Trilayer multiorbital models of ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{10}$

Recently, the discovery of superconductivity in Ruddlesden-Popper (RP) ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{10}$ under pressure has further expanded the realm of nickelate-based superconductor family. In this paper, we perform a first-principles study of ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{10}$ for both the $P{2}_1/a$ phase at ambient pressure and $I4/mmm$ phase at high pressure, with $U=0$, 3.5 eV. Our results confirm the characteristic upward shift of a $\mathrm{Ni}\text{−}{d}_{z^2}$ bonding band under pressure. Moreover, our analysis of electronic spectrum and orbital occupancy unveil the dynamic mechanism of electronic reconstructions under pressure, embedded in a critical dual effect. Based on our results, we further propose a trilayer two-orbital model by performing Wannier downfolding on $\mathrm{Ni}\text{−}{e}_g$ orbitals. Our model reveals four Fermi surface sheets with $\alpha ,\beta ,{\beta }^{\prime },\gamma$ pockets, bearing resemblance to that of bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{O}_7$. According to the model, our calculated spin susceptibility under random phase approximation shows that the $d_{x^2-y^2}$ orbital is also important for the magnetic fluctuation in the RP series. Finally, a high energy 16-orbital model with direct $dp,pp$ hoppings is proposed, which implies that ${\mathrm{La}}_4{\mathrm{Ni}}_3{O}_{10}$ also lies in the charge-transfer picture within the Zaanen-Sawatzky-Allen scheme. Our exposition of electronic reconstructions and multiorbital models shed light on theoretical electronic correlation study and experimental exploration of lower pressure superconductors in the RP series.