Non-Fermi Liquid and Hund Correlation in La$_4$Ni$_3$O$_{10}$ under High Pressure

Abstract: High temperature superconductivity was recently found in the bilayer nickelate $\rm{La}3 \rm{Ni}_2 \rm{O}_7$ (La327), followed by the discovery of superconductivity in the trilayer $\rm{La}_4 \rm{Ni}_3 \rm{O}{10}$ (La4310), under high pressure. Through studying the electronic correlation of La4310 with DFT+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.