Strong-coupling high-$T_{\rm c}$ superconductivity in doped correlated band insulators

We explore the superconducting properties of the bilayer Hubbard model, which exhibits a high transition temperature ($T_{\rm c}$) for an $s_{\pm}$ pairing, using a cluster extension of the dynamical mean-field theory. Unlike the single-layer Hubbard model, where the $d$-wave superconductivity emerges by doping the Mott insulator, the parent state of the bilayer system is a correlated band insulator. Above $T_{\rm c}$, slight hole (electron) doping introduces a striking dichotomy between electron and hole pockets: the electron (hole) pocket develops a pseudogap while the other becomes a nearly incipient band. We reveal that the superconductivity is driven by kinetic (potential) energy gain in the underdoped (overdoped) region. We also find a very short coherence length, for which we argue the relevance to multi-orbital physics. Our study offers crucial insights into the superconductivity in the bilayer Hubbard model potentially relevant to La$_3$Ni$_2$O$_7$.