Triple point semimetal 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 {\it ab-initio} calculations, we propose that the 3D honeycomb crystal NaCu$_3$Te$_2$ hosts triply degenerate nodal points (TDNPs) which are perfectly separated from the bulk states. We find a tunable phase transition between TDNPs and a weak TI triggered by a symmetry-allowed perturbation, and we further reveal the crucial role played by the spin-orbital coupling (SOC) for the emergence of the TDNPs in this system. 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.