  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.
