Pressure dependence of superconducting transition temperature in bilayer nickelate La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub>: Itinerant electrons and local spin picture

Recent experimental studies on the bilayer Ruddlesden-Popper phase nickelate La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub> have shown that in the superconducting region, its superconducting transition temperature decreases monotonically from 83 K at 18 GPa as pressure further increases, exhibiting a nearly right-triangular temperature-pressure phase diagram that is different from the dome-shaped diagrams observed in cuprates and iron-based superconductors under either doping or pressure. It is important to understand this anomalous phase diagram in elucidating the superconducting mechanism of La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub>. Since the electron-phonon coupling mechanism cannot account for the high superconducting transition temperatures in nickelate superconductors, in this work, the pressure dependence of the transition temperature is investigated from the perspective of the itinerant electrons picture and the local spin picture. By combining the density functional theory (DFT) and the unbiased singular-mode functional renormalization group (SM-FRG) method, it is found that the pairing symmetry is consistently an <inline-formula><tex-math id="M1">\begin{document}$s_\pm$\end{document}</tex-math></inline-formula>-wave, driven by spin fluctuations that become progressively weakened under pressure, thereby decreasing in the superconducting transition temperature, which is in qualitative agreement with the experimental observation. On the other hand, we estimate that the pressure dependence in the local spin picture contradicts with the experimental result. Therefore, the pressure dependence of superconducting transition temperature is more consistent with the itinerant electrons picture. Admittedly, we only made a rough estimation based on the local spin picture. It is expected that further and more detailed research will be conducted on the pressure dependence of superconducting transition temperature from the local spin picture, providing deeper insights into the underlying superconducting mechanism of La<sub>3</sub>Ni<sub>2</sub>O<sub>7</sub>.