Weak coupling theory of nickel-based 327 superconductors

Abstract: This review provides a comprehensive survey of weak-coupling theoretical approaches applied to understand the emergent superconductivity in the pressurized nickelate bilayer system $La_{3}Ni_{2}O_{7}$. Following the landmark discovery of its high-Tc superconductivity under pressure, this material has rapidly become a new paradigmatic platform in the field of unconventional superconductivity, joining cuprates and iron-based systems. We focus on three pivotal theoretical frameworks: the random phase approximation (RPA), the fluctuation-exchange approximation (FLEX), and the functional renormalization group (FRG). These methods are deployed to analyze the effective pairing interactions and emergent instabilities arising from the low-energy electronic structure, which is commonly modeled by a bilayer two-orbital Hubbard Hamiltonian incorporating the Ni $d_{x<sup>2-y<sup>2}$ and $d_{3z<sup>2-r<sup>2}$ orbitals.