Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormalization Group Study for the High-T _c Superconductivity in La ₃Ni ₂O ₇ under High Pressure

Abstract

High- T _c superconductivity with possible T _c ≈ 80 K has been reported in the single crystal of La ₃Ni ₂O 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 ₃Ni ₂O ₇ under high pressure.