Strong electron-phonon coupling driven pseudogap modulation and density-wave fluctuations in a correlated polar metal

Abstract

There is tremendous interest in employing collective excitations of the lattice, spin, charge, and orbitals to tune strongly correlated electronic phenomena. We report such an effect in a ruthenate, Ca₃Ru₂O₇, where two phonons with strong electron-phonon coupling modulate the electronic pseudogap as well as mediate charge and spin density wave fluctuations. Combining temperature-dependent Raman spectroscopy with density functional theory reveals two phonons, B₂^P and B₂^M, that are strongly coupled to electrons and whose scattering intensities respectively dominate in the pseudogap versus the metallic phases. The B₂^P squeezes the octahedra along the out of plane c-axis, while the B₂^M elongates it, thus modulating the Ru 4d orbital splitting and the bandwidth of the in-plane electron hopping; Thus, B₂^P opens the pseudogap, while B₂^M closes it. Moreover, the B₂ phonons mediate incoherent charge and spin density wave fluctuations, as evidenced by changes in the background electronic Raman scattering that exhibit unique symmetry signatures. The polar order breaks inversion symmetry, enabling infrared activity of these phonons, paving the way for coherent light-driven control of electronic transport.

Fig. 1. Raman spectra coupled to the ground states of Ca₃Ru₂O₇.

a Crystal structure of Ca₃Ru₂O₇ with illustrated magnetic space group, symmetry operations and magnetic spins in the AFM-a and AFM-b phases. b Electronic and magnetic phase diagram of Ca₃Ru₂O₇. c Schematically depicted Raman lab geometry with respect to the crystal lattice of Ca₃Ru₂O₇. The $E_{i,s}$ and $k_{is}$ are polarization and wavevector or incident and scattered light respectively. d Representative polarized Raman intensities for Ca₃Ru₂O₇ at AFM-b and AFM-a phases respectively.

Fig. 2. Temperature dependent Raman spectra and a comparison with density functional theory.

a Temperature dependent Raman spectra in $\overline{z}$(xy)z with B₂⁽¹¹⁾ to B₂⁽¹⁵⁾ modes highlighted. The intensity is normalized to strongest Raman peak. b B₂ spectrum at 48 K (T_c) showcase features of shoulder peaks highlighted with black arrows, compared with spectra at 18 K and 98 K. The DFT calculated B₂⁽¹¹⁾ to B₂⁽¹⁵⁾ phonon energies compared to experimental observations in c AFM-a and d AFM-b phases.

Fig. 3. Temperature-dependent reconstruction of B₂^M and B₂^P phonon spectra.

a Fitting of $\overline{z}$(xy)z Raman spectra between 340 cm^–1 and 470 cm^–1 at 50 K (top panel) and 10 K (bottom panel). the celeste/pink color-coded peak correspond to B₂^P/B₂^M. b The temperature dependent plots of amplitude ($I$) and FWHM ($\Gamma$) of B₂^P (celeste) and B₂^M (pink) modes. Error bars are standard deviations from fitting values. The celeste/pink lines are guides to the eye. c Raman colormap plot of the intensity difference between specified temperature and 13 K. The total area of region of interest highlighted in blue and red boxes in c are replotted in d to indicate an intensity anomaly observed at T^* = 30 K. The pseudogap size (Δ) is extracted from ARPES data and is represented as grey data points. The broad grey line is a guide to the eye.

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.

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

Temperature dependence of a B₂ and b A₁ Raman response function (${\chi }_u^{’’}\left(\omega ,T\right)$) of Ca₃Ru₂O₇ across T_c. The corresponding momentum-space structure of the form factor ${\gamma }_{\mathit{k}}^{\mu }$ 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^{, ,} . 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 $\mathrm{\Delta }{\chi }_{B_2}^{’’}\left(\omega ,T\right)$ (red circles) and $\mathrm{\Delta }{\chi }_{A_1}^{’’}\left(\omega ,T\right)$ (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 ${\mathrm{\Delta }\chi }_u^{’’}\left(\omega ,T\right)$, and the errorbars of phonon spectral weight are standard deviations from fitting results.