Lorentz-violating type-II Dirac fermions in full-Heusler compounds XMg₂Ag (X = Pr, Nd, Sm)

Lorentz-violating type-II Dirac fermion, as a new type of quasiparticles beyond the high-energy physics, has received intense attention recently. However, excellent candidate materials which contain sufficiently more type-II Dirac points near the Fermi level are still in scarcity. Here, we report a family of existing full-Heusler compounds, namely XMg₂Ag (X = Pr, Nd, Sm), can serve as excellent Lorentz-violating type-II Dirac semimetals. We find they show several symmetry-protected nodal loops and triply degenerate nodal points (TDNPs) when spin–orbit coupling (SOC) is not considered. These fermions show clear nontrivial surface states. When SOC is included, the TDNPs transform into type-II Dirac points, characterized by Fermi arc surface states. The type-II DPs are protected by the C _4v symmetry in the Γ–X path. Comparing with other type-II Dirac semimetals, XMg₂Ag compounds have additional advantages including: (i) they contain as much as three pairs of type-II Dirac points; (ii) all the Dirac points locate very close to the Fermi level. These advantages make XMg₂Ag compounds are suitable for studying the novel properties of type-II Dirac fermions in future experiments. (paper)