Fig. 5: Electronic structure of monolayer 1T-VS₂ from DFT.

Data for the undistorted structure and the \(7\times \sqrt{3}{{{{{{{\rm{R}}}}}}}}3{0}^{\circ }\) CDW is shown in black and blue, respectively. The CDW data has been unfolded to the Brillouin zone of the undistorted structure. Here, the linewidth/saturation corresponds to the overlap of CDW and undistorted wave functions for the same k point. Analogous results for 1T-VSe₂ and the \(9\times \sqrt{3}{{{{{{{\rm{R}}}}}}}}3{0}^{\circ }\) CDW are shown in Supplementary Fig. 3. a Electronic band structure and density of states (DOS) for 0 %, 1/3, 2/3, and 100 % of the displacements of the relaxed CDW structure. Please note that since the CDW breaks the C₃ symmetry, the chosen path, indicated in b, does not represent the full Brillouin zone. The bands along an extended path are shown in Supplementary Fig. 9. b, c Lifshitz transition. The Fermi surface is shown for displacements toward the relaxed CDW structure (b) and its projection onto unstable transverse-acoustic (TA) phonon modes (c). The Supplementary Movies 1 and 2 show animations of the transitions in b and c, respectively (including bands, DOS, and structures).