Fig. 2

Local spectra of the correlated orbitals in V₂O₃ and Sr₂RuO₄. The results for V₂O₃ (a, c, d) and Sr₂RuO₄ (b, e, f) exhibit very different temperature-dependent behaviors. a, b The density of states at the Fermi level, estimated by \(D(i\omega _0) = - \frac{1}{\pi }{\mathrm{Im}}G(i\omega _0)\). c–f The correlated real-frequency spectra (PDOS), \(A(\omega ) = - \frac{1}{\pi }{\mathrm{Im}}G(\omega )\). D(iω₀) shows a suppression at a characteristic temperature T_M = 1000 K (indicated by the orange arrow) in V₂O₃ (a), while it evolves smoothly in Sr₂RuO₄ (b). As temperature decreases, in V₂O₃ the coherence resonance of both \({e}_{g}^\pi\) and a_1g orbitals emerges from the pseudogap regime with low density of states between two incoherent peaks (c, d), while in Sr₂RuO₄ the coherence resonance of both d_xz/yz and d_xy orbitals emerges from a single broad incoherent peak with large finite density of states at the Fermi level (e, f). The insets in (d, f), repeated from Fig. 1, are cartoons of the temperature dependence of the Mott and Hund PDOS