Density Functional Theory Study of CDW Structure in TiSe₂

1T-TiSe₂ is a well-studied TMDC (Transition Metal Dichalcogenide) material known for exhibiting a CDW (Charge Density Wave) at 165K. Despite extensive research, it is not clear whether this material is a semimetal or a semiconductor. Additionally, a second CDW transition at 165K has been identified. Here, we perform first-principles electronic structure calculations to investigate potential CDW patterns in 1T-TiSe₂ and their impact on electronic structures. When considering a 2x2x1 supercell, only a single type of CDW pattern is observed, as reported in previous theoretical studies. However, in the case of a 2x2x2 supercell, we found four different types of CDW orders, which are almost degenerate in energy. Furthermore, we utilized the band unfolding technique to compare the band structures of the four CDW phases with angle-resolved photoemission data and discussed the effects of spin-orbit coupling on the band structures. Additionally, we computed lattice-induced free energies to determine the presence of potential thermal phase transitions.