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Since the discovery of superconductivity in cuprate materials, the minimalingredients for high-T$_c$ superconductivity have been an outstanding puzzle.Motivated by the recently discovered nickelate bilayer superconductorLa$_3$Ni$_2$O$_3$ under pressure, we study a minimal bilayer model, in which,as in La$_3$Ni$_2$O$_3$, inter- and intralayer magnetic interactions but nointerlayer hopping are present: a mixed-dimensional (mixD) $t-J$ model. In thesetting of a mixD ladder, we show that the system exhibits a crossoverassociated with a Feshbach resonance: from a closed-channel dominated regime oftightly bound bosonic pairs of holes to an open-channel dominated regime ofspatially more extended Cooper pairs. The crossover can be tuned by varyingdoping, or by a nearest-neighbor Coulomb repulsion $V$ that we include in ourmodel. Using density matrix renormalization group (DMRG) simulations andanalytical descriptions of both regimes, we find that the ground state is aLuther-Emery liquid, competing with a density wave of tetraparton plaquettes atcommensurate filling $\delta=0.5$ at large repulsion, and exhibits a pairingdome where binding is facilitated by doping. Our observations can be understoodin terms of pairs of correlated spinon-chargon excitations constituting theopen channel, which are subject to attractive interactions mediated by theclosed channel of tightly bound chargon-chargon pairs. When the closed channelis lowered in energy by doping or tuning $V$, a Feshbach resonance is realized,associated with a dome in the binding energy. Our predictions can be directlytested in state-of-the art quantum simulators, and we argue that the pairingmechanism we describe may be realized in the nickelate bilayer superconductorLa$_3$Ni$_2$O$_3$.

Feshbach resonance in a strongly repulsive bilayer model: a possible scenario for bilayer nickelate superconductors