Unique topological surface states of full-Heusler topological crystalline insulators

Our theoretical analysis reveals that a family of full-Heusler materials exhibit unique topological surface states with type-I and type-II Dirac quasiparticles. The type-I Dirac surface state is characterized by an enclosed Fermi surface, while the type-II Dirac surfaces occur at the touching of the electron and hole pockets. In addition, due to the layered nature of the full-Heusler crystals structured with a wide range of various elements, such structures induce multiple Dirac surface states with different Lifshitz transitions protected by more than one mirror plane.