Eightfold Fermionic Excitation in a Charge Density Wave Compound

The 230 space group symmetries of three-dimensional crystal lattices permit the existence of quasiparticle excitations beyond the standard model of high-energy physics. Here, the authors propose that the TaTe${}_{4}$ crystal, with a quasi-one-dimensional lattice structure, holds an eightfold degenerate double Dirac point and a fourfold degenerate Dirac point in the charge density wave (CDW) ground state. The calculated band structure is consistent with Shubnikov--de Haas oscillation measurements. Further, an atomic step edge state is detected, suggesting nontrivial topology. This work reveals the CDW-induced topological phases and provides new insight into the interplay between the CDW and fermionic excitations.