Phonon Instabilities and the Emergence of Charge Density Waves in VSe₂

The formation of charge density waves (CDWs) in two-dimensional (2D) materials, such as those driven by Peierls instabilities, remains a central topic in condensed matter physics. For example, in a previous study, we reported on the role of specific q-vectors in showing the phase transition pathway for the CDW structures in NbSe₂ [1]. In this work, we systematically investigate the correlation between phonon instabilities and the emergence of CDW phases in monolayer VSe₂ using first-principles calculations. Our phonon calculation of the pristine 1T phase reveals several imaginary-frequency modes at different wavevectors (q-vectors). Several known CDW structures with distinct periodicities, including the 4×1, √7×√3, and √3×4 phases, can be identified to be associated with the unstable vibrational modes at their corresponding q-vectors, thereby establishing a direct link between the lattice instabilities and the charge orders. More significantly, we have uncovered a new CDW phase, namely, the 2√7×4 phase, which is energetically more favorable than all previously reported phases of monolayer VSe₂. Our findings demonstrate that phonon-instability analysis serves as a powerful and predictive tool for identifying stable CDW ground states, offering crucial insights into the interplay between lattice and electronic degrees of freedom in 2D materials in general.