Chiral charge density waves in transition metal dichalcogenide

The emergence of chirality in the charge density wave (CDW) phase of 1$T$-TiSe$_2$ has recently attracted significant attention, yet its microscopic origin remains debated. The prevailing interpretation attributes chirality to a relative phase shift between the charge density components. Here, using density functional theory and symmetry analysis, it is demonstrated that such phase-shifted states entail prohibitive energy costs, rendering them unlikely candidates for the ground state. Instead, a nearly degenerate metastable CDW phase stacking order with monoclinic symmetry is identified, that naturally breaks mirror and inversion symmetries. The CDW in 1$T$-TiSe$_2$ possesses a dual physical nature: the electronic charge redistribution is intrinsically bond-modulated, while the periodic lattice distortion is atom-centered transverse. This spatial separation allows a specific optical coupling mechanism where circularly polarized light breaks the energetic degeneracy between chiral domains. These results reconcile conflicting experimental observations, identifying the "spontaneous" chirality observed in local probes as a statistical distribution of CDW phase stacking domains, while establishing the mechanism for macroscopic, light-induced gyrotropic order.