Optimal superconductivity near a Lifshitz transition in strained bilayer nickelates

Bilayer nickelates (La,Pr)₃Ni₂O₇ under pressure and strain have recently emerged as a platform for high-temperature superconductivity. A distinctive feature of these materials is a shallow electronic band whose maximum lies very close to the Fermi level. Depending on strain or doping, this band may either remain just below the Fermi level - forming an incipient band with no Fermi surface - or shift slightly upward to create a small Fermi-surface pocket – the so-called γ-pocket. In this talk, we will show that the superconducting state is governed by the evolution of this incipient band. Using a microscopic analysis of spin-fluctuation–mediated pairing, we find that superconductivity is optimized precisely at the Lifshitz transition where the band crosses the Fermi level. At this point, the system balances competing pair-forming and pair-breaking processes in a way that maximizes the pairing strength. This mechanism naturally explains the observed superconducting dome and its strong sensitivity to pressure, doping, and strain.