Chiral phonon-mediated superconductivity in alkali-doped fullerides: a unified framework connecting molecular...

We argue that the Jahn-Teller phonon manifold responsible for superconductivity in alkali-doped fulleridesA3C60supports circular, chiral combinations in a symmetry-adapted basis, and that this perspective gives a clean group-theoretical account of why these materials are robusts-wave superconductors. Embedding the fivefoldHgirrep in thel=2parent representation of SO(3), we use Clebsch-Gordan algebra in the circular basis to obtain the channel weightsW(q)=3/5for allq∈{-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 experimentalTc=19.3K of K3C60, and the same calculation reveals that thes-wave channel is parametrically robust against any equilibrium time-reversal-breaking perturbation becauseμBB≪ωphfor the stiff intramolecularHgmodes. 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 chiralp-wave channel, placing fullerides and RTG as two limits of a single mechanism controlled by the dimensionless ratioδε/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.