Superconductivity in the Bilayer Two-orbital Hubbard Model

Motivated by the recently discovered high $T_c$ nickelate superconductor $\mathrm{La_3Ni_2O_7}$, we investigate superconductivity in a two dimensional Hubbard model on square lattice that consists of two layers of hybridizing $d_{x^2-y^2}$ and $d_{z^2}$ orbitals. Employing cluster dynamical mean-field theory, we establish phase diagrams resolving the crucial dependence of superconducting $T_c$ on electron hybridization $V$ between $d_{x^2-y^2}$ and $d_{z^2}$ orbitals at the same layer, and on the hopping $t_{\perp}$ between two $d_{z^2}$ orbitals at different layers. $V$ and $t_{\perp}$ are presumably linked to the pairing phase coherence, and "pairing glue" of the system respectively. Our result favors a two-component theory explanation of superconductivity in a composite system. The influence of the pseudogap effect and Hund's coupling on superconductivity are discussed, and also the implication of our result to the understanding of $\mathrm{La_3Ni_2O_7}$ superconductivity.