Orbital-selective superconductivity in the pressurized bilayer nickelate La3Ni2O7 : An infinite projected entangled-pair state study

The newly discovered high-${T}_{c}$ nickelate superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ 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., ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals. Here we conduct an infinite projected entangled-pair state (iPEPS) study of the bilayer $t\text{\ensuremath{-}}J$ model, directly in the thermodynamic limit and with orbitally selective parameters for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals, respectively. The ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ electrons exhibit significant intralayer hopping ${t}_{\ensuremath{\parallel}}$ (and spin couplings ${J}_{\ensuremath{\parallel}}$) as well as strong interlayer ${J}_{\ensuremath{\perp}}$ passed from the ${d}_{{z}^{2}}$ electrons. However, the interlayer ${t}_{\ensuremath{\perp}}$ is negligible in this case. In contrast, the ${d}_{{z}^{2}}$ orbital demonstrates strong interlayer ${t}_{\ensuremath{\perp}}$ and ${J}_{\ensuremath{\perp}}$, while the inherent intralayer ${t}_{\ensuremath{\parallel}}$ and ${J}_{\ensuremath{\parallel}}$ are small. Based on the iPEPS results, we find clear orbital-selective behaviors in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$. The ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals exhibit robust superconductive (SC) order driven by the interlayer coupling ${J}_{\ensuremath{\perp}}$, while the ${d}_{{z}^{2}}$ band shows relatively weak SC order as a result of small ${t}_{\ensuremath{\parallel}}$ (lack of coherence) but large ${t}_{\ensuremath{\perp}}$ (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 ${T}_{c}$.