Topological signatures of triply degenerate fermions in Heusler alloys: an ab initio study

Abstract Triply degenerate nodal point (TP) fermions, lacking elementary particle counterparts, have been theoretically anticipated as quasiparticle excitations near specific band crossing points constrained by distinct space-group symmetries instead of Lorentz invariance. Here, based on first-principles calculations and symmetry analysis, we demonstrate the presence of TP fermions in Heusler alloys. Furthermore, we predict that these Heusler alloys are dynamically stable, exhibiting TP fermions along four distinct C 3 axes in the F-43m space group. We show that α -LiCaPdSb harbours peculiar Fermi arcs and surface states on the (111) and (001) crystal facets, owing to the coexistence of threefold rotational and time reversal symmetry. More interestingly, a modest tensile strain can increase the distance of fermions along the Γ- L high symmetric line by as much as 21.10%, which give rise to measurable Fermi arcs. Furthermore, we investigate non-trivial topological insulator phase in β -LiCaPdSb, by changing the chemical environment through placing transition metal atoms at various Wyckoff positions. The β -LiCaPdSb harbour a semi-metallic nature, and by breaking cubic symmetry, it undergoes a transition from semi-metal to a non-trivial topological insulator. In addition, for the first time, rare-earth LaPtBi half-Heusler alloy is examined under strain to uncover multiple band inversions associated with the TP fermionic phase. The observed multiple band inversion is entirely unaffected by spin–orbit coupling. We show that the LaPtBi compound hosts TP fermions, which are linked to a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> topological invariant. Remarkably, with clear band crossings and multiple band inversion, we point out the possibilities of the LaPtBi for displaying a rich topological phase diagram. Our work provides a prototype material platform for experimental detection through angle-resolved photoemission spectroscopy or scanning tunnelling spectroscopy and practical spintronic applications.