Electronic and topological properties in heavy-element based Heusler compounds X $$_2$$ 2 RuPb (X=Sc,Y,La): first-principle method

In this paper, we study the feasibility of converting Heusler compounds X $$_2$$ 2 RuPb (X=Sc, Y, La) into three dimensional topological insulators. We perform first-principle calculations based on the full-potential linearized augmented plane wave (FP-LAPW) method within the density functional theory (DFT) using the general gradient approximation for the exchange and correlation potential (GGA-PBE). We investigate the topological insulator behavior of our compounds in the Hg $$_2$$ 2 CuTi-type Heusler structure in terms of the electronic band inversion mechanism tuned by the spin-orbit coupling and by applying a hydrostatic strain along with a uni-axial strain which inverts the band order between $$\varGamma _6$$ Γ 6 and $$\varGamma _8$$ Γ 8 bands: we realized a topological phase transition from a trivial semiconductor to nontrivial topological insulator. Then, we discuss the effects of these various strains on the topology band as well as on the real and imaginary parts of the dielectric function and related optical constants. Graphic abstract