Multiband Metallic Ground State in Multilayered Nickelates La${}_3$Ni${}_2$O${}_7$ and La${}_4$Ni${}_3$O${}_{10}$ Probed by ${}^{139}$La-NMR at Ambient Pressure

We report a ${}^{139}$La-NMR study of polycrystalline samples of multi($n$)-layered nickelates, La${}_3$Ni${}_2$O${}_{7-\delta }$ ($n=2$) and La${}_4$Ni${}_3$O${}_{10-\delta }$ ($n=3$), at ambient pressure. Measurements of the nuclear magnetic resonance (NMR) spectra and nuclear spin relaxation rate ($1\mathrm{/}{T}_1$) indicate the emergence of a density wave order with a gap below $T^{\ast }\sim 150$ K for La${}_3$Ni${}_2$O${}_{7-\delta }$ and $\sim 130$ K for La${}_4$Ni${}_3$O${}_{10-\delta }$. The finite value of $1\mathrm{/}{T}_1$ below $T^{\ast }$ indicates metallic ground states with the remaining density of states at the Fermi level ($E_{\mathrm{F}}$) under the density wave order. These features are attributed to multiple $d$ electron bands with different characteristics. Above $T^{\ast }$, the gradual decrease in $1\mathrm{/}{T}_{1}T$ upon cooling implies the presence of a band with flat dispersion near $E_{\mathrm{F}}$. From our microscopic probes, we point out that these nickelates ($n=2$ and $3$) possess similar electronic states despite the difference in the formal valence of the Ni-$d$ electron states, which provides a basis for understanding the novel high-$T_{\mathrm{c}}$ superconductivity under high pressures.