Theoretical Prediction of Optimal $T_c$ and Fermi Pockets in Nickelate Superconductors

Abstract

High-pressure bilayer $L{a}_{3-x}S{m}_{x}N{i}_2{O}_{7-\delta }$ (LSNO) reaches a record $T_c=96K$, 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 $YB{a}_{2}C{u}_3{O}_{7-\delta }$ (YBCO). Using the Planckian quantum-well scaling $T_c=\Lambda /{\xi }^2$ ($\xi$: lattice-modulated quantum-well depth), we obtain $T_c=93.4K$ and $97.1K$ for monoclinic and tetragonal LSNO, matching experimental values $92K$ and $96K$. Despite distinct stoichiometry and global symmetry ($P{2}_1/m$ for LSNO, $Pmmm$ for orthorhombic YBCO), both systems have nearly identical $\xi$ ($3.6629$ angstrom vs. $3.6720$ angstrom) and consistent $T_c$ responses. Further calculations yield a universal $T_c$ limit $\sim 100K$ 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 $\gamma$ 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.

10 pages, 6 figures