Motivated by a recent experiment (Y. Zhang et al., arXiv:2205.05087), we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate ${\mathrm{WSe}}_2$ monolayer. We show that the virtual tunneling between ${\mathrm{WSe}}_2$ and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as functions of the twist angle between Bernal bilayer graphene and the ${\mathrm{WSe}}_2$ monolayer. Our theory provides an intuitive and physical explanation for the intertwined relation between Ising spin-orbit coupling and superconductivity enhancement, which should motivate future studies.

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• Superconductivity
• Bilayer graphene
• Transition metal dichalcogenides