Topological theory of inversion-breaking charge-density-wave monolayer 1\textit{T}-TiSe${}_2$

Abstract

A charge density wave (CDW) of a nonzero ordering vector $\mathbf{q}$ couple electronic states at $\mathbf{k}$ and $\mathbf{k}+\mathbf{q}$ statically, giving rise to a reduced Brillouin zone (RBZ) due to the band folding effect. Its structure, in terms of an irreducible representation of the little group of $\mathbf{q}$, would change the symmetry of the system and electronic structure accompanying possible change of band inversion, offering a chance of the topological phase transition. Monolayer 1\textit{T}-TiSe${}_2$ is investigated for it shows an unconventional CDW phase having a triple-$q$ $M_1^{-}$ structure. Moreover, the coupling between the triple-$q$ component of the $M_1^{-}$ CDW will inevitably produce a small $M_1^{+}$ CDW. The CDW yields a band inversion in 1\textit{T}-TiSe${}_2$ but different types of CDW can affect the electronic structure and system topology differently. The impact of CDW of different types was studied by utilizing a symmetrization-antisymmetrization technique to extract the $M_1^{-}$ and $M_1^{+}$ CDW contributions in the DFT-based tight-binding model and study their effects. The results are consistent with the parity consideration, improving understanding of topology for a CDW system with and without parity.

arXiv comment8 pages, 6 figures. Accepted by New. J. Phys

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