Triple Point Fermions and Topological Phase Transitions in NaCu₃Te₂

Quasiparticle excitations of free electrons in condensed-matter physics, characterized by the dimensionality of the band crossing, can find their elementary-particle analogs in high-energy physics, such as Majorana, Weyl, and Dirac fermions. While crystalline symmetry allows more quasiparticle excitations and exotic fermions to emerge. Using symmetry analysis and ab-initio calculations, we propose that the three-dimensional honeycomb crystal NaCu₃Te₂ hosts triply degenerate nodal points (TDNPs) residing at the Fermi level. Furthermore, in this system we find a tunable phase transition between a trivial insulator, a TDNP phase and a weak topological insulator (TI) triggered by a symmetry-allowed perturbation and the spin-orbital coupling (SOC). Such topological non-trivial ternary compound not only serves as a perfect candidate for studying three-component fermions, but also provides a beautiful playground for understanding the topological phase transitions between TDNPs, TIs and trivial insulators, which distinguishes this system from other TDNP candidates.