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First-principles study of the low-temperature charge density wave phase in the quasi-one-dimensional Weyl chiral compound (TaSe$_4$)$_2$I

Using {\it ab initio} density functional theory, we study the lattice phase transition of quasi-one-dimensional (TaSe$_4$)$_2$I. In the undistorted state, the strongly anisotropic semimetal band structure presents two non-equivalent Weyl points. In previous efforts, two possible Ta-tetramerization patterns were proposed to be associated with the low-temperature structure. Our phonon calculations indicate that the orthorhombic $F222$ CDW-I phase is the most likely ground state for this quasi-one-dimensional system. In addition, the monoclinic $C2$ CDW-II phase may also be stable according to the phonon dispersion spectrum. Since these two phases have very similar energies in our DFT calculations, both these Ta-tetramerization distortions likely compete or coexist at low temperatures. The semimetal to insulator transition is induced by a Fermi-surface-driven instability that supports the Peierls scenario, which affects the Weyl physics developed above $T_{\rm CDW}$. Furthermore, the spin-orbit coupling generates Rashba-like band splittings in the insulating CDW phases.