Title: Interlayer Pairing Induced Partially Gapped Fermi Surface in Trilayer La$_4$Ni$_3$O$_{10}$ Superconductors

Abstract: We explore the superconducting pairing mechanisms in the trilayer $\mathrm{La}_4\mathrm{Ni}_3\mathrm{O}_{10}$ material through self-consistent mean-field calculations. Our findings demonstrate that intralayer pairings are substantially weaker compared to interlayer ones. Remarkably, in the state characterized by interlayer pairing, we detect the presence of partially gapped Fermi surfaces, a fascinating occurrence attributable to the disparity between the inner and outer conducting layers of $\mathrm{La}_4\mathrm{Ni}_3\mathrm{O}_{10}$. Moreover, this study provides valuable insights into the lower superconducting transition temperatures observed in $\mathrm{La}_4\mathrm{Ni}_3\mathrm{O}_{10}$ compounds. This contributes to a deeper understanding of its distinct superconducting attributes.