Prediction of Ideal Topological Semimetals with Triply Degenerate Points in NaCu$_3$Te$_2$ Family

Triply degenerate points (TDPs) in band structure of a crystal can generate novel TDP fermions without high-energy counterparts. Although identifying ideal TDP semimetals, which host clean TDP fermions around the Fermi level ($E_F$) without coexisting of other quasiparticles, is critical to explore the intrinsic properties of this new fermion, it is still a big challenge and has not been achieved up to now. Here, we disclose an effective approach to search for ideal TDP semimetals via selective band crossing between antibonding $s$ and bonding $p$ orbitals along a line in the momentum space with $C_{3v}$ symmetry. Applying this approach, we have successfully identified the NaCu$_3$Te$_2$ family of compounds to be ideal TDP semimetals, where two and only two pairs of TDPs are located around the $E_F$. Moreover, we reveal an interesting mechanism to modulate energy splitting between a pair of TDPs, and illustrate the intrinsic features of TDP Fermi arcs in these ideal TDP semimetals.