Ab initio overestimation of the topological region in Eu-based compounds.

An overestimation of the fundamental band gap values by the density functional theory within the local density approximation and associated approaches is a well-known challenge of ab initio electronic structure computations. Motivated by recent optical experiments, we have revisited first-principle results obtained earlier for $EuCd_2As_2$ and extended the computations to the whole class of systems $EuCd_2X_2i$ (X = P, As, Sb, Bi), to $EuIn_2X_2$ (X = P, As, Sb) and to the Eu-free $AEIn_2As_2$ (AE = Ca, Sr, Ba) employing a hybrid functional method. We find that our approach provides the magnitude of the energy gap for $EuCd_2As_2$ in agreement with the experimental value. Actually, our results indicate that $EuCd_2Bi_2$ and $BaIn_2As_2$ are robust topological insulators, while all other compounds are topologically trivial semiconductors. The Eu-based systems are AFM semiconductors with a strong red shift of the energy gap in a magnetic field caused by the exchange coupling of the band states to spins localized on the 4$f$-shell of Eu ions. Additionally, the $EuIn_2X_2$ (X = P, As) compounds show altermagnetism.