Superconductivity of the bilayer t-J ladder

Recently, by considering the crucial role of the interlayer spin exchange interaction of the electrons on dz2 orbitals, the bilayer t-J model has been proposed as a potential minimum model to study the nickelate superconductor La3Ni2O7 under high pressure. To investigate the superconductivity of this model near the quarter filling, we consider the bilayer $t-J-J_{\bot}$ ladder where $t$ is the in-plane electron hopping, $J$ is the in-plane spin interaction, and $J_{\bot}$ is the interlayer spin interaction. Using density matrix renormalization group method, we study the model on the Ly = 2 and 3 bilayer ladders by tunning $J_{\bot}$. We find that by coupling the two layers in both the Luttinger liquid and the Luther-Emery liquid states, increased $J_{\bot}$ can induce the dominant s-wave pairing between the two layers. In the special case of Ly = 2 at the quarter filling, the gapped charge mode appears robust with growing $J_{\bot}$, and superconductivity cannot be induced in this case.