Theoretical Prediction of Optimal T c and Fermi Pockets in Nickelate Superconductors

High-pressure bilayer La 3-xSm xNi 2O 7-δ (LSNO) reaches a record T c=96 K, triggering wide discussion on the T c ceiling of nickelate superconductors. We show monoclinic and tetragonal LSNO share the same octahedral quantum-well motif governing T c with YBa 2Cu 3O 7-δ (YBCO). Using the Planckian quantum-well scaling T c = Λ/ξ squared (ξ: lattice-modulated quantum-well depth), we obtain T c=93.4 K and 97.1 K for monoclinic and tetragonal LSNO, matching experimental values 92 K and 96 K. Despite distinct stoichiometry and global symmetry (P2 1/m for LSNO, Pmmm for orthorhombic YBCO), both systems have nearly identical ξ (3.6629 angstrom vs. 3.6720 angstrom) and consistent T c responses. Further calculations yield a universal T c limit about100 K for rare-earth nickelates, irrespective of stacking sequences. We examine four nickelate multilayer stacking variants: 2222 (pure bilayer), 1212 (alternating single-bilayer), 2323 (bilayer-trilayer), and 1313 (single-trilayer). Mirror symmetry breaking of coupled twin quantum wells, unique to bilayer nickelates, dictates γ Fermi pocket formation and ambient-pressure superconductivity. We further prove Fermi surfaces constitute a hologram of quantum-well electrons, establishing intrinsic links between quantum-well symmetry breaking, Fermi pocket structural evolution, and superconducting properties.