Theory of Pressure Dependence of Superconductivity in Bilayer Nickelate La 3 Ni 2 O 7

A recent experiment showed the superconducting transition temperature in the Ruddlesden-Popper bilayer La_{3}Ni_{2}O_{7} decreases monotonically with increasing pressure above 14 GPa. In order to unravel the underlying mechanism for this unusual dependence, we performed theoretical investigations by combining the density functional theory (DFT) and the unbiased functional renormalization group (FRG). Our DFT calculations show that the Fermi pockets are essentially unchanged with increasing pressure (above 14 GPa), but the bandwidth is enlarged, and particularly the interlayer hopping integral between the nickel 3d_{3z^{2}-r^{2}} orbitals is enhanced. From the DFT band structure, we construct the bilayer tight-binding model in terms of the nickel 3d_{3z^{2}-r^{2}} and 3d_{x^{2}-y^{2}} orbitals. On this basis, we investigate the superconductivity induced by correlation effects by FRG calculations. We find consistently s_{±}-wave pairing triggered by spin fluctuations, but the latter are weakened by pressure and lead to a decreasing transition temperature versus pressure, in qualitative agreement with the experiment. We emphasize that the itinerancy of the d orbitals is important and captured naturally in our FRG calculations, and we argue that the unusual pressure dependence would be unnatural, if not impossible, in the otherwise local-moment picture of the nickel d orbitals. This sheds light on the pertinent microscopic description, and more importantly the mechanism, of superconductivity in La_{3}Ni_{2}O_{7}.