# Stable charge density wave phase in a 1T-TiSe$_2$ monolayer

## TL;DR

This study uses density functional theory to demonstrate that a monolayer of 1T-TiSe$_2$ exhibits a stable charge density wave phase with a $2\times2$ lattice distortion, similar to the bulk, with implications for understanding electron interactions.

## Contribution

First-principles analysis showing the stability of a commensurate CDW and lattice distortion in a 1T-TiSe$_2$ monolayer, aligning with experimental observations and highlighting electron-electron interactions.

## Key findings

- Monolayer 1T-TiSe$_2$ is unstable without distortion at low temperature.
- The $2\times2$ lattice distortion is the stable ground state at 0 K.
- Band structure in the CDW phase matches experimental data.

## Abstract

Charge density wave (CDW) phases are symmetry-reduced states of matter in which a periodic modulation of the electronic charge frequently leads to drastic changes of the electronic spectrum, including the emergence of energy gaps. We analyze the CDW state in a 1T-TiSe$_2$ monolayer within a density functional theory framework and show that, similarly to its bulk counterpart, the monolayer is unstable towards a commensurate $2{\times}2$ periodic lattice distortion (PLD) and CDW at low temperatures. Analysis of the electron and phonon spectrum establishes the PLD as the stable $T=0$ K configuration with a narrow bandgap, whereas the undistorted and semi-metalic state is stable only above a threshold temperature. The lattice distortions as well as the unfolded and reconstructed band structure in the CDW phase agree well with experimental results. We also address evidence in our results for the role of electron-electron interactions in the CDW instability of 1T-TiSe$_2$ monolayers.