The discovery of bilayer nickelate superconductor La₃Ni₂O₇ under high pressure has attracted worldwide attention, in which theoretical research plays a vital role. So far, theoretical calculations show that the two e_g Ni 3d_x2-y2 and 3d_z2 orbitals in La₃Ni₂O₇ are crucial to the formation of superconductivity, while the O₂ p orbital also appears on the Fermi surface. Multi-orbital models have been proposed based on the above analysis. Various calculations show that La₃Ni₂O₇ has a s^± wave pairing symmetry although other pairing symmetries can be obtained. Theoretical calculations shows that the superconducting mechanism is unconventional and closely related to antiferromagnetic fluctuation. The vacancy of apical oxygen has a significant impact on the occurrence of superconductivity. The discovery of trilayer nickelate superconductor La₄Ni₃O₁₀ under pressure has further enriched the family of nickelate superconductors. And its electronic band structure, multi-orbital model, superconducting pairing symmetry and so on have been investigated and explored theoretically.

nickelate superconductors  /  theoretical model  /  pairing symmetry  /  correlation effect