Superconductivity in imbalanced bilayer Hubbard model: enhanced $d$-wave and weakened $s^\pm$-wave pairing

We investigate the bilayer model with two layers of imbalanced densities coupled by the interlayer hybridization. Using the large-scale dynamical cluster quantum Monte Carlo simulation, we discovered that increased hybridization induces a transition in the superconducting pairing from $d$-wave to $s^{\pm}$-wave and the superconducting $T_c$ of $d$-wave pairing exhibits a non-monotonic dependence on the density imbalance. Remarkably, the optimal superconductivity(SC) occurs at a moderate imbalance. Our results support the possibility of $T_c$ enhancement in composite picture where the underdoped layer provides the pairing strength while the overdoped layer promotes the phase coherence. In addition, the SC can be possibly hosted by a single layer, which is reminiscent of our recent exploration on the trilayer Hubbard model. Our present study thus provides new insight that the SC can be enhanced via the layer differentiation.