Superconductivity governed by Janus-faced fermiology in strained bilayer nickelates

TL;DR

This paper reveals that the $ ext{γ}$ pocket in strained bilayer nickelates plays a dual role in superconductivity, acting both as a pair-breaker and a pair-former, and that optimal $T_c$ occurs when this pocket is at the Fermi level.

Contribution

It uncovers the Janus-faced role of the $ ext{γ}$ pocket in mediating superconductivity and explains conflicting experimental observations in bilayer nickelates.

Findings

The $ ext{γ}$ pocket induces both pair-breaking and pair-forming channels.

Optimal $T_c$ occurs near a Lifshitz transition when the $ ext{γ}$ pocket is at the Fermi level.

Superconductivity emerges when the $ ext{γ}$ pocket's energy level is close to the Fermi level.

Abstract

High-temperature superconductivity in pressurized and strained bilayer nickelates (La,Pr)$_3$Ni$_2$O$_7$ has emerged as a new frontier. One of the key unresolved issues concerns the fermiology that underlies superconductivity. On both theoretical and experimental sides, no general consensus has been reached, and conflicting results exist regarding whether the relevant Fermi surface involves a $\gamma$ pocket -- a hole pocket with $d_{z^2}$-orbital character centered at the Brillouin zone corner. Here, we address this issue by unveiling a Janus-faced role of the $\gamma$ pocket in spin-fluctuation-mediated superconductivity. We show that this pocket simultaneously induces dominant pair-breaking and pair-forming channels for the leading $s_\pm$-wave pairing. Consequently, an optimal superconducting transition temperature $T_\mathrm{c}$ is achieved when the $\gamma$ pocket surfaces at the Fermi level, placing the system near a Lifshitz transition. This suggests that superconductivity can emerge, provided the maximum energy level of the $\gamma$ pocket lies sufficiently close to the Fermi level, either from below or above. Our finding not only reconciles two opposing viewpoints on the fermiology, but also naturally explains recent experiments on (La,Pr)$_3$Ni$_2$O$_7$ thin films, including the superconductivity under compressive strain, two conflicting measurements on the Fermi surface, and the dome shape of $T_\mathrm{c}$ as a function of hole doping.