Fig. 5: Phonon mediated charge density fluctuation observed in electronic Raman scattering.

Temperature dependence of a B₂ and b A₁ Raman response function (\({\chi }_{u}^{{{{\hbox{'}}}{{\hbox{'}}}}}\left(\omega,T\right)\)) of Ca₃Ru₂O₇ across T_c. The corresponding momentum-space structure of the form factor \({\gamma }_{{{{{{\boldsymbol{k}}}}}}}^{\mu }\) are depicted in the insets (Supplementary Note 10) overlayed with a schematic of momentum resolved electronic band features in the low-energy excitation near the Fermi surface from ARPES studies^{25, 35, 36}. The background responses of c B₂ and d A₁, after subtracting the background response at 49 K to highlight the dip feature below 400 cm^-1 arising from the pseudogap opening, and the hump feature seen above 550 cm^-1. e Temperature dependence of the pseudogap Raman signal obtained by summing between 120 cm^-1 and 400 cm^-1 in \(\Delta {\chi }_{{B}_{2}}^{{{{\hbox{'}}}{{\hbox{'}}}}}\left(\omega,T\right)\) (red circles) and \(\Delta {\chi }_{{A}_{1}}^{{{{\hbox{'}}}{{\hbox{'}}}}}\left(\omega,T\right)\) (black circles). The signal is normalized to the maximum signal at 28 K and the solid line is a BCS gap model. f Correlation between B₂^P spectral weight and charge transfer Raman response at 300\(\mu\)W (black circles) and 600\(\mu\)W (red circles) incident laser power. g A schematic diagram of the proposed 3 step mechanism for the hump feature in B₂: the orbital flip excitation is mediated by B₂ phonons. The orbital flip excitation transiently differentiates the neighboring RuO₆ octahedra and induces dynamical charge and spin density fluctuations. Errorbars of integrated area is estimated from variance of featureless section in \({\Delta \chi }_{u}^{{{{\hbox{'}}}{{\hbox{'}}}}}\left(\omega,T\right)\), and the errorbars of phonon spectral weight are standard deviations from fitting results.