Fig. 4: The DMRG results.

a The δ − ε phase diagram of the ground state. The red region corresponds to the s-wave pairing and the blue region to the d-wave pairing. The absolute value of the intra-bottom-layer pairing correlation functions \(| {\Phi }_{b}^{\parallel }(r)|\) under different electric fields ε = 0, 0.4t∥, 0.8t∥, 1.2t∥, 1.6t∥ for δ = 0 in (b) and δ = 1/16 in (c). \(| {\Phi }_{b}^{\parallel }(r)|\) for different transferred \({d}_{{x}^{2}-{y}^{2}}\)-electron-doping levels δ = 0, 1/16, 1/8 under ε = 0.4t∥ in (d) and ε = 0.8t∥ in (e). The algebraic decay exponents KSC are written in the four figures as well, reflecting the decay rate of the pairing correlation function with spatial distance, negatively correlated with the corresponding pairing strength. In (a–e), δ and ε are set as independent variables, since their exact relationship is unclear.