Fig. 4: Phonon eigenmodes and microscopic mechanism of electronic band modulation.

a Illustration of the Ru and O atoms, bond lengths between oxygens and the bond angle of O-Ru-O. b The illustrations of the eigen mode of B₂^P, and c that of B₂^M. d The averaged ratio of RuO₆ octahedra cage apical Ru-O bond length (\({d}_{\perp }\)) over in-plane bond length (\({d}_{\parallel }\)) modulated by two phonons. e Averaged in-plane bond angle (\(\theta\)) modulated by the two phonons.  (see Supplementary Figs. 15 for phonon modulated bond length and angles in two types of RuO₆) f The density of states plots of the AFM-b ground state (middle) and the modulated AFM-b state by B₂^M (top) and B₂^P (bottom). g Correlation between octahedra distortion (\({d}_{\perp }\)/\({d}_{\parallel }\)), in plane bond angle (\(\theta\)) and the density of states near the Fermi surface. The lines are guides to the eye.