Quantum phase transition driven by competing intralayer and interlayer hopping in bilayer nickelates

Bilayer nickelates exhibit high-temperature superconductivity under proper hydrostatic pressure or epitaxial strain, signifying the emergence of quantum phase transitions whose physical mechanisms remain unclear. Using a minimal bilayer Hubbard model incorporating only the Ni-$d_{3z^2-r^2}$ orbitals, we demonstrate that a phase transition naturally arises from tuning the ratio of intralayer to interlayer hopping amplitudes. The transition point separates regimes with a rich interplay between superconducting and density-wave orders. In the regime of weaker intralayer hopping, the ground state is characterized by quasi-long-range spin-density-wave order. As the intralayer hopping increases, the system undergoes a transition marked by the opening of a finite spin gap and the disappearance of spin-density-wave order. Meanwhile, superconductivity is dramatically enhanced, accompanied by the emergence of quasi-long-range charge-density-wave order, indicating that the system enters Luther-Emery phase. This quantum phase transition, driven by the competition between intralayer and interlayer hopping, provides a plausible microscopic explanation for the experimentally observed correlation between the superconducting transition temperature and ratio of out-of-plane to in-plane lattice constants. Our findings reveal a possible link between the suppression of spin-density-wave order and the prominence of superconducting order, which may assist future efforts to optimize experimental conditions for further enhancing superconductivity in bilayer nickelates.