Chiral phonon-mediated superconductivity in alkali-doped fullerides: A unified framework connecting molecular superconductors to two-dimensional chiral superconductivity

We argue that the Jahn-Teller (JT) phonon manifold responsible for superconductivity in alkali-doped fullerides A3C60 supports circular, chiral combinations in a symmetry-adapted basis, and that this perspective gives a clean group-theoretical account of why these materials are robust s-wave superconductors. Embedding the fivefold Hg irrep in the l = 2 parent representation of SO(3), we use Clebsch-Gordan algebra in the circular basis to obtain the channel weights W(q) = 3/5 for all q ∈ {-2,-1, 0, +1, +2}. The chiral channels (q ̸= 0) carry 80% of the total coupling weight, the achiral channel (q = 0) the remaining 20%, but the central robust result is the equality between opposite chiral sectors, W(+m) = W(-m), enforced by time-reversal symmetry. The angular-momentum-weighted contribution of the chiral channels cancels identically, so the Cooper pair carries zero net angular momentum in any time-reversal-symmetric environment. A McMillan calculation reproduces the experimental Tc = 19.3 K of K3C60, and the same calculation reveals that the s-wave channel is parametrically robust against any equilibrium time-reversal-breaking perturbation because μBB ≪ ωph for the stiff intramolecular Hg modes. In two-dimensional systems with soft acoustic phonons and strong effective time-reversal breaking-most notably the chiral superconductor in valley-polarized rhombohedral trilayer graphene (RTG)-the same symmetry analysis allows a chiral p-wave channel, placing fullerides and RTG as two limits of a single mechanism controlled by the dimensionless ratio δε/ωph. We provide an order-of-magnitude estimate of mode-resolved phonon Zeeman splittings as a possible experimental signature, while emphasizing that a quantitative prediction requires a microscopic calculation of the orbit-lattice coupling.