Topological theory of inversion-breaking charge-density-wave monolayer 1T-TiSe2

Abstract

A charge density wave (CDW) of a nonzero ordering vector q couple electronic states at k and k + q statically, giving rise to a reduced Brillouin zone due to the band folding effect. Its structure, referred to an irreducible representation of the little group of 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 1T-TiSe2 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 produces a small {M}{1}{+} CDW. The CDW yields a band inversion in 1T-TiSe2 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 density functional theory-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.