We investigate the bilayer model with two layers of imbalanced densities coupled by 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 nonmonotonic dependence on the density imbalance. Remarkably, optimal superconductivity (SC) occurs at a moderate imbalance. Our results support the possibility of $T_c$ enhancement in a composite picture where the underdoped layer provides pairing strength while the overdoped layer promotes 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 insight that the SC can be enhanced via the layer differentiation.

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• Quantum phase transitions
• Superconductivity
• Bilayer films
• Strongly correlated systems
• Unconventional superconductors
• Hubbard model
• Quantum Monte Carlo