We present a systematic theory of acoustic-phonon-mediated superconductivity which incorporates Coulomb repulsion, explaining the recent experiment in Bernal bilayer graphene under a large displacement field. The acoustic-phonon mechanism predicts that $s$-wave spin-singlet and $f$-wave spin-triplet pairings are degenerate and dominant. Assuming a spin-polarized valley-unpolarized normal state, we obtain $f$-wave spin-triplet superconductivity with $T_c\sim 20$ mK near $n_e=-0.6\times {10}^{12} {\mathrm{cm}}^{-2}$ for hole doping, in approximate agreement with the experiment. We further predict the existence of superconductivity for larger doping in both electron-doped and hole-doped regimes. Our results indicate that the observed spin-triplet superconductivity in Bernal bilayer graphene arises from acoustic phonons.

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• Electron-phonon coupling
• Superconductivity
• Graphene