Dirac and triple point semimetallic phases in Heusler alloys*

We predict full Heusler compounds XInPd₂ (X = Zr, Hf and Ti) to be potential candidates for type-II Dirac semimetals. The crystal symmetry of these compounds have appropriate chemical environment with a unique interplay of inversion, time reversal and mirror ymmetry. These symmetries help to give six pairs of type-II Dirac nodes on the C₄ rotation axis, closely located at/near the Fermi level. Using first principle calculations, symmetry arguments and crystal field splitting analysis, we illustrate the occurrence of such Dirac nodes in these compounds. Bulk Fermi surfaces have been studied to understand the Lorentz symmetry breaking and Lifshitz transition (LT) of Fermi surfaces. Bulk nodes are projected on the (001) and (111) surfaces which form the surface Fermi arcs, that can further be detected by photo-emission and scanning tunneling spectroscopy. By analyzing the evolution of arcs with changing chemical potential, we prove the fragile nature and the absence of topological protection of the Dirac arcs. Our predicted compounds overcome the limitations of the previously reported PtTe₂ class of compounds. Further we show breaking of inversion symmetry leads to realize triply degenerate nodal points in Heusler family.