We analyze the transition temperature $T_c$ of bipolaronic superconductivity in a bond Su-Schrieffer-Heeger (bond-SSH) model—also known as a bond Peierls model—where bond phonons modulate the electron hoppings. Using a semiclassical instanton approximation justifiable in the adiabatic limit of slow phonons, we find that the bipolaron mass is only weakly enhanced in contrast to the typically large mass enhancement found in models where the phonons couple to electron density. Strikingly, in the “atomic” limit, we find a bond bipolaron can freely slide within a continuously degenerate energy manifold, explaining the origin of the weak mass enhancement in the strong coupling limit. A gas of these bipolarons can undergo a superfluid transition at a critical temperature for which we obtain an upper bound. This bound is exponentially larger than that in the Holstein model. Our study provides an analytical understanding of the mechanism behind the high-$T_c$ bipolaronic superconductivity numerically observed in [Phys. Rev. X 13, 011010 (2023)].

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• Electron-phonon coupling
• Polarons
• Superconducting phase transition
• Superconductors
• Adiabatic approximation