Feshbach resonance in a strongly repulsive ladder of mixed dimensionality: A possible scenario for bilayer nickelate superconductors

Since the discovery of superconductivity in cuprate materials, the minimal ingredients for high-Tc superconductivity have been an outstanding puzzle. Motivated by the recently discovered nickelate bilayer superconductor La3Ni2O7 under pressure, we study a minimal bilayer model, in which, as in La3Ni2O7, interlayer and intralayer magnetic interactions but no interlayer hopping are present: A mixed-dimensional (mixD) t-J model. In the setting of a mixD ladder, we show that the system exhibits a crossover associated with a Feshbach resonance: From a closed-channel-dominated regime of tightly bound bosonic pairs of holes to an open-channel-dominated regime of spatially more extended Cooper pairs. The crossover can be tuned by varying doping, or by a nearest-neighbor Coulomb repulsion V that we include in our model. Using density matrix renormalization group simulations and analytical descriptions of both regimes, we find that the ground state is a Luther-Emery liquid, competing with a density wave of tetraparton plaquettes at commensurate filling delta = 0.5 at large repulsion, and exhibits a pairing dome where binding is facilitated by doping. Our observations can be understood in terms of pairs of correlated spinon-chargon excitations constituting the open channel, which are subject to attractive interactions mediated by the closed channel of tightly bound chargon-chargon pairs. When the closed channel is 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 directly tested in state-of-the art quantum simulators, and we argue that the pairing mechanism we describe may be realized in the nickelate bilayer superconductor La3Ni2O7.