Recent Advances and Prospects in Theoretical Study of Bilayer Nickelate Superconductor La₃Ni₂O₇

The discovery of high-temperature superconductivity in bilayer nickelate La₃Ni₂O₇ under high pressures in 2023 has spurred intensive theoretical and numerical investigations. These studies aim to unravel physical properties of La₃Ni₂O₇ in various aspects, with a particular emphasis on its pairing symmetry and underlying superconducting mechanism. On the other hand, significant effort has also been made to explore and predict novel nickel-based superconductors related to La₃Ni₂O₇. This article reviews these recent advancements aimed at elucidating the physical properties and superconducting mechanism of La₃Ni₂O₇, whose multi-orbital character and intricate electronic correlations have spawned diverse theories for its pairing mechanism. We summarize recent findings regarding its macroscopic models, pairing symmetry, normal state characteristics, and the structure of spin and charge density waves. Particular attention is given to the debate surrounding the role of σ-bonding band metallization and its connection to superconductivity. Finally, we provide an outlook on future studies crucial for advancing our understanding of La₃Ni₂O₇ superconductivity.