Multiorbital character of the density wave instability in La$_4$Ni$_3$O$_{10}$

Abstract: Ruddlesden-Popper nickelates exhibit high-temperature superconductivity closely intertwined with charge and spin density wave order. However, fundamental questions persist regarding the interplay between the associated density wave (DW) fluctuations and superconductivity, as well as the orbital character and symmetry underlying the DW instabilities. Here we utilize polarized Raman scattering to investigate the phononic and electronic Raman responses of the trilayer nickelate La$4$Ni$_3$O${10}$ across its concomitant charge and spin density wave transitions. In addition to distinct phonon anomalies occurring below the transition temperature, we observe a depletion of continuum spectral weight up to 114 meV and a pronounced peak centered at this energy. By combining momentum-selective information from polarized electronic Raman scattering with model calculations involving both Ni-3$d_{x^2 - y^2}$ and Ni-3$d_{z^2}$ orbitals, we identify 114 meV as the energy scale $2\Delta_\mathrm{DW}$ of the DW gap, characterized by incoherent opening and non-mean-field behavior. Furthermore, the model calculations reveal that the corresponding $2\Delta_\mathrm{DW}$ peak exhibits a multiorbital origin, thus shedding light on the nature of the DW instabilities in La$4$Ni$_3$O${10}$.