Fig. 1: Crystal and calculated electronic structure of ScV₆Sn₆.

a Crystal structure without CDW. The top-view corresponds to a 2 × 2 cell. b Brillouin Zone with high-symmetry points and directions. c Crystal structure in the CDW phase with the out-of-plane distortions indicated by the arrows. The length of the arrow is proportional to the displacement. d Electronic structure of ScV₆Sn₆ without (red lines) and with CDW (green color) along the high symmetry directions. For visual clarity, the pristine bands have been translated in energy by +0.029 eV. In this way the van-Hove singularities and the \({d}_{{z}^{2}}\) flat band of the CDW and pristine systems are aligned. It is indeed expected that a structural distortion leads to a tuning in the electronic band structure, especially around E_F⁷⁶. A similar but disentangled figure can be found in Supplementary Fig. 9. The main changes are here indicated: at \(\bar{{{\Gamma }}}\) (red box, label '1') the CDW induces an increment in the bands separation. Along both \(\bar{{{\Gamma }}}\)-\(\bar{K}\) and \(\bar{{{\Gamma }}}\)-\(\bar{M}\) the bands appear to have slightly different k-loci (blue arrow and label '2'). The main changes are observed along the A-H and A-L directions (yellow arrows and label '3') and are characterized by a marked Sn p_z-states.