Multiple triple-point fermions in Heusler compounds

Using the density functional theoretical calculations, we report a new set of topological semimetals X₂YZ (X  =  {Cu, Rh, Pd, Ag, Au, Hg}, Y  =  {Li, Na, Sc, Zn, Y, Zr, Hf, La, Pr, Pm, Sm, Tb, Dy, Ho, Tm} and Z  =  {Mg, Al, Zn, Ga, Y, Ag, Cd, In, Sn, Ta, Sm}), which show the existence of multiple topological triple point fermions along four independent [Formula: see text] axes. These fermionic quasiparticles have no analogues elementary particle in the standard model. The angle-resolved photoemission spectroscopy is simulated to obtain the exotic topological surface states and the characteristic Fermi arcs. The inclusion of spin-orbit coupling splits the triple-point to two Dirac points. The triple-point fermions are exhibited on the easily cleavable (1 1 1) surface and are well separated from the surface [Formula: see text] point, allowing them to be resolved in the surface spectroscopic techniques. This intermediate linearly dispersive degeneracy between Weyl and Dirac points may offer prospective candidates for quantum transport applications.