Complex charge density waves in simple electronic systems of two-dimensional III₂–VI₃ materials

Charge density wave (CDW) is the phenomenon of a material that undergoes a spontaneous lattice distortion and modulation of the electron density. Typically, the formation of CDW is attributed to Fermi surface nesting or electron-phonon coupling, where the CDW vector (Q_CDW) corresponds to localized extreme points of electronic susceptibility or imaginary phonon frequencies. Here, we propose a new family of multiple CDW orders, including chiral Star-of-David configuration in nine 2D III₂–VI₃ van der Waals materials, backed by first-principles calculations. The distinct feature of this system is the presence of large and flat imaginary frequencies in the optical phonon branch across the Brillouin zone, which facilitates the formation of the diverse CDW phases. The electronic structures of 2D III₂–VI₃ materials are relatively simple, with only III-s,p and VI-p orbitals contributing to the formation of the CDW order. Despite that, the CDW transitions involve both metal-to-insulator and insulator-to-insulator transitions, accompanied by a significant increase in the bandgap caused by an enhanced electronic localization. Our study not only reveals a new dimension in the family of 2D CDWs, but is also expected to offer deeper insights into the origins of the CDWs.