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

Using ab initio density functional theory, we study the lattice phase transition of quasi-one-dimensional $({\mathrm{TaSe}}_4{)}_2\mathrm{I}$. In the undistorted state, the strongly anisotropic semimetal band structure presents two nonequivalent 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 density functional theory 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 $T_{\mathrm{CDW}}$. Furthermore, the spin-orbit coupling generates Rashba-like band splittings in the insulating charge density wave phases.

Figure 1

Schematic crystal structure of the conventional cell of $({\mathrm{TaSe}}_4{)}_2\mathrm{I}$ with the following conventions: blue, Ta; green, Se; purple, I. (a, b) The crystal structure is shown from the perspectives of the $bc$ plane [(100) direction] (a) and the top [(001) direction] (b). (c, d) The two different Ta-tetramerization patterns along the chains.

Figure 2

Band structure of the undistorted $({\mathrm{TaSe}}_4{)}_2\mathrm{I}$ along a high-symmetry path. (a) Without SOC. (b) With SOC.

Figure 3

Phonon spectrum of $({\mathrm{TaSe}}_4{)}_2\mathrm{I}$ for the undistorted (No. 97), CDW-I (No. 22), and CDW-II (No. 5) phases. Here, a $2\times 2\times 2$ supercell was selected from the original primitive cell in our calculations. The coordinates of the high-symmetry points in the bulk Brillouin zone are obtained using the Seek-path software [46].

Figure 4

(a) Schematic of the DOS semimetal-to-insulator transition. (b–d) DOS (without SOC) near the Fermi level for the undistorted parent (non-CDW), orthorhombic (CDW-I), and monoclinic (CDW-II) phases, respectively. Black, total; red, Ta; blue, I; green, Se.

Figure 5

(a) The energy well of the CDW-I and undistorted phases corresponding to the ${\mathrm{\Gamma }}_4$ mode vs distortion. (b) The energy wells of the CDW-I and CDW-II phases.

Figure 6

Band structure of $({\mathrm{TaSe}}_4{)}_2\mathrm{I}$ with the effect of SOC shown along high-symmetry paths. The coordinates of the high-symmetry points in the bulk Brillouin zone are obtained from the Seek-path software [46]. (a, c) For the orthorhombic $F222$ CWD-I phase. (b, d) For the monoclinic $C2$ CDW-II phase.