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Dirac, triple-point and Weyl fermions represent three topological semimetalphases, characterized with a descending degree of band degeneracy, which havebeen realized separately in specific crystalline materials with differentlattice symmetries. Here we demonstrate an alloy engineering approach torealize all three types of fermions in one single material system ofMgTa$_{2-x}$Nb$_x$N$_3$. Based on symmetry analysis and first-principlescalculations, we map out a phase diagram of topological order in the parameterspace of alloy concentration and crystalline symmetry, where the intrinsicMgTa$_2$N$_3$ with the highest symmetry hosts the Dirac semimetal phase whichtransforms into the triple-point and then the Weyl semimetal phase with theincreasing Nb concentration that lowers the crystalline symmetries. Therefore,alloy engineering affords a unique approach for experimental investigation oftopological transitions of semimetallic phases manifesting different fermionicbehaviors.

Alloy engineering of topological semimetal phase transition in MgTa$_{2-x}$Nb$_x$N$_3$