Daily Overview: Today’s research highlight focuses on the competition between out-of-plane s-wave superconductivity and the out-of-plane bond-order phase (z-BOP) instability in bilayer nickelates, both simultaneously driven by the interlayer spin exchange J⊥. Based on a controlled large-N expansion of the Hubbard-operator path integral, this work studies the strongly correlated single-orbital d_{x^2-y^2} bilayer t-J⊥-V model at the mean-field and beyond-mean-field levels to describe pressurized and thin-film bilayer nickelates. Its central conclusion is that the complex z-BOP gap is dominated by its imaginary part, which endows the interlayer hopping with a complex phase, thereby generating an interlayer current and inducing an in-plane current, and forming a time-reversal-symmetry-breaking loop-current state. This loop-current phase competes with superconductivity, yielding a doping-dependent dome-shaped superconducting region, with optimal superconductivity appearing near the z-BOP quantum critical point. The phase diagram encompasses a pure loop-current phase, a low-doping loop-current–superconductivity coexistence phase, a higher-doping pure superconducting phase, and a correlated metallic state, while the Coulomb interaction has little effect on the formation and stability of the loop current. This strong-coupling single-orbital picture not only provides new insights into nickelate physics but may also inspire quantum simulations of spontaneous loop-current many-body models on platforms such as optical lattices and superconducting quantum circuits. arXiv submission processing window: 2026-09-11 00:00 to 2026-09-11 00:00 UTC.

1. Competing Interlayer Loop Currents and Superconductivity in the Bilayer $t$-$J_\perp$-$V$ Model

Summary: This paper employs a controlled large-N expansion based on the Hubbard-operator path integral to study the strongly correlated single-orbital d_{x^2-y^2} bilayer t-J⊥-V model at the mean-field and beyond-mean-field levels, aiming to characterize pressurized and thin-film bilayer nickelates. Focusing on the interlayer spin exchange J⊥, we find that it simultaneously drives out-of-plane s-wave superconductivity and an out-of-plane bond-order phase z-BOP instability; the self-consistent solution for the complex z-BOP gap is dominated by its imaginary part, which endows the interlayer hopping with a complex phase, thereby generating an interlayer current and inducing an in-plane current, and spontaneously forms a time-reversal-symmetry-breaking loop-current state on the vertical plaquette of the bilayer. Competition between the loop-current phase and superconductivity leads to a doping-dependent dome-shaped superconducting region, with optimal superconductivity appearing near the z-BOP quantum critical point. The phase diagram includes a pure loop-current region, a low-doping coexistence phase of loop current and superconductivity, a higher-doping pure superconducting state, and a correlated metallic state; the Coulomb interaction plays an unimportant role in the formation and stability of the loop current. We conclude that these strongly coupled single-orbital results may provide insights into nickelate physics and into many-body models with spontaneous loop currents that can be quantum simulated on platforms such as optical lattices and superconducting quantum circuits.