Structural symmetry effects on the competition of density waves and superconductivity in bilayer nickelates

We investigate the interplay between spin-density-wave (SDW) order and superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ using the functional renormalization group~(fRG) applied to multiorbital weak-coupling models of both the ambient- and high-pressure crystal structures. As Hund's coupling increases, the leading instability evolves from superconductivity to an SDW state with ordering vector $\mathbf{Q}_1 \approx (\pi/2,\pi/2)$ (equivalently $\mathbf{Q}_Y \approx (0,\pi)$ in the orthorhombic $Amam$ unit cell), in agreement with experimental observations. Surprisingly, the ambient- and high-pressure structures exhibit nearly identical non-interacting susceptibilities and leading fRG instabilities, indicating that the emergence of superconductivity under pressure cannot be explained solely by changes in the low-energy electronic structure. Instead, our results identify the suppression of orthorhombicity as a key ingredient for superconductivity. As the system approaches the tetragonal limit, symmetry-related SDW fluctuations become nearly degenerate, frustrating long-range magnetic order while enhancing pairing interactions. These findings highlight lattice symmetry as a central tuning parameter of the competing ordered states in bilayer nickelates and suggest that reducing orthorhombicity through uniaxial strain could stabilize bulk superconductivity already at ambient pressure.