Daily Overview: Today’s highlight focuses on an in-depth understanding of the interplay among charge, spin, and pairing symmetry in the bilayer nickelate La₃Ni₂O₇. Two studies reveal the rich physics of this system from the perspectives of intrinsic order competition and external field tuning of pairing, respectively. On one hand, self-consistent calculations based on an eight-orbital tight-binding model show that, in the low-pressure orthorhombic phase, a double-stripe spin-density wave forms first and triggers an intertwined charge-density wave at lower temperatures, leading to low-spin states at certain Ni sites. The discovery of this spin–charge hierarchical order provides a key link between the ambient-pressure density-wave phase and the high-pressure superconducting phase. On the other hand, dynamical cluster approximation combined with quantum Monte Carlo simulations indicates that applying a vertical electric field in La₃Ni₂O₇ thin films can effectively tune the interlayer orbital distribution, suppressing the high-temperature dominant s±-wave pairing while significantly enhancing d-wave pairing. In particular, under electron doping, an electric-field-induced pairing symmetry transition may occur, offering new many-body computational evidence for understanding the pairing mechanism of nickel-based superconductivity and its control. arXiv submission processing window: 2026-08-11 00:00 to 2026-08-11 00:00 UTC.

1. Density waves in low-pressure bilayer nickelates

Summary: Using the unrestricted Hartree-Fock method based on an eight-orbital tight-binding model fitted from density functional theory and the Slater-Kanamori interaction, we investigate the origin of density waves in the bilayer nickelate La₃Ni₂O₇ at low pressure. In the orthorhombic structure with lifted degeneracy, the electronic system first develops a double-stripe spin density wave with wave vector Q_Y = (0, π) at around 150 K. Calculations show that the pure double-stripe spin state becomes unstable at lower temperatures, triggering a concomitant charge density wave instability that leads to a spin-modulated double-stripe order, in which charge density waves and spin density waves intertwine. The charge order parameter is an order of magnitude smaller than the magnetic one, and its emergence breaks the equivalence of in-plane Ni sites, causing a redistribution of magnetic moments at certain sites and producing a low-spin state. The charge density wave transition temperature is sensitive to the crystal field splitting, which can explain the experimentally observed evolution of T_DW with pressure. These findings are clearly manifested in band folding, Fermi surface reconstruction, and the density-of-states profile, establishing a hierarchical structure and coexistence mechanism of spin and charge orders in La₃Ni₂O₇ and providing key clues for connecting its ambient-pressure phase to the high-pressure superconducting phase.

2. Perpendicular electric field induced competing $s^\pm$- and $d$-wave pairings in La$_3$Ni$_2$O$_7$ thin film

Summary: This study employs the dynamical cluster approximation combined with quantum Monte Carlo simulations to investigate a bilayer two-orbital Hubbard model subject to an interlayer potential bias, aiming to explore the influence of a perpendicular electric field on the superconducting pairing symmetry of Ruddlesden-Popper phase nickelate La₃Ni₂O₇ thin films. By analyzing the eigenvalues of the Bethe-Salpeter equation and the orbitally resolved pairing polarizabilities in undoped, hole-doped, and electron-doped regimes, we find that the s±-wave pairing is dominated by the d_z² orbital at high temperatures but transitions to d_x²-y²-orbital dominance at lower temperatures, while its strength is generally suppressed with increasing potential bias. In contrast, d-wave pairing on the d_x²-y² orbital is significantly enhanced as the electric field increases, particularly in electron-doped systems, and may exhibit a dome-like feature near half-filling of that orbital. This complementary evolution of s±-wave and d-wave pairing is driven by interlayer orbital mismatch and electron transfer to the d_x²-y² orbital, suggesting a possible electric-field-induced pairing symmetry transition. The computational results agree with previous weak-coupling theoretical predictions and provide new many-body computational insights into the superconducting mechanism of RP nickelates.