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

TL;DR

This paper develops a topological framework for understanding how different charge density wave (CDW) structures in monolayer 1T-TiSe2 influence its electronic topology and potential phase transitions, using symmetry analysis and DFT models.

Contribution

It introduces a symmetry-based method to analyze the effects of various CDW types on electronic topology in monolayer TiSe2, revealing how band inversion and topological phases depend on CDW symmetry.

Findings

Different CDW types induce distinct band inversions.

Symmetry analysis clarifies the topological nature of CDW phases.

The study enhances understanding of topology in CDW systems with parity considerations.

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.