Orbital-selective Superconductivity in the Pressurized Bilayer Nickelate La_3Ni_2O_7: An Infinite Projected Entangled-Pair State Study

The newly discovered high-T_c nickelate superconductor La_3Ni_2O_7 has generated significant research interest. To uncover the pairing mechanism, it is essential to investigate the intriguing interplay between the two e_g, i.e., d_x^2-y^2 and d_z^2 orbitals. Here we perform an infinite projected entangled-pair state (iPEPS) study of the bilayer t-J model, directly in the thermodynamic limit and with orbitally selective parameters for d_x^2-y^2 and d_z^2 orbitals, respectively. The d_x^2-y^2 electrons exhibit significant intralayer hopping t_∥ and spin couplings J_∥, with interlayer J_⊥ passed from the d_z^2 electrons. However, the interlayer t_⊥ is negligible in this case. In contrast, the d_z^2 orbital demonstrates strong interlayer t_⊥ and J_⊥, while the inherent intralayer t_∥ and J_∥ are small. Based on the iPEPS results, we find clear orbital-selective behaviors in La_3Ni_2O_7. The d_x^2-y^2 orbitals exhibit robust superconductive (SC) order driven by the interlayer coupling J_⊥; while the d_z^2 band shows relatively weak SC order as a result of small t_∥ (lack of coherence) but large t_⊥ (strong Pauli blocking). Furthermore, by substituting rare-earth element Pm or Sm with La, we find an enhanced SC order, which opens up a promising avenue for discovering nickelate superconductors with even higher T_c.