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High- T c superconductivity with possible T c ≈ 80 K has been reported in the single crystal of La 3 Ni 2 O 7 under high pressure. Based on the electronic structure given by the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both 3 d z 2 and 3 d x 2 – y 2 orbital electrons of the nickel cations. The main feature of the model is that the 3 d z 2 electrons form inter-layer σ -bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the 3 d x 2 – y 2 electrons hybridize with the 3 d z 2 electrons within each NiO 2 plane. The chemical potential difference of these two orbital electrons ensures that the 3 d z 2 orbitals are close to half-filling and the 3 d x 2 – y 2 orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the 3 d z 2 orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange J . Applying pressure can self dope holes on the 3 d z 2 orbitals with the same amount of electrons doped on the 3 d x 2 – y 2 orbitals. By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large J and small doping of 3 d z 2 orbitals, we find the superconducting instability on both the 3 d z 2 and 3 d x 2 – y 2 orbitals by calculating the equal-time spin singlet pair–pair correlation function. Our numerical results may provide useful insights in the high- T c superconductivity in single crystal La 3 Ni 2 O 7 under high pressure.
Shen et al. (Wed,) studied this question.