassing crystalline symmetries have revealed rich possibilities for solid-state systems to support a tapestry of exotic topological states. However, finding materials that realize such states remains a daunting challenge. Here, we show how the interplay of topology, symmetry, and magnetism combined with doping and external electric and magnetic field controls can be used to drive the ${\mathrm{SrIn}}_{2}{\mathrm{As}}_{2}$ materials family into a variety of topological phases. Our first-principles calculations and symmetry analysis reveal that ${\mathrm{SrIn}}_{2}{\mathrm{As}}_{2}$ is a dual topological insulator with ${Z}_{2}=(1;000)$ and mirror Chern number ${C}_{M}=\ensuremath{-}1$. Its isostructural and isovalent antiferromagnetic cousin ${\mathrm{EuIn}}_{2}{\mathrm{As}}_{2}$ is found to be an axion insulator with ${Z}_{4}=2$. The broken time-reversal symmetry via Eu doping in ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{In}}_{2}{\mathrm{As}}_{2}$ results in a higher-order or topological crystalline insulator state depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic ${\mathrm{EuIn}}_{2}{\mathrm{P}}_{2}$ is a trivial insulator with ${Z}_{4}=0$, and that it undergoes a magnetic-field-driven transition to an ideal Weyl fermion or nodal fermion state with ${Z}_{4}=1$ with applied magnetic field. Our study identifies ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Eu}}_{x}{\mathrm{In}}_{2}{(\text{As},\mathrm{P})}_{2}$ as a tunable materials platform for investigating the physics and applications of Weyl and nodal fermions in the scaffolding of crystalline and axion insulator states.