Highly Anisotropic Charge Dynamics and Spectral Weight Redistribution in the Trilayer Nickelate La$_{4}$Ni$_{3}$O$_{10}$

Abstract

We study the $ab$-plane and $c$-axis charge dynamics of La$_{4}$Ni$_{3}$O$_{10}$ using optical spectroscopy. While a pronounced Drude profile, i.e. metallic response, is observed in the $ab$-plane optical conductivity $\sigma_{1}^{ab}(\omega)$, the $c$-axis optical spectra $\sigma_{1}^{c}(\omega)$ exhibit semiconducting behavior. The zero-frequency extrapolation of the optical conductivity $\sigma_{1}(\omega \rightarrow 0) \equiv 1/\rho_{\text{dc}}$ gives a resistivity anisotropy of $\rho_{c}/\rho_{ab} \simeq 366$ at 300~K for La$_{4}$Ni$_{3}$O$_{10}$, which is much larger than the values in iron-based superconductors but comparable to those in high-$T_{c}$ cuprates. The interband response is also highly anisotropic, showing salient orbital selectivity for light polarized in the $ab$ plane and along the $c$ axis. The interband-transition peaks in both $\sigma_{1}^{ab}(\omega)$ and $\sigma_{1}^{c}(\omega)$ are located at lower energies compared to density-functional-theory predictions, signifying considerable electronic correlations. By investigating the spectral weight transfer, we find that in the pristine phase, Coulomb correlations have a marked impact on the charge dynamics of \LNO, whereas in the density-wave state, a gap opens with the Ni-$d_{z^{2}}$ orbital being involved.