Frustrated superconductivity and intrinsic reduction of $T_c$ in trilayer nickelate

Identifying the key factors controlling the magnitude of $T_c$ is of critical importance in the pursuit of high-temperature superconductivity. In cuprates, $T_c$ reaches its maximal value in trilayer structure, leading to the belief that interlayer coupling may help promote the pairing. In contrast, for the recently discovered nickelate superconductors under high pressure, the maximum $T_c$ is reduced from about 80 K in the bilayer La$_3$Ni$_2$O$_{7}$ to 30 K in the trilayer La$_4$Ni$_3$O$_{10}$. Motivated by this opposite trend, we propose an interlayer pairing scenario for the superconductivity of La$_4$Ni$_3$O$_{10}$. Our theory reveals intrinsic frustration in the spin-singlet pairing that the inner layer tends to form with both of the two outer layers respectively, leading to strong superconducting fluctuations between layers. This explains the reduction of its maximum $T_c$ compared to that of the bilayer La$_3$Ni$_2$O$_{7}$. Our findings support a fundamental distinction between multilayer nickelate and cuprate superconductors, and ascribe it to their different (interlayer versus intralayer) pairing mechanisms. Furthermore, our theory predicts extended $s^\pm$-wave gap structures in La$_4$Ni$_3$O$_{10}$, with varying signs and possible nodes on different Fermi pockets. We also find an intrinsic Josephson coupling with potentially interesting consequences that may be examined in future experiments. Our work reveals the possibility of rich novel physics in multilayer superconductors with interlayer pairing.