Origin of the chiral charge density wave in transition-metal dichalcogenide

Chirality refers to a structure that lacks mirror symmetry. It can be observed in a wide range of platforms, from subatomic particles and molecules to living organisms. However, the underlying mechanisms that give rise to chirality in condensed matter systems have been a subject of considerable interest. Here we elucidate the mechanism of chiral charge density wave formation in the transition-metal dichalcogenide 1T-TiSe₂. Based on symmetry analysis, we demonstrate that charge density modulations and ionic displacements follow distinct irreducible representations of the space group, despite exhibiting similar wave vectors and a strong coupling. This charge-lattice symmetry frustration induces lattice distortions that further break all symmetries that are not common to both sectors. This ultimately gives rise to chirality. Our theory is verified using Raman spectroscopy and inelastic X-ray scattering.