Non-Fermi liquid and Hund correlation in ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ under high pressure

High temperature superconductivity was recently found in the bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ (La327), followed by the discovery of superconductivity in the trilayer ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$ (La4310), under high pressure. Through studying the electronic correlation of La4310 with $\mathrm{DFT}+\mathrm{DMFT}$, and further comparing it with that of La327, we find that the $e_g$ orbitals of the outer-layer Ni cations in La4310 have a similar (but slightly weaker) electronic correlation to those in La327, in which the electrons behave as a non-Fermi liquid with Hund correlation and linear-in-temperature scattering rate. Our results suggest that the experimentally observed “strange metal” behavior may be explained by the Hund spin correlation featuring high spin states and spin-orbital separation. In contrast, the electrons in the inner-layer Ni cations in La4310 behave as a Fermi liquid. The weaker electronic correlation in La4310 is attributed to more hole doping, which may explain its lower superconducting transition temperature.

Figure 1

(a) The crystal structure of ${\mathrm{La}}_4{\mathrm{Ni}}_3{\mathrm{O}}_{10}$. (b), (c) The imaginary parts of the self-energy functions at the Matsubara axis $\text{Im}\mathrm{\Sigma }\left(i{\omega }_n\right)$ at 290 and 116 K, respectively. (d), (e) The real frequency $\text{Im}\mathrm{\Sigma }\left(\omega \right)$ for the inner- and outer-layer Ni atoms at 290 K.

Figure 2

Momentum-resolved spectral functions $A(\mathbf{k},w)$ of La4310 by $\mathrm{DFT}+\mathrm{DMFT}$ calculated at 290 K. The DFT band structure is plotted with green lines for reference. The Fermi level is set to zero energy as marked by the white dashed line. The energy bands of the Ni $e_g$ orbitals are mainly in the energy range of $-1$ to 3 eV, which are somewhat blurry and narrowed by the correlation-induced renormalization. The flat bands are clearly visible at the Fermi level (near the M point), which are dominantly from the Ni-$3d_{z^2}$ orbitals.

Figure 3

The imaginary part of the self-energy at zero frequency, $-\mathrm{Im}\mathrm{\Sigma }(\omega =0)$, plotted as functions of temperature by $\mathrm{DFT}+\mathrm{DMFT}$ calculated. The green and blue lines are temperature linear fit for the outer-layer Ni $e_g$ orbitals that exhibit “strange metal” and non-Fermi liquid behavior at low temperatures. The red and black lines are temperature squared $(\sim T^2)$ fit for the inner-layer $e_g$ orbitals, showing Fermi-liquid behavior.

Figure 4

(a) The imaginary-time spin-spin correlation functions $C_{\text{ss}}\left(\tau \right)$ and orbital-orbital correlation functions $C_{\text{oo}}\left(\tau \right)$ for the $e_g$ orbitals at 290 $\mathrm{K}$. (c) $C_{\text{ss}}(\tau =\beta /2)$ plotted as functions of temperature. The inset in (c) is an enlarged view of the low-temperature range. (b), (d) $C_{\text{ss}}\left(\tau \right)/C_{\text{ss}}(\tau =\beta /4)$ and $F\left(\tau \right)/F(\beta /4)$ plotted as functions of temperatures.

Figure 5

Projected density of states (PDOS), $A\left(\omega \right)=-1/\pi \mathrm{Im}G\left(\omega \right)$, with several different temperatures for the inner-layer $d_{z^2}$ (a), outer-layer $d_{z^2}$ (b), inner-layer $d_{x^2-y^2}$ (c), and outer-layer $d_{x^2-y^2}$ orbitals (d), respectively.

Figure 6

Static local susceptibilities of spin ${\chi }_{\mathrm{spin}}$ and orbital ${\chi }_{\mathrm{orb}}$ as functions of temperature.