Effective bi-layer model Hamiltonian and density-matrix renormalization group study for the high-Tc superconductivity in La${}_3$Ni${}_2$O${}_7$ under high pressure

Abstract

High-Tc superconductivity with possible $T_c\approx 80K$ has been reported in the single crystal of ${\text{La}}_3{\text{Ni}}_2{\text{O}}_7$ under high pressure. Based on the electronic structure given from the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both $3d_{z^2}$ and $3d_{x^2-y^2}$ orbital electrons of the nickel cations. The main feature of the model is that the $3d_{z^2}$ electrons form inter-layer $\sigma$-bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the $3d_{x^2-y^2}$ electrons hybridize with the $3d_{z^2}$ electrons within each NiO${}_2$ plane. The chemical potential difference of these two orbital electrons ensures that the $3d_{z^2}$ orbitals are close to half-filling and the $3d_{x^2-y^2}$ orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the $3d_{z^2}$ orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange $J$. Applying pressure can self-dope holes on the $3d_{z^2}$ orbitals with the same amount of electrons doped on the $3d_{x^2-y^2}$ 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 $3d_{z^2}$ orbitals, we find the superconducting instability on both the $3d_{z^2}$ and $3d_{x^2-y^2}$ orbitals by calculating the equal-time spin singlet pair-pair correlation function. Our numerical results have provided useful insights in the high-Tc superconductivity in single crystal La${}_3$Ni${}_2$O${}_7$ under high pressure.

6 pages, 4 figures; published version