Type-II Dirac semimetals in the YPd$_2$Sn class

Abstract: The Lorentz-invariance-violating Weyl and Dirac fermions have recently attracted intensive interests as new types of particles beyond high-energy physics, and they demonstrate novel physical phenomena such as angle-dependent chiral anomaly and topological Lifshitz transition. Here we predict the existence of Lorentz-invariance-violating Dirac fermions in the YPd$_2$Sn class of Heusler alloys that emerge at the boundary between the electron-like and hole-like pockets in the Brillouin zone, based on the first-principles electronic structure calculations. In combination with the fact that this class of materials was all reported to be superconductors, the YPd$_2$Sn class provides an appropriate platform for studying exotic physical properties distinguished from conventional Dirac fermions, especially for realizing possible topological superconductivity.