charge density wave*

Monolayer 1T-TiSe₂ has been found to have charge density wave (CDW) experimentally. The primary CDW order parameter takes the M₁^- symmetry having odd parity and will change parity of electronic states of the system. Due to the coexistence of three q vectors from the primary order parameter, a secondary order parameter of even parity is induced inevitably. The mixture of the two opposite-parity order parameters will break inversion symmetry, which fails connection between symmetry and topology. Here we propose a method to decouple the parity-odd and parity- even CDW gaps, so that we can perform continuously the inversion-asymmetric CDW state into an inversion-symmetric one. In this way it helps to understand topological phase transitions in inversion asymmetric systems from the inversion-symmetry point of view.