Fig. 7: Schematic of the electronic and structural disproportionation characterizing the metal–insulator transition of Ca₂RuO₄.

a In the metallic phase, all 3 t_2g orbitals of Ca₂RuO₄ are approximately equally occupied; ΔN ≈ 0. b In the insulating phase, the xy orbital is doubly occupied, while the yz and xz are singly occupied; ΔN = 1. c Representation of Q₀ structural mode, in which all bond lengths change equally. d Representation of structural mode Q₃ in which octahedral volume is preserved and the change in the two in-plane Ru–O bond lengths are equal, and opposite in sign to the change in the apical bond length. The electronic state in b is associated with a structural term of the form −(Q₃ − λ₀Q₀), with λ₀ > 0 Legend: a, b: black lines correspond to orbital energy levels, blue circles signify electrons; c, d: purple circle = Ru atom, red circle, O atom; arrows and dotted lines signify bonds and their changes with the two different structural modes.