Revealing the Charge Density Wave caused by Peierls instability in two-dimensional NbSe$_{2}$

The formation of a charge density wave (CDW) in two-dimensional (2D) materials caused by Peierls instability is a controversial topic. This study investigates the extensively debated role of Fermi surface nesting in causing the CDW state in 2H-NbSe$_{2}$ materials. Four NbSe$_{2}$ structures (i.e., normal, stripe, filled, and hollow structures) are identified on the basis of the characteristics in scanning tunneling microscopy images and first-principles simulations. The calculations reveal that the filled phase corresponds to Peierls' description; that is, it exhibits fully opened gaps at the CDW Brillouin zone boundary, resulting in a drop at the Fermi level in the density of states and the scanning tunneling spectroscopy spectra. The electronic susceptibility and phonon instability in the normal phase indicate that the Fermi surface nesting is triggered by two nesting vectors, whereas the involvement of only one nesting vector leads to the stripe phase. This comprehensive study demonstrates that the filled phase of NbSe$_{2}$ can be categorized as a Peierls-instability-induced CDW in 2D systems.