Theory of Pressure Dependence of Superconductivity in Bilayer Nickelate La$_3$Ni$_2$O$_{7}$

TL;DR

This paper combines DFT and FRG methods to explain why the superconducting transition temperature in La$_3$Ni$_2$O$_{7}$ decreases with pressure, highlighting the role of itinerant electron behavior and spin fluctuations.

Contribution

It introduces a theoretical framework using DFT and FRG to analyze pressure effects on superconductivity in bilayer nickelates, emphasizing the importance of itinerant electrons.

Findings

Superconductivity is mediated by $s_$-wave pairing from spin fluctuations.

Pressure weakens spin fluctuations, reducing the transition temperature.

Itinerant electron behavior is crucial for understanding the pressure dependence.

Abstract

The recent experiment shows 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 $s_\pm$-wave pairing triggered by spin fluctuations, but the latter are weakened by pressure and lead to a decreasing transition temperature versus pressure, in qualitatively 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 lights on the pertinent microscopic description of, and more importantly the mechanism of superconductivity in La$_3$Ni$_2$O$_{7}$.